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xmlns="http://www.w3.org/2000/svg" class="icon-sm"><path fill-rule="evenodd" clip-rule="evenodd" d="M12.5001 3.44338C12.1907 3.26474 11.8095 3.26474 11.5001 3.44338L4.83984 7.28868C4.53044 7.46731 4.33984 7.79744 4.33984 8.1547V15.8453C4.33984 16.2026 4.53044 16.5327 4.83984 16.7113L11.5001 20.5566C11.8095 20.7353 12.1907 20.7353 12.5001 20.5566L19.1604 16.7113C19.4698 16.5327 19.6604 16.2026 19.6604 15.8453V8.1547C19.6604 7.79744 19.4698 7.46731 19.1604 7.28868L12.5001 3.44338ZM10.5001 1.71133C11.4283 1.17543 12.5719 1.17543 13.5001 1.71133L20.1604 5.55663C21.0886 6.09252 21.6604 7.0829 21.6604 8.1547V15.8453C21.6604 16.9171 21.0886 17.9075 20.1604 18.4434L13.5001 22.2887C12.5719 22.8246 11.4283 22.8246 10.5001 22.2887L3.83984 18.4434C2.91164 17.9075 2.33984 16.9171 2.33984 15.8453V8.1547C2.33984 7.0829 2.91164 6.09252 3.83984 5.55663L10.5001 1.71133Z" fill="currentColor"></path><path d="M9.44133 11.4454L9.92944 9.98105C10.0321 9.67299 10.4679 9.67299 10.5706 9.98105L11.0587 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fill="currentColor"></path></svg></span><div class="flex flex-col"><span>升级套餐</span><span class="line-clamp-1 text-xs text-token-text-tertiary">对最佳模型的更多访问权限</span></div></div></span></a><div class="flex w-full items-center md:hidden"><div class="max-w-[100%] grow"><div class="group relative" data-headlessui-state=""><button class="flex w-full max-w-[100%] items-center gap-2 rounded-lg text-sm group-ui-open:bg-token-sidebar-surface-secondary p-2 hover:bg-token-sidebar-surface-secondary" data-testid="accounts-profile-button" aria-label="打开以下工作空间中的用户“Tobby Evans”的“个人资料”菜单：个人帐户" id="headlessui-menu-button-:r2l:" type="button" aria-haspopup="menu" aria-expanded="false" data-headlessui-state=""><div class="flex-shrink-0" style="view-transition-name: var(--vt-profile-avatar-sidebar);"><div class="flex items-center justify-center overflow-hidden rounded-full"><div class="relative flex"><img alt="User" width="32" height="32" class="rounded-sm" referrerpolicy="no-referrer" src="./布尔表达式解析器_files/8ad52ba1129f6a7f330e03fe788d4223"></div></div></div><div class="relative -top-px grow -space-y-px truncate text-start text-token-text-primary"><div dir="auto">Tobby Evans</div></div></button></div></div></div></div></nav></div></div></div></div><div class="relative flex h-full max-w-full flex-1 flex-col overflow-hidden"><div class="draggable sticky top-0 z-10 flex min-h-[60px] items-center justify-center border-transparent bg-token-main-surface-primary pl-0 md:hidden"><div class="no-draggable absolute bottom-0 left-0 top-0 ml-3 inline-flex items-center justify-center"><button type="button" class="inline-flex rounded-md hover:text-token-text-primary focus:outline-none focus:ring-2 focus:ring-inset focus:ring-white active:opacity-50" data-testid="open-sidebar-button"><span class="sr-only">打开边栏</span><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-lg mx-2 text-token-text-secondary"><path fill-rule="evenodd" clip-rule="evenodd" d="M3 8C3 7.44772 3.44772 7 4 7H20C20.5523 7 21 7.44772 21 8C21 8.55228 20.5523 9 20 9H4C3.44772 9 3 8.55228 3 8ZM3 16C3 15.4477 3.44772 15 4 15H14C14.5523 15 15 15.4477 15 16C15 16.5523 14.5523 17 14 17H4C3.44772 17 3 16.5523 3 16Z" fill="currentColor"></path></svg></button></div><div class="no-draggable"><button aria-label="" type="button" id="radix-:r2m:" aria-haspopup="menu" aria-expanded="false" data-state="closed" data-testid="model-switcher-dropdown-button" class="group flex cursor-pointer items-center gap-1 rounded-lg py-1.5 px-3 text-lg hover:bg-token-main-surface-secondary radix-state-open:bg-token-main-surface-secondary font-semibold text-token-text-secondary overflow-hidden whitespace-nowrap" style="view-transition-name: var(--vt-thread-model-switcher);"><div class="text-token-text-secondary">ChatGPT <span class="text-token-text-secondary"></span></div><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md text-token-text-tertiary"><path fill-rule="evenodd" clip-rule="evenodd" d="M5.29289 9.29289C5.68342 8.90237 6.31658 8.90237 6.70711 9.29289L12 14.5858L17.2929 9.29289C17.6834 8.90237 18.3166 8.90237 18.7071 9.29289C19.0976 9.68342 19.0976 10.3166 18.7071 10.7071L12.7071 16.7071C12.5196 16.8946 12.2652 17 12 17C11.7348 17 11.4804 16.8946 11.2929 16.7071L5.29289 10.7071C4.90237 10.3166 4.90237 9.68342 5.29289 9.29289Z" fill="currentColor"></path></svg></button></div><div class="no-draggable absolute bottom-0 right-0 top-0 mr-3 inline-flex items-center justify-center"><span class="flex" data-state="closed"><button aria-label="新聊天" class="h-10 rounded-lg px-2 text-token-text-secondary focus-visible:bg-token-surface-hover focus-visible:outline-0 enabled:hover:bg-token-surface-hover disabled:text-token-text-quaternary"><svg width="24" height="24" viewBox="0 0 24 24" fill="currentColor" xmlns="http://www.w3.org/2000/svg" class="icon-xl-heavy"><path d="M15.6729 3.91287C16.8918 2.69392 18.8682 2.69392 20.0871 3.91287C21.3061 5.13182 21.3061 7.10813 20.0871 8.32708L14.1499 14.2643C13.3849 15.0293 12.3925 15.5255 11.3215 15.6785L9.14142 15.9899C8.82983 16.0344 8.51546 15.9297 8.29289 15.7071C8.07033 15.4845 7.96554 15.1701 8.01005 14.8586L8.32149 12.6785C8.47449 11.6075 8.97072 10.615 9.7357 9.85006L15.6729 3.91287ZM18.6729 5.32708C18.235 4.88918 17.525 4.88918 17.0871 5.32708L11.1499 11.2643C10.6909 11.7233 10.3932 12.3187 10.3014 12.9613L10.1785 13.8215L11.0386 13.6986C11.6812 13.6068 12.2767 13.3091 12.7357 12.8501L18.6729 6.91287C19.1108 6.47497 19.1108 5.76499 18.6729 5.32708ZM11 3.99929C11.0004 4.55157 10.5531 4.99963 10.0008 5.00007C9.00227 5.00084 8.29769 5.00827 7.74651 5.06064C7.20685 5.11191 6.88488 5.20117 6.63803 5.32695C6.07354 5.61457 5.6146 6.07351 5.32698 6.63799C5.19279 6.90135 5.10062 7.24904 5.05118 7.8542C5.00078 8.47105 5 9.26336 5 10.4V13.6C5 14.7366 5.00078 15.5289 5.05118 16.1457C5.10062 16.7509 5.19279 17.0986 5.32698 17.3619C5.6146 17.9264 6.07354 18.3854 6.63803 18.673C6.90138 18.8072 7.24907 18.8993 7.85424 18.9488C8.47108 18.9992 9.26339 19 10.4 19H13.6C14.7366 19 15.5289 18.9992 16.1458 18.9488C16.7509 18.8993 17.0986 18.8072 17.362 18.673C17.9265 18.3854 18.3854 17.9264 18.673 17.3619C18.7988 17.1151 18.8881 16.7931 18.9393 16.2535C18.9917 15.7023 18.9991 14.9977 18.9999 13.9992C19.0003 13.4469 19.4484 12.9995 20.0007 13C20.553 13.0004 21.0003 13.4485 20.9999 14.0007C20.9991 14.9789 20.9932 15.7808 20.9304 16.4426C20.8664 17.116 20.7385 17.7136 20.455 18.2699C19.9757 19.2107 19.2108 19.9756 18.27 20.455C17.6777 20.7568 17.0375 20.8826 16.3086 20.9421C15.6008 21 14.7266 21 13.6428 21H10.3572C9.27339 21 8.39925 21 7.69138 20.9421C6.96253 20.8826 6.32234 20.7568 5.73005 20.455C4.78924 19.9756 4.02433 19.2107 3.54497 18.2699C3.24318 17.6776 3.11737 17.0374 3.05782 16.3086C2.99998 15.6007 2.99999 14.7266 3 13.6428V10.3572C2.99999 9.27337 2.99998 8.39922 3.05782 7.69134C3.11737 6.96249 3.24318 6.3223 3.54497 5.73001C4.02433 4.7892 4.78924 4.0243 5.73005 3.54493C6.28633 3.26149 6.88399 3.13358 7.55735 3.06961C8.21919 3.00673 9.02103 3.00083 9.99922 3.00007C10.5515 2.99964 10.9996 3.447 11 3.99929Z" fill="currentColor"></path></svg></button></span></div></div><div class="no-draggable flex w-full items-center justify-center bg-token-main-surface-primary md:hidden"></div><main class="relative h-full w-full flex-1 overflow-auto transition-width"><div role="presentation" class="composer-parent flex flex-col focus-visible:outline-0 h-full"><div class="flex-1 overflow-hidden @container/thread translate-y-[2rem] -mt-[2rem] pb-[1.5rem]"><div class="flex h-full flex-col overflow-y-auto"><div class="flex flex-col text-sm md:pb-9"><div class="draggable no-draggable-children sticky top-0 p-3 mb-1.5 flex items-center justify-between z-10 h-header-height font-semibold bg-token-main-surface-primary max-md:hidden"><div class="absolute start-1/2 ltr:-translate-x-1/2 rtl:translate-x-1/2"></div><div class="flex items-center gap-0 overflow-hidden"><button aria-label="" type="button" id="radix-:r2o:" aria-haspopup="menu" aria-expanded="false" data-state="closed" data-testid="model-switcher-dropdown-button" class="group flex cursor-pointer items-center gap-1 rounded-lg py-1.5 px-3 text-lg hover:bg-token-main-surface-secondary radix-state-open:bg-token-main-surface-secondary font-semibold text-token-text-secondary overflow-hidden whitespace-nowrap" style="view-transition-name: var(--vt-thread-model-switcher);"><div class="text-token-text-secondary">ChatGPT <span class="text-token-text-secondary"></span></div><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md text-token-text-tertiary"><path fill-rule="evenodd" clip-rule="evenodd" d="M5.29289 9.29289C5.68342 8.90237 6.31658 8.90237 6.70711 9.29289L12 14.5858L17.2929 9.29289C17.6834 8.90237 18.3166 8.90237 18.7071 9.29289C19.0976 9.68342 19.0976 10.3166 18.7071 10.7071L12.7071 16.7071C12.5196 16.8946 12.2652 17 12 17C11.7348 17 11.4804 16.8946 11.2929 16.7071L5.29289 10.7071C4.90237 10.3166 4.90237 9.68342 5.29289 9.29289Z" fill="currentColor"></path></svg></button></div><div class="gap-2 flex items-center pr-1 leading-[0]"><button aria-label="打开“个人资料”菜单" data-testid="profile-button" class="flex h-10 w-10 items-center justify-center rounded-full hover:bg-token-main-surface-secondary focus-visible:bg-token-main-surface-secondary focus-visible:outline-0" type="button" id="radix-:r1g:" aria-haspopup="menu" aria-expanded="false" data-state="closed" style="--legacy-sidebar-offset: 260px;"><div class="flex items-center justify-center overflow-hidden rounded-full"><div class="relative flex"><img alt="User" width="32" height="32" class="rounded-sm" referrerpolicy="no-referrer" src="./布尔表达式解析器_files/8ad52ba1129f6a7f330e03fe788d4223"></div></div></button></div></div><div class="mx-auto flex flex-1 gap-4 text-base md:gap-5 lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><p class="text-xs text-gray-500">这是 ChatGPT 与匿名用户之间的对话副本。</p></div><div class="text-center text-xs font-semibold text-token-text-primary"><button>举报内容</button></div><article class="w-full text-token-text-primary focus-visible:outline-2 focus-visible:outline-offset-[-4px]" dir="auto" data-testid="conversation-turn-2" data-scroll-anchor="false"><h5 class="sr-only">您说：</h5><div class="m-auto text-base py-[18px] px-6"><div class="mx-auto flex flex-1 gap-4 text-base md:gap-5 lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col @xs/thread:px-0 @sm/thread:px-1.5 @md/thread:px-4"><div class="flex-col gap-1 md:gap-3"><div class="flex max-w-full flex-col flex-grow"><div data-message-author-role="user" data-message-id="248da6d4-b818-49ee-a588-767850054a97" dir="auto" class="min-h-8 text-message flex w-full flex-col items-end gap-2 whitespace-normal break-words text-start [.text-message+&]:mt-5"><div class="flex w-full flex-col gap-1 empty:hidden items-end rtl:items-start"><div class="relative max-w-[var(--user-chat-width,70%)] rounded-3xl bg-token-message-surface px-5 py-2.5"><div class="whitespace-pre-wrap">基于java，实现一个布尔表达式解析器。表达式允许的字符包括：
- 与运算 &
- 或运算 |
- 取非运算 !
- 空格
- 布尔变量 x_{i} ，如 x_1, x_20
表达式形如 x1 & (x2 | ! x3)
请实现一个函数，能够将字符串表达式解析为一个二叉树。</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 [.group\/conversation-turn:hover_&]:block"><span class="" data-state="closed"><button aria-label="编辑消息" class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md"><path fill-rule="evenodd" clip-rule="evenodd" d="M13.2929 4.29291C15.0641 2.52167 17.9359 2.52167 19.7071 4.2929C21.4784 6.06414 21.4784 8.93588 19.7071 10.7071L18.7073 11.7069L11.6135 18.8007C10.8766 19.5376 9.92793 20.0258 8.89999 20.1971L4.16441 20.9864C3.84585 21.0395 3.52127 20.9355 3.29291 20.7071C3.06454 20.4788 2.96053 20.1542 3.01362 19.8356L3.80288 15.1C3.9742 14.0721 4.46243 13.1234 5.19932 12.3865L13.2929 4.29291ZM13 7.41422L6.61353 13.8007C6.1714 14.2428 5.87846 14.8121 5.77567 15.4288L5.21656 18.7835L8.57119 18.2244C9.18795 18.1216 9.75719 17.8286 10.1993 17.3865L16.5858 11L13 7.41422ZM18 9.5858L14.4142 6.00001L14.7071 5.70712C15.6973 4.71693 17.3027 4.71693 18.2929 5.70712C19.2831 6.69731 19.2831 8.30272 18.2929 9.29291L18 9.5858Z" fill="currentColor"></path></svg></button></span></div></div></div></div></div></div></div></div></div></article><article class="w-full text-token-text-primary focus-visible:outline-2 focus-visible:outline-offset-[-4px]" dir="auto" data-testid="conversation-turn-3" data-scroll-anchor="false"><h6 class="sr-only">ChatGPT 说：</h6><div class="m-auto text-base py-[18px] px-6"><div class="mx-auto flex flex-1 gap-4 text-base md:gap-5 lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn @xs/thread:px-0 @sm/thread:px-1.5 @md/thread:px-4"><div class="flex-col gap-1 md:gap-3"><div class="flex max-w-full flex-col flex-grow"><div data-message-author-role="assistant" data-message-id="65167b6e-0fe9-4ff0-ab18-1f096e6de947" dir="auto" class="min-h-8 text-message flex w-full flex-col items-end gap-2 whitespace-normal break-words text-start [.text-message+&]:mt-5" data-message-model-slug="gpt-4o"><div class="flex w-full flex-col gap-1 empty:hidden first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert light"><p data-start="0" data-end="103">要实现一个布尔表达式解析器并将其解析为二叉树，可以通过递归下降解析（Recursive Descent Parsing）的方法来构建这个解析器。首先，我们定义一个二叉树节点类，然后利用递归来解析布尔表达式。</p><h3 data-start="105" data-end="112">步骤：</h3><ol data-start="114" data-end="290"><li data-start="114" data-end="152"><strong data-start="117" data-end="128">定义二叉树节点</strong>：每个节点表示一个布尔表达式的操作符或布尔变量。</li><li data-start="153" data-end="196"><strong data-start="156" data-end="164">递归解析</strong>：首先从左到右解析表达式，处理括号、操作符（&、|、!）和变量。</li><li data-start="197" data-end="249"><strong data-start="200" data-end="210">操作符优先级</strong>：根据布尔操作符的优先级，<code data-start="223" data-end="226">!</code> 优先级最高，其次是 <code data-start="237" data-end="240">&</code>，最后是 <code data-start="245" data-end="248">|</code>。</li><li data-start="250" data-end="290"><strong data-start="253" data-end="262">构建二叉树</strong>：每个操作符都会成为一个节点，它的左右子节点代表操作数。</li></ol><h3 data-start="292" data-end="305">Java代码实现：</h3><pre class="!overflow-visible" data-start="307" data-end="3495"><div class="contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary dark:bg-gray-950"><div class="flex items-center text-token-text-secondary px-4 py-2 text-xs font-sans justify-between rounded-t-[5px] h-9 bg-token-sidebar-surface-primary dark:bg-token-main-surface-secondary select-none">java</div><div class="sticky top-9 md:top-[5.75rem]"><div class="absolute bottom-0 right-2 flex h-9 items-center"><div class="flex items-center rounded bg-token-sidebar-surface-primary px-2 font-sans text-xs text-token-text-secondary dark:bg-token-main-surface-secondary"><span class="" data-state="closed"><button class="flex gap-1 items-center select-none px-4 py-1" aria-label="复制"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-xs"><path fill-rule="evenodd" clip-rule="evenodd" d="M7 5C7 3.34315 8.34315 2 10 2H19C20.6569 2 22 3.34315 22 5V14C22 15.6569 20.6569 17 19 17H17V19C17 20.6569 15.6569 22 14 22H5C3.34315 22 2 20.6569 2 19V10C2 8.34315 3.34315 7 5 7H7V5ZM9 7H14C15.6569 7 17 8.34315 17 10V15H19C19.5523 15 20 14.5523 20 14V5C20 4.44772 19.5523 4 19 4H10C9.44772 4 9 4.44772 9 5V7ZM5 9C4.44772 9 4 9.44772 4 10V19C4 19.5523 4.44772 20 5 20H14C14.5523 20 15 19.5523 15 19V10C15 9.44772 14.5523 9 14 9H5Z" fill="currentColor"></path></svg>复制</button></span><span class="" data-state="closed"><button class="flex select-none items-center gap-1"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-xs"><path d="M2.5 5.5C4.3 5.2 5.2 4 5.5 2.5C5.8 4 6.7 5.2 8.5 5.5C6.7 5.8 5.8 7 5.5 8.5C5.2 7 4.3 5.8 2.5 5.5Z" fill="currentColor" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round"></path><path d="M5.66282 16.5231L5.18413 19.3952C5.12203 19.7678 5.09098 19.9541 5.14876 20.0888C5.19933 20.2067 5.29328 20.3007 5.41118 20.3512C5.54589 20.409 5.73218 20.378 6.10476 20.3159L8.97693 19.8372C9.72813 19.712 10.1037 19.6494 10.4542 19.521C10.7652 19.407 11.0608 19.2549 11.3343 19.068C11.6425 18.8575 11.9118 18.5882 12.4503 18.0497L20 10.5C21.3807 9.11929 21.3807 6.88071 20 5.5C18.6193 4.11929 16.3807 4.11929 15 5.5L7.45026 13.0497C6.91175 13.5882 6.6425 13.8575 6.43197 14.1657C6.24513 14.4392 6.09299 14.7348 5.97903 15.0458C5.85062 15.3963 5.78802 15.7719 5.66282 16.5231Z" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"></path><path d="M14.5 7L18.5 11" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"></path></svg>编辑</button></span></div></div></div><div class="overflow-y-auto p-4" dir="ltr"><code class="!whitespace-pre language-java"><span><span class="hljs-keyword">import</span> java.util.*;
<span class="hljs-keyword">public</span> <span class="hljs-keyword">class</span> <span class="hljs-title class_">BooleanExpressionParser</span> {
<span class="hljs-keyword">static</span> <span class="hljs-keyword">class</span> <span class="hljs-title class_">TreeNode</span> {
String value;
TreeNode left;
TreeNode right;
TreeNode(String value) {
<span class="hljs-built_in">this</span>.value = value;
<span class="hljs-built_in">this</span>.left = <span class="hljs-literal">null</span>;
<span class="hljs-built_in">this</span>.right = <span class="hljs-literal">null</span>;
}
}
<span class="hljs-comment">// 解析布尔表达式为二叉树</span>
<span class="hljs-keyword">public</span> <span class="hljs-keyword">static</span> TreeNode <span class="hljs-title function_">parse</span><span class="hljs-params">(String expression)</span> {
<span class="hljs-comment">// 清理输入，去除空格</span>
expression = expression.replaceAll(<span class="hljs-string">"\\s+"</span>, <span class="hljs-string">""</span>);
<span class="hljs-comment">// 使用递归下降解析</span>
<span class="hljs-keyword">return</span> parseOr(expression, <span class="hljs-keyword">new</span> <span class="hljs-title class_">int</span>[] {<span class="hljs-number">0</span>});
}
<span class="hljs-comment">// 解析 OR 表达式</span>
<span class="hljs-keyword">private</span> <span class="hljs-keyword">static</span> TreeNode <span class="hljs-title function_">parseOr</span><span class="hljs-params">(String expression, <span class="hljs-type">int</span>[] index)</span> {
<span class="hljs-type">TreeNode</span> <span class="hljs-variable">left</span> <span class="hljs-operator">=</span> parseAnd(expression, index);
<span class="hljs-keyword">while</span> (index[<span class="hljs-number">0</span>] < expression.length() && expression.charAt(index[<span class="hljs-number">0</span>]) == <span class="hljs-string">'|'</span>) {
index[<span class="hljs-number">0</span>]++; <span class="hljs-comment">// 跳过 '|'</span>
<span class="hljs-type">TreeNode</span> <span class="hljs-variable">node</span> <span class="hljs-operator">=</span> <span class="hljs-keyword">new</span> <span class="hljs-title class_">TreeNode</span>(<span class="hljs-string">"|"</span>);
node.left = left;
node.right = parseAnd(expression, index);
left = node; <span class="hljs-comment">// 更新左子树</span>
}
<span class="hljs-keyword">return</span> left;
}
<span class="hljs-comment">// 解析 AND 表达式</span>
<span class="hljs-keyword">private</span> <span class="hljs-keyword">static</span> TreeNode <span class="hljs-title function_">parseAnd</span><span class="hljs-params">(String expression, <span class="hljs-type">int</span>[] index)</span> {
<span class="hljs-type">TreeNode</span> <span class="hljs-variable">left</span> <span class="hljs-operator">=</span> parseNot(expression, index);
<span class="hljs-keyword">while</span> (index[<span class="hljs-number">0</span>] < expression.length() && expression.charAt(index[<span class="hljs-number">0</span>]) == <span class="hljs-string">'&'</span>) {
index[<span class="hljs-number">0</span>]++; <span class="hljs-comment">// 跳过 '&'</span>
<span class="hljs-type">TreeNode</span> <span class="hljs-variable">node</span> <span class="hljs-operator">=</span> <span class="hljs-keyword">new</span> <span class="hljs-title class_">TreeNode</span>(<span class="hljs-string">"&"</span>);
node.left = left;
node.right = parseNot(expression, index);
left = node; <span class="hljs-comment">// 更新左子树</span>
}
<span class="hljs-keyword">return</span> left;
}
<span class="hljs-comment">// 解析 NOT 表达式</span>
<span class="hljs-keyword">private</span> <span class="hljs-keyword">static</span> TreeNode <span class="hljs-title function_">parseNot</span><span class="hljs-params">(String expression, <span class="hljs-type">int</span>[] index)</span> {
<span class="hljs-keyword">if</span> (index[<span class="hljs-number">0</span>] < expression.length() && expression.charAt(index[<span class="hljs-number">0</span>]) == <span class="hljs-string">'!'</span>) {
index[<span class="hljs-number">0</span>]++; <span class="hljs-comment">// 跳过 '!'</span>
<span class="hljs-type">TreeNode</span> <span class="hljs-variable">node</span> <span class="hljs-operator">=</span> <span class="hljs-keyword">new</span> <span class="hljs-title class_">TreeNode</span>(<span class="hljs-string">"!"</span>);
node.right = parseFactor(expression, index); <span class="hljs-comment">// 取非操作只有右子树</span>
<span class="hljs-keyword">return</span> node;
}
<span class="hljs-keyword">return</span> parseFactor(expression, index);
}
<span class="hljs-comment">// 解析基本的因子：布尔变量或括号</span>
<span class="hljs-keyword">private</span> <span class="hljs-keyword">static</span> TreeNode <span class="hljs-title function_">parseFactor</span><span class="hljs-params">(String expression, <span class="hljs-type">int</span>[] index)</span> {
<span class="hljs-keyword">if</span> (index[<span class="hljs-number">0</span>] < expression.length() && expression.charAt(index[<span class="hljs-number">0</span>]) == <span class="hljs-string">'('</span>) {
index[<span class="hljs-number">0</span>]++; <span class="hljs-comment">// 跳过 '('</span>
<span class="hljs-type">TreeNode</span> <span class="hljs-variable">node</span> <span class="hljs-operator">=</span> parseOr(expression, index); <span class="hljs-comment">// 递归解析括号中的表达式</span>
index[<span class="hljs-number">0</span>]++; <span class="hljs-comment">// 跳过 ')'</span>
<span class="hljs-keyword">return</span> node;
}
<span class="hljs-keyword">return</span> parseVariable(expression, index);
}
<span class="hljs-comment">// 解析布尔变量（例如 x1, x20）</span>
<span class="hljs-keyword">private</span> <span class="hljs-keyword">static</span> TreeNode <span class="hljs-title function_">parseVariable</span><span class="hljs-params">(String expression, <span class="hljs-type">int</span>[] index)</span> {
<span class="hljs-type">int</span> <span class="hljs-variable">start</span> <span class="hljs-operator">=</span> index[<span class="hljs-number">0</span>];
<span class="hljs-keyword">while</span> (index[<span class="hljs-number">0</span>] < expression.length() && (Character.isLetterOrDigit(expression.charAt(index[<span class="hljs-number">0</span>])) || expression.charAt(index[<span class="hljs-number">0</span>]) == <span class="hljs-string">'_'</span>)) {
index[<span class="hljs-number">0</span>]++;
}
<span class="hljs-type">String</span> <span class="hljs-variable">variable</span> <span class="hljs-operator">=</span> expression.substring(start, index[<span class="hljs-number">0</span>]);
<span class="hljs-keyword">return</span> <span class="hljs-keyword">new</span> <span class="hljs-title class_">TreeNode</span>(variable);
}
<span class="hljs-comment">// 打印二叉树，用于测试</span>
<span class="hljs-keyword">public</span> <span class="hljs-keyword">static</span> <span class="hljs-keyword">void</span> <span class="hljs-title function_">printTree</span><span class="hljs-params">(TreeNode node, String indent)</span> {
<span class="hljs-keyword">if</span> (node != <span class="hljs-literal">null</span>) {
System.out.println(indent + node.value);
printTree(node.left, indent + <span class="hljs-string">" "</span>);
printTree(node.right, indent + <span class="hljs-string">" "</span>);
}
}
<span class="hljs-comment">// 测试</span>
<span class="hljs-keyword">public</span> <span class="hljs-keyword">static</span> <span class="hljs-keyword">void</span> <span class="hljs-title function_">main</span><span class="hljs-params">(String[] args)</span> {
<span class="hljs-type">String</span> <span class="hljs-variable">expression</span> <span class="hljs-operator">=</span> <span class="hljs-string">"x1 & (x2 | ! x3)"</span>;
<span class="hljs-type">TreeNode</span> <span class="hljs-variable">root</span> <span class="hljs-operator">=</span> parse(expression);
printTree(root, <span class="hljs-string">""</span>);
}
}
</span></code></div></div></pre><h3 data-start="3497" data-end="3510">解析器的工作原理：</h3><ol data-start="3512" data-end="3782"><li data-start="3512" data-end="3570"><strong data-start="3515" data-end="3524">parse</strong>：接受一个字符串表示的布尔表达式，先去除所有空格，然后开始从 <code data-start="3555" data-end="3564">parseOr</code> 开始解析。</li><li data-start="3571" data-end="3607"><strong data-start="3574" data-end="3585">parseOr</strong>：解析 OR (<code data-start="3593" data-end="3596">|</code>) 操作，优先级最低。</li><li data-start="3608" data-end="3640"><strong data-start="3611" data-end="3623">parseAnd</strong>：解析 AND (<code data-start="3632" data-end="3635">&</code>) 操作。</li><li data-start="3641" data-end="3679"><strong data-start="3644" data-end="3656">parseNot</strong>：解析 NOT (<code data-start="3665" data-end="3668">!</code>) 操作，优先级最高。</li><li data-start="3680" data-end="3734"><strong data-start="3683" data-end="3698">parseFactor</strong>：解析一个布尔因子，它可以是布尔变量（如 <code data-start="3719" data-end="3723">x1</code>）或者括号内的表达式。</li><li data-start="3735" data-end="3782"><strong data-start="3738" data-end="3755">parseVariable</strong>：处理布尔变量的解析，如 <code data-start="3768" data-end="3772">x1</code>, <code data-start="3774" data-end="3779">x20</code> 等。</li></ol><h3 data-start="3784" data-end="3790">测试</h3><p data-start="3792" data-end="3830">对于表达式 <code data-start="3798" data-end="3817">"x1 & (x2 | !x3)"</code>，程序会构建如下的二叉树：</p><pre class="!overflow-visible" data-start="3832" data-end="3890"><div class="contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary dark:bg-gray-950"><div class="flex items-center text-token-text-secondary px-4 py-2 text-xs font-sans justify-between rounded-t-[5px] h-9 bg-token-sidebar-surface-primary dark:bg-token-main-surface-secondary select-none">markdown</div><div class="sticky top-9 md:top-[5.75rem]"><div class="absolute bottom-0 right-2 flex h-9 items-center"><div class="flex items-center rounded bg-token-sidebar-surface-primary px-2 font-sans text-xs text-token-text-secondary dark:bg-token-main-surface-secondary"><span class="" data-state="closed"><button class="flex gap-1 items-center select-none px-4 py-1" aria-label="复制"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-xs"><path fill-rule="evenodd" clip-rule="evenodd" d="M7 5C7 3.34315 8.34315 2 10 2H19C20.6569 2 22 3.34315 22 5V14C22 15.6569 20.6569 17 19 17H17V19C17 20.6569 15.6569 22 14 22H5C3.34315 22 2 20.6569 2 19V10C2 8.34315 3.34315 7 5 7H7V5ZM9 7H14C15.6569 7 17 8.34315 17 10V15H19C19.5523 15 20 14.5523 20 14V5C20 4.44772 19.5523 4 19 4H10C9.44772 4 9 4.44772 9 5V7ZM5 9C4.44772 9 4 9.44772 4 10V19C4 19.5523 4.44772 20 5 20H14C14.5523 20 15 19.5523 15 19V10C15 9.44772 14.5523 9 14 9H5Z" fill="currentColor"></path></svg>复制</button></span><span class="" data-state="closed"><button class="flex select-none items-center gap-1"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-xs"><path d="M2.5 5.5C4.3 5.2 5.2 4 5.5 2.5C5.8 4 6.7 5.2 8.5 5.5C6.7 5.8 5.8 7 5.5 8.5C5.2 7 4.3 5.8 2.5 5.5Z" fill="currentColor" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round"></path><path d="M5.66282 16.5231L5.18413 19.3952C5.12203 19.7678 5.09098 19.9541 5.14876 20.0888C5.19933 20.2067 5.29328 20.3007 5.41118 20.3512C5.54589 20.409 5.73218 20.378 6.10476 20.3159L8.97693 19.8372C9.72813 19.712 10.1037 19.6494 10.4542 19.521C10.7652 19.407 11.0608 19.2549 11.3343 19.068C11.6425 18.8575 11.9118 18.5882 12.4503 18.0497L20 10.5C21.3807 9.11929 21.3807 6.88071 20 5.5C18.6193 4.11929 16.3807 4.11929 15 5.5L7.45026 13.0497C6.91175 13.5882 6.6425 13.8575 6.43197 14.1657C6.24513 14.4392 6.09299 14.7348 5.97903 15.0458C5.85062 15.3963 5.78802 15.7719 5.66282 16.5231Z" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"></path><path d="M14.5 7L18.5 11" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"></path></svg>编辑</button></span></div></div></div><div class="overflow-y-auto p-4" dir="ltr"><code class="!whitespace-pre"><span>&
├── x1
└── |
<span class="hljs-code"> ├── x2
└── !
└── x3
</span></span></code></div></div></pre><h3 data-start="3892" data-end="3898">输出</h3><pre class="!overflow-visible" data-start="3900" data-end="3940"><div class="contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary dark:bg-gray-950"><div class="flex items-center text-token-text-secondary px-4 py-2 text-xs font-sans justify-between rounded-t-[5px] h-9 bg-token-sidebar-surface-primary dark:bg-token-main-surface-secondary select-none">markdown</div><div class="sticky top-9 md:top-[5.75rem]"><div class="absolute bottom-0 right-2 flex h-9 items-center"><div class="flex items-center rounded bg-token-sidebar-surface-primary px-2 font-sans text-xs text-token-text-secondary dark:bg-token-main-surface-secondary"><span class="" data-state="closed"><button class="flex gap-1 items-center select-none px-4 py-1" aria-label="复制"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-xs"><path fill-rule="evenodd" clip-rule="evenodd" d="M7 5C7 3.34315 8.34315 2 10 2H19C20.6569 2 22 3.34315 22 5V14C22 15.6569 20.6569 17 19 17H17V19C17 20.6569 15.6569 22 14 22H5C3.34315 22 2 20.6569 2 19V10C2 8.34315 3.34315 7 5 7H7V5ZM9 7H14C15.6569 7 17 8.34315 17 10V15H19C19.5523 15 20 14.5523 20 14V5C20 4.44772 19.5523 4 19 4H10C9.44772 4 9 4.44772 9 5V7ZM5 9C4.44772 9 4 9.44772 4 10V19C4 19.5523 4.44772 20 5 20H14C14.5523 20 15 19.5523 15 19V10C15 9.44772 14.5523 9 14 9H5Z" fill="currentColor"></path></svg>复制</button></span><span class="" data-state="closed"><button class="flex select-none items-center gap-1"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-xs"><path d="M2.5 5.5C4.3 5.2 5.2 4 5.5 2.5C5.8 4 6.7 5.2 8.5 5.5C6.7 5.8 5.8 7 5.5 8.5C5.2 7 4.3 5.8 2.5 5.5Z" fill="currentColor" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round"></path><path d="M5.66282 16.5231L5.18413 19.3952C5.12203 19.7678 5.09098 19.9541 5.14876 20.0888C5.19933 20.2067 5.29328 20.3007 5.41118 20.3512C5.54589 20.409 5.73218 20.378 6.10476 20.3159L8.97693 19.8372C9.72813 19.712 10.1037 19.6494 10.4542 19.521C10.7652 19.407 11.0608 19.2549 11.3343 19.068C11.6425 18.8575 11.9118 18.5882 12.4503 18.0497L20 10.5C21.3807 9.11929 21.3807 6.88071 20 5.5C18.6193 4.11929 16.3807 4.11929 15 5.5L7.45026 13.0497C6.91175 13.5882 6.6425 13.8575 6.43197 14.1657C6.24513 14.4392 6.09299 14.7348 5.97903 15.0458C5.85062 15.3963 5.78802 15.7719 5.66282 16.5231Z" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"></path><path d="M14.5 7L18.5 11" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"></path></svg>编辑</button></span></div></div></div><div class="overflow-y-auto p-4" dir="ltr"><code class="!whitespace-pre"><span>&
x1
|
<span class="hljs-code"> x2
!
x3
</span></span></code></div></div></pre><p data-start="3942" data-end="4036" data-is-last-node="">这个实现是一个基本的递归下降解析器，能够处理布尔表达式中的 <code data-start="3972" data-end="3975">&</code>、<code data-start="3976" data-end="3979">|</code> 和 <code data-start="3982" data-end="3985">!</code> 操作符，支持括号和布尔变量。你可以根据需求对其进行扩展和优化，例如支持更多的错误检查和优化解析过程。</p></div></div></div></div></div></div></div></div></article><article class="w-full text-token-text-primary focus-visible:outline-2 focus-visible:outline-offset-[-4px]" dir="auto" data-testid="conversation-turn-4" data-scroll-anchor="false"><h5 class="sr-only">您说：</h5><div class="m-auto text-base py-[18px] px-6"><div class="mx-auto flex flex-1 gap-4 text-base md:gap-5 lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col @xs/thread:px-0 @sm/thread:px-1.5 @md/thread:px-4"><div class="flex-col gap-1 md:gap-3"><div class="flex max-w-full flex-col flex-grow"><div data-message-author-role="user" data-message-id="486a666e-6495-4fd4-baa8-7cd1b61978ad" dir="auto" class="min-h-8 text-message flex w-full flex-col items-end gap-2 whitespace-normal break-words text-start [.text-message+&]:mt-5"><div class="flex w-full flex-col gap-1 empty:hidden items-end rtl:items-start"><div class="relative max-w-[var(--user-chat-width,70%)] rounded-3xl bg-token-message-surface px-5 py-2.5"><div class="whitespace-pre-wrap">能否不依赖编译原理的知识背景，只通过基本的数据结构与算法知识解决？</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 [.group\/conversation-turn:hover_&]:block"><span class="" data-state="closed"><button aria-label="编辑消息" class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md"><path fill-rule="evenodd" clip-rule="evenodd" d="M13.2929 4.29291C15.0641 2.52167 17.9359 2.52167 19.7071 4.2929C21.4784 6.06414 21.4784 8.93588 19.7071 10.7071L18.7073 11.7069L11.6135 18.8007C10.8766 19.5376 9.92793 20.0258 8.89999 20.1971L4.16441 20.9864C3.84585 21.0395 3.52127 20.9355 3.29291 20.7071C3.06454 20.4788 2.96053 20.1542 3.01362 19.8356L3.80288 15.1C3.9742 14.0721 4.46243 13.1234 5.19932 12.3865L13.2929 4.29291ZM13 7.41422L6.61353 13.8007C6.1714 14.2428 5.87846 14.8121 5.77567 15.4288L5.21656 18.7835L8.57119 18.2244C9.18795 18.1216 9.75719 17.8286 10.1993 17.3865L16.5858 11L13 7.41422ZM18 9.5858L14.4142 6.00001L14.7071 5.70712C15.6973 4.71693 17.3027 4.71693 18.2929 5.70712C19.2831 6.69731 19.2831 8.30272 18.2929 9.29291L18 9.5858Z" fill="currentColor"></path></svg></button></span></div></div></div></div></div></div></div></div></div></article><article class="w-full text-token-text-primary focus-visible:outline-2 focus-visible:outline-offset-[-4px]" dir="auto" data-testid="conversation-turn-5" data-scroll-anchor="false"><h6 class="sr-only">ChatGPT 说：</h6><div class="m-auto text-base py-[18px] px-6"><div class="mx-auto flex flex-1 gap-4 text-base md:gap-5 lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn @xs/thread:px-0 @sm/thread:px-1.5 @md/thread:px-4"><div class="flex-col gap-1 md:gap-3"><div class="flex max-w-full flex-col flex-grow"><div data-message-author-role="assistant" data-message-id="6777da8e-e075-4919-9a1a-e47a1fbc826d" dir="auto" class="min-h-8 text-message flex w-full flex-col items-end gap-2 whitespace-normal break-words text-start [.text-message+&]:mt-5" data-message-model-slug="gpt-4o"><div class="flex w-full flex-col gap-1 empty:hidden first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert light"><p data-start="0" data-end="74">当然可以！如果不依赖编译原理的知识，我们可以通过栈和递归来实现一个解析器，使用基本的数据结构（栈）和算法（递归）来逐步解析表达式，并构建一个二叉树。</p><p data-start="76" data-end="130">下面是一个更简单的实现方法，不依赖于编译原理的知识，使用的是常见的栈和递归算法来解析布尔表达式并构建二叉树。</p><h3 data-start="132" data-end="140">关键思想</h3><ol data-start="142" data-end="261"><li data-start="142" data-end="212"><strong data-start="145" data-end="153">栈的使用</strong>：我们可以使用栈来处理运算符的优先级，确保正确地处理操作顺序（例如，<code data-start="187" data-end="190">!</code> 优先于 <code data-start="195" data-end="198">&</code>，<code data-start="199" data-end="202">&</code> 优先于 <code data-start="207" data-end="210">|</code>）。</li><li data-start="213" data-end="261"><strong data-start="216" data-end="225">递归的使用</strong>：遇到括号时，我们通过递归来解析括号内的表达式，避免过于复杂的状态管理。</li></ol><h3 data-start="263" data-end="271">代码实现</h3><pre class="!overflow-visible" data-start="273" data-end="3939"><div class="contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary dark:bg-gray-950"><div class="flex items-center text-token-text-secondary px-4 py-2 text-xs font-sans justify-between rounded-t-[5px] h-9 bg-token-sidebar-surface-primary dark:bg-token-main-surface-secondary select-none">java</div><div class="sticky top-9 md:top-[5.75rem]"><div class="absolute bottom-0 right-2 flex h-9 items-center"><div class="flex items-center rounded bg-token-sidebar-surface-primary px-2 font-sans text-xs text-token-text-secondary dark:bg-token-main-surface-secondary"><span class="" data-state="closed"><button class="flex gap-1 items-center select-none px-4 py-1" aria-label="复制"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-xs"><path fill-rule="evenodd" clip-rule="evenodd" d="M7 5C7 3.34315 8.34315 2 10 2H19C20.6569 2 22 3.34315 22 5V14C22 15.6569 20.6569 17 19 17H17V19C17 20.6569 15.6569 22 14 22H5C3.34315 22 2 20.6569 2 19V10C2 8.34315 3.34315 7 5 7H7V5ZM9 7H14C15.6569 7 17 8.34315 17 10V15H19C19.5523 15 20 14.5523 20 14V5C20 4.44772 19.5523 4 19 4H10C9.44772 4 9 4.44772 9 5V7ZM5 9C4.44772 9 4 9.44772 4 10V19C4 19.5523 4.44772 20 5 20H14C14.5523 20 15 19.5523 15 19V10C15 9.44772 14.5523 9 14 9H5Z" fill="currentColor"></path></svg>复制</button></span><span class="" data-state="closed"><button class="flex select-none items-center gap-1"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-xs"><path d="M2.5 5.5C4.3 5.2 5.2 4 5.5 2.5C5.8 4 6.7 5.2 8.5 5.5C6.7 5.8 5.8 7 5.5 8.5C5.2 7 4.3 5.8 2.5 5.5Z" fill="currentColor" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round"></path><path d="M5.66282 16.5231L5.18413 19.3952C5.12203 19.7678 5.09098 19.9541 5.14876 20.0888C5.19933 20.2067 5.29328 20.3007 5.41118 20.3512C5.54589 20.409 5.73218 20.378 6.10476 20.3159L8.97693 19.8372C9.72813 19.712 10.1037 19.6494 10.4542 19.521C10.7652 19.407 11.0608 19.2549 11.3343 19.068C11.6425 18.8575 11.9118 18.5882 12.4503 18.0497L20 10.5C21.3807 9.11929 21.3807 6.88071 20 5.5C18.6193 4.11929 16.3807 4.11929 15 5.5L7.45026 13.0497C6.91175 13.5882 6.6425 13.8575 6.43197 14.1657C6.24513 14.4392 6.09299 14.7348 5.97903 15.0458C5.85062 15.3963 5.78802 15.7719 5.66282 16.5231Z" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"></path><path d="M14.5 7L18.5 11" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"></path></svg>编辑</button></span></div></div></div><div class="overflow-y-auto p-4" dir="ltr"><code class="!whitespace-pre language-java"><span><span class="hljs-keyword">import</span> java.util.*;
<span class="hljs-keyword">public</span> <span class="hljs-keyword">class</span> <span class="hljs-title class_">BooleanExpressionParser</span> {
<span class="hljs-keyword">static</span> <span class="hljs-keyword">class</span> <span class="hljs-title class_">TreeNode</span> {
String value;
TreeNode left;
TreeNode right;
TreeNode(String value) {
<span class="hljs-built_in">this</span>.value = value;
<span class="hljs-built_in">this</span>.left = <span class="hljs-literal">null</span>;
<span class="hljs-built_in">this</span>.right = <span class="hljs-literal">null</span>;
}
}
<span class="hljs-comment">// 解析布尔表达式为二叉树</span>
<span class="hljs-keyword">public</span> <span class="hljs-keyword">static</span> TreeNode <span class="hljs-title function_">parse</span><span class="hljs-params">(String expression)</span> {
expression = expression.replaceAll(<span class="hljs-string">"\\s+"</span>, <span class="hljs-string">""</span>); <span class="hljs-comment">// 去除空格</span>
<span class="hljs-keyword">return</span> parseExpression(expression);
}
<span class="hljs-comment">// 解析布尔表达式</span>
<span class="hljs-keyword">private</span> <span class="hljs-keyword">static</span> TreeNode <span class="hljs-title function_">parseExpression</span><span class="hljs-params">(String expression)</span> {
Stack<TreeNode> operands = <span class="hljs-keyword">new</span> <span class="hljs-title class_">Stack</span><>();
Stack<Character> operators = <span class="hljs-keyword">new</span> <span class="hljs-title class_">Stack</span><>();
<span class="hljs-type">int</span> <span class="hljs-variable">index</span> <span class="hljs-operator">=</span> <span class="hljs-number">0</span>;
<span class="hljs-keyword">while</span> (index < expression.length()) {
<span class="hljs-type">char</span> <span class="hljs-variable">ch</span> <span class="hljs-operator">=</span> expression.charAt(index);
<span class="hljs-keyword">if</span> (ch == <span class="hljs-string">'('</span>) {
<span class="hljs-comment">// 递归解析括号内的表达式</span>
<span class="hljs-type">int</span> <span class="hljs-variable">end</span> <span class="hljs-operator">=</span> findClosingParenthesis(expression, index);
operands.push(parseExpression(expression.substring(index + <span class="hljs-number">1</span>, end)));
index = end + <span class="hljs-number">1</span>; <span class="hljs-comment">// 更新索引</span>
} <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (ch == <span class="hljs-string">'!'</span>) {
<span class="hljs-comment">// 取非操作，立即应用</span>
index++;
operands.push(<span class="hljs-keyword">new</span> <span class="hljs-title class_">TreeNode</span>(<span class="hljs-string">"!"</span>));
} <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (ch == <span class="hljs-string">'&'</span> || ch == <span class="hljs-string">'|'</span>) {
<span class="hljs-comment">// 操作符处理</span>
operators.push(ch);
index++;
} <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (ch == <span class="hljs-string">'x'</span>) {
<span class="hljs-comment">// 变量处理，如 x1, x20</span>
<span class="hljs-type">int</span> <span class="hljs-variable">start</span> <span class="hljs-operator">=</span> index;
<span class="hljs-keyword">while</span> (index < expression.length() && (Character.isDigit(expression.charAt(index)) || expression.charAt(index) == <span class="hljs-string">'_'</span>)) {
index++;
}
<span class="hljs-type">String</span> <span class="hljs-variable">variable</span> <span class="hljs-operator">=</span> expression.substring(start, index);
operands.push(<span class="hljs-keyword">new</span> <span class="hljs-title class_">TreeNode</span>(variable));
} <span class="hljs-keyword">else</span> {
index++; <span class="hljs-comment">// 忽略不需要的字符</span>
}
<span class="hljs-comment">// 处理运算符优先级</span>
<span class="hljs-keyword">while</span> (!operators.isEmpty() && (operators.peek() == <span class="hljs-string">'!'</span> || operators.peek() == <span class="hljs-string">'&'</span> || operators.peek() == <span class="hljs-string">'|'</span>)) {
<span class="hljs-type">char</span> <span class="hljs-variable">op</span> <span class="hljs-operator">=</span> operators.peek();
<span class="hljs-keyword">if</span> (op == <span class="hljs-string">'!'</span>) {
<span class="hljs-type">TreeNode</span> <span class="hljs-variable">operand</span> <span class="hljs-operator">=</span> operands.pop();
<span class="hljs-type">TreeNode</span> <span class="hljs-variable">node</span> <span class="hljs-operator">=</span> <span class="hljs-keyword">new</span> <span class="hljs-title class_">TreeNode</span>(<span class="hljs-string">"!"</span>);
node.right = operand;
operands.push(node);
operators.pop();
} <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (op == <span class="hljs-string">'&'</span> || op == <span class="hljs-string">'|'</span>) {
<span class="hljs-type">TreeNode</span> <span class="hljs-variable">right</span> <span class="hljs-operator">=</span> operands.pop();
<span class="hljs-type">TreeNode</span> <span class="hljs-variable">left</span> <span class="hljs-operator">=</span> operands.pop();
<span class="hljs-type">TreeNode</span> <span class="hljs-variable">node</span> <span class="hljs-operator">=</span> <span class="hljs-keyword">new</span> <span class="hljs-title class_">TreeNode</span>(String.valueOf(op));
node.left = left;
node.right = right;
operands.push(node);
operators.pop();
}
}
}
<span class="hljs-keyword">return</span> operands.isEmpty() ? <span class="hljs-literal">null</span> : operands.pop();
}
<span class="hljs-comment">// 找到匹配的右括号</span>
<span class="hljs-keyword">private</span> <span class="hljs-keyword">static</span> <span class="hljs-type">int</span> <span class="hljs-title function_">findClosingParenthesis</span><span class="hljs-params">(String expression, <span class="hljs-type">int</span> index)</span> {
<span class="hljs-type">int</span> <span class="hljs-variable">count</span> <span class="hljs-operator">=</span> <span class="hljs-number">1</span>;
<span class="hljs-type">int</span> <span class="hljs-variable">i</span> <span class="hljs-operator">=</span> index + <span class="hljs-number">1</span>;
<span class="hljs-keyword">while</span> (i < expression.length() && count > <span class="hljs-number">0</span>) {
<span class="hljs-keyword">if</span> (expression.charAt(i) == <span class="hljs-string">'('</span>) {
count++;
} <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (expression.charAt(i) == <span class="hljs-string">')'</span>) {
count--;
}
i++;
}
<span class="hljs-keyword">return</span> i - <span class="hljs-number">1</span>; <span class="hljs-comment">// 返回右括号的索引</span>
}
<span class="hljs-comment">// 打印二叉树，用于测试</span>
<span class="hljs-keyword">public</span> <span class="hljs-keyword">static</span> <span class="hljs-keyword">void</span> <span class="hljs-title function_">printTree</span><span class="hljs-params">(TreeNode node, String indent)</span> {
<span class="hljs-keyword">if</span> (node != <span class="hljs-literal">null</span>) {
System.out.println(indent + node.value);
printTree(node.left, indent + <span class="hljs-string">" "</span>);
printTree(node.right, indent + <span class="hljs-string">" "</span>);
}
}
<span class="hljs-comment">// 测试</span>
<span class="hljs-keyword">public</span> <span class="hljs-keyword">static</span> <span class="hljs-keyword">void</span> <span class="hljs-title function_">main</span><span class="hljs-params">(String[] args)</span> {
<span class="hljs-type">String</span> <span class="hljs-variable">expression</span> <span class="hljs-operator">=</span> <span class="hljs-string">"x1 & (x2 | ! x3)"</span>;
<span class="hljs-type">TreeNode</span> <span class="hljs-variable">root</span> <span class="hljs-operator">=</span> parse(expression);
printTree(root, <span class="hljs-string">""</span>);
}
}
</span></code></div></div></pre><h3 data-start="3941" data-end="3949">关键点：</h3><ol data-start="3951" data-end="4235"><li data-start="3951" data-end="4051"><strong data-start="3954" data-end="3962">括号处理</strong>：当遇到左括号 <code data-start="3970" data-end="3973">(</code> 时，我们递归解析括号内的子表达式，直到遇到右括号 <code data-start="3999" data-end="4002">)</code> 为止。这是通过 <code data-start="4011" data-end="4035">findClosingParenthesis</code> 方法来找到匹配的右括号实现的。</li><li data-start="4052" data-end="4138"><strong data-start="4055" data-end="4065">运算符优先级</strong>：在解析运算符时，我们使用栈来保存操作符。对于每个操作符，首先检查栈顶的操作符优先级，按照优先级（<code data-start="4114" data-end="4117">!</code> > <code data-start="4120" data-end="4123">&</code> > <code data-start="4126" data-end="4129">|</code>）构建二叉树节点。</li><li data-start="4139" data-end="4235"><strong data-start="4142" data-end="4153">操作数和运算符</strong>：对于变量（如 <code data-start="4161" data-end="4165">x1</code>），我们直接从字符串中提取并构建二叉树节点；对于运算符（如 <code data-start="4195" data-end="4198">&</code>, <code data-start="4200" data-end="4203">|</code>），我们在栈中存储操作符，并在遇到运算符时进行二叉树节点的合并。</li></ol><h3 data-start="4237" data-end="4243">测试</h3><p data-start="4245" data-end="4285">对于输入表达式 <code data-start="4253" data-end="4273">"x1 & (x2 | ! x3)"</code>，程序构建的二叉树将是：</p><pre class="!overflow-visible" data-start="4287" data-end="4345"><div class="contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary dark:bg-gray-950"><div class="flex items-center text-token-text-secondary px-4 py-2 text-xs font-sans justify-between rounded-t-[5px] h-9 bg-token-sidebar-surface-primary dark:bg-token-main-surface-secondary select-none">markdown</div><div class="sticky top-9 md:top-[5.75rem]"><div class="absolute bottom-0 right-2 flex h-9 items-center"><div class="flex items-center rounded bg-token-sidebar-surface-primary px-2 font-sans text-xs text-token-text-secondary dark:bg-token-main-surface-secondary"><span class="" data-state="closed"><button class="flex gap-1 items-center select-none px-4 py-1" aria-label="复制"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-xs"><path fill-rule="evenodd" clip-rule="evenodd" d="M7 5C7 3.34315 8.34315 2 10 2H19C20.6569 2 22 3.34315 22 5V14C22 15.6569 20.6569 17 19 17H17V19C17 20.6569 15.6569 22 14 22H5C3.34315 22 2 20.6569 2 19V10C2 8.34315 3.34315 7 5 7H7V5ZM9 7H14C15.6569 7 17 8.34315 17 10V15H19C19.5523 15 20 14.5523 20 14V5C20 4.44772 19.5523 4 19 4H10C9.44772 4 9 4.44772 9 5V7ZM5 9C4.44772 9 4 9.44772 4 10V19C4 19.5523 4.44772 20 5 20H14C14.5523 20 15 19.5523 15 19V10C15 9.44772 14.5523 9 14 9H5Z" fill="currentColor"></path></svg>复制</button></span><span class="" data-state="closed"><button class="flex select-none items-center gap-1"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-xs"><path d="M2.5 5.5C4.3 5.2 5.2 4 5.5 2.5C5.8 4 6.7 5.2 8.5 5.5C6.7 5.8 5.8 7 5.5 8.5C5.2 7 4.3 5.8 2.5 5.5Z" fill="currentColor" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round"></path><path d="M5.66282 16.5231L5.18413 19.3952C5.12203 19.7678 5.09098 19.9541 5.14876 20.0888C5.19933 20.2067 5.29328 20.3007 5.41118 20.3512C5.54589 20.409 5.73218 20.378 6.10476 20.3159L8.97693 19.8372C9.72813 19.712 10.1037 19.6494 10.4542 19.521C10.7652 19.407 11.0608 19.2549 11.3343 19.068C11.6425 18.8575 11.9118 18.5882 12.4503 18.0497L20 10.5C21.3807 9.11929 21.3807 6.88071 20 5.5C18.6193 4.11929 16.3807 4.11929 15 5.5L7.45026 13.0497C6.91175 13.5882 6.6425 13.8575 6.43197 14.1657C6.24513 14.4392 6.09299 14.7348 5.97903 15.0458C5.85062 15.3963 5.78802 15.7719 5.66282 16.5231Z" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"></path><path d="M14.5 7L18.5 11" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"></path></svg>编辑</button></span></div></div></div><div class="overflow-y-auto p-4" dir="ltr"><code class="!whitespace-pre"><span>&
├── x1
└── |
<span class="hljs-code"> ├── x2
└── !
└── x3
</span></span></code></div></div></pre><h3 data-start="4347" data-end="4353">输出</h3><pre class="!overflow-visible" data-start="4355" data-end="4395"><div class="contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary dark:bg-gray-950"><div class="flex items-center text-token-text-secondary px-4 py-2 text-xs font-sans justify-between rounded-t-[5px] h-9 bg-token-sidebar-surface-primary dark:bg-token-main-surface-secondary select-none">markdown</div><div class="sticky top-9 md:top-[5.75rem]"><div class="absolute bottom-0 right-2 flex h-9 items-center"><div class="flex items-center rounded bg-token-sidebar-surface-primary px-2 font-sans text-xs text-token-text-secondary dark:bg-token-main-surface-secondary"><span class="" data-state="closed"><button class="flex gap-1 items-center select-none px-4 py-1" aria-label="复制"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-xs"><path fill-rule="evenodd" clip-rule="evenodd" d="M7 5C7 3.34315 8.34315 2 10 2H19C20.6569 2 22 3.34315 22 5V14C22 15.6569 20.6569 17 19 17H17V19C17 20.6569 15.6569 22 14 22H5C3.34315 22 2 20.6569 2 19V10C2 8.34315 3.34315 7 5 7H7V5ZM9 7H14C15.6569 7 17 8.34315 17 10V15H19C19.5523 15 20 14.5523 20 14V5C20 4.44772 19.5523 4 19 4H10C9.44772 4 9 4.44772 9 5V7ZM5 9C4.44772 9 4 9.44772 4 10V19C4 19.5523 4.44772 20 5 20H14C14.5523 20 15 19.5523 15 19V10C15 9.44772 14.5523 9 14 9H5Z" fill="currentColor"></path></svg>复制</button></span><span class="" data-state="closed"><button class="flex select-none items-center gap-1"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-xs"><path d="M2.5 5.5C4.3 5.2 5.2 4 5.5 2.5C5.8 4 6.7 5.2 8.5 5.5C6.7 5.8 5.8 7 5.5 8.5C5.2 7 4.3 5.8 2.5 5.5Z" fill="currentColor" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round"></path><path d="M5.66282 16.5231L5.18413 19.3952C5.12203 19.7678 5.09098 19.9541 5.14876 20.0888C5.19933 20.2067 5.29328 20.3007 5.41118 20.3512C5.54589 20.409 5.73218 20.378 6.10476 20.3159L8.97693 19.8372C9.72813 19.712 10.1037 19.6494 10.4542 19.521C10.7652 19.407 11.0608 19.2549 11.3343 19.068C11.6425 18.8575 11.9118 18.5882 12.4503 18.0497L20 10.5C21.3807 9.11929 21.3807 6.88071 20 5.5C18.6193 4.11929 16.3807 4.11929 15 5.5L7.45026 13.0497C6.91175 13.5882 6.6425 13.8575 6.43197 14.1657C6.24513 14.4392 6.09299 14.7348 5.97903 15.0458C5.85062 15.3963 5.78802 15.7719 5.66282 16.5231Z" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"></path><path d="M14.5 7L18.5 11" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"></path></svg>编辑</button></span></div></div></div><div class="overflow-y-auto p-4" dir="ltr"><code class="!whitespace-pre"><span>&
x1
|
<span class="hljs-code"> x2
!
x3
</span></span></code></div></div></pre><h3 data-start="4397" data-end="4403">总结</h3><p data-start="4405" data-end="4475" data-is-last-node="">这个实现方法不依赖编译原理知识，而是通过栈和递归的基本算法来处理运算符优先级和括号结构。它足够简单，适合没有编译原理背景的开发者理解和实现。</p></div></div></div></div></div></div></div></div></article><article class="w-full text-token-text-primary focus-visible:outline-2 focus-visible:outline-offset-[-4px]" dir="auto" data-testid="conversation-turn-6" data-scroll-anchor="false"><h5 class="sr-only">您说：</h5><div class="m-auto text-base py-[18px] px-6"><div class="mx-auto flex flex-1 gap-4 text-base md:gap-5 lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col @xs/thread:px-0 @sm/thread:px-1.5 @md/thread:px-4"><div class="flex-col gap-1 md:gap-3"><div class="flex max-w-full flex-col flex-grow"><div data-message-author-role="user" data-message-id="85ff7d5a-9c75-469a-b98b-41dc5510b3b9" dir="auto" class="min-h-8 text-message flex w-full flex-col items-end gap-2 whitespace-normal break-words text-start [.text-message+&]:mt-5"><div class="flex w-full flex-col gap-1 empty:hidden items-end rtl:items-start"><div class="relative max-w-[var(--user-chat-width,70%)] rounded-3xl bg-token-message-surface px-5 py-2.5"><div class="whitespace-pre-wrap">我简化一下问题，如果输入不是表达式字符串，而是已经切分好的token数组，如 ["x1", "&", "(", "x2", "|", "!", "x3", ")"] ，重新实现一下这个函数</div><div class="absolute bottom-0 right-full top-0 -mr-3.5 hidden pr-5 pt-1 [.group\/conversation-turn:hover_&]:block"><span class="" data-state="closed"><button aria-label="编辑消息" class="flex h-9 w-9 items-center justify-center rounded-full text-token-text-secondary transition hover:bg-token-main-surface-tertiary"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-md"><path fill-rule="evenodd" clip-rule="evenodd" d="M13.2929 4.29291C15.0641 2.52167 17.9359 2.52167 19.7071 4.2929C21.4784 6.06414 21.4784 8.93588 19.7071 10.7071L18.7073 11.7069L11.6135 18.8007C10.8766 19.5376 9.92793 20.0258 8.89999 20.1971L4.16441 20.9864C3.84585 21.0395 3.52127 20.9355 3.29291 20.7071C3.06454 20.4788 2.96053 20.1542 3.01362 19.8356L3.80288 15.1C3.9742 14.0721 4.46243 13.1234 5.19932 12.3865L13.2929 4.29291ZM13 7.41422L6.61353 13.8007C6.1714 14.2428 5.87846 14.8121 5.77567 15.4288L5.21656 18.7835L8.57119 18.2244C9.18795 18.1216 9.75719 17.8286 10.1993 17.3865L16.5858 11L13 7.41422ZM18 9.5858L14.4142 6.00001L14.7071 5.70712C15.6973 4.71693 17.3027 4.71693 18.2929 5.70712C19.2831 6.69731 19.2831 8.30272 18.2929 9.29291L18 9.5858Z" fill="currentColor"></path></svg></button></span></div></div></div></div></div></div></div></div></div></article><article class="w-full text-token-text-primary focus-visible:outline-2 focus-visible:outline-offset-[-4px]" dir="auto" data-testid="conversation-turn-7" data-scroll-anchor="true"><h6 class="sr-only">ChatGPT 说：</h6><div class="m-auto text-base py-[18px] px-6"><div class="mx-auto flex flex-1 gap-4 text-base md:gap-5 lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="group/conversation-turn relative flex w-full min-w-0 flex-col agent-turn @xs/thread:px-0 @sm/thread:px-1.5 @md/thread:px-4"><div class="flex-col gap-1 md:gap-3"><div class="flex max-w-full flex-col flex-grow"><div data-message-author-role="assistant" data-message-id="511d6fb9-6d30-4c33-b884-0c944373e301" dir="auto" class="min-h-8 text-message flex w-full flex-col items-end gap-2 whitespace-normal break-words text-start [.text-message+&]:mt-5" data-message-model-slug="gpt-4o"><div class="flex w-full flex-col gap-1 empty:hidden first:pt-[3px]"><div class="markdown prose w-full break-words dark:prose-invert light"><p data-start="0" data-end="75">好的，如果输入是一个已经切分好的 token 数组，那么问题就变得更简单了，我们可以直接基于这些 token 逐步构建二叉树，而不需要解析原始字符串。</p><h3 data-start="77" data-end="85">关键点：</h3><ol data-start="86" data-end="174"><li data-start="86" data-end="132"><strong data-start="89" data-end="96">使用栈</strong>：由于我们需要处理优先级和括号的结构，栈可以帮助我们管理运算符和操作数。</li><li data-start="133" data-end="174"><strong data-start="136" data-end="144">递归解析</strong>：递归会处理括号内的子表达式，并根据优先级构建相应的二叉树。</li></ol><h3 data-start="176" data-end="184">代码实现</h3><pre class="!overflow-visible" data-start="186" data-end="3088"><div class="contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary dark:bg-gray-950"><div class="flex items-center text-token-text-secondary px-4 py-2 text-xs font-sans justify-between rounded-t-[5px] h-9 bg-token-sidebar-surface-primary dark:bg-token-main-surface-secondary select-none">java</div><div class="sticky top-9 md:top-[5.75rem]"><div class="absolute bottom-0 right-2 flex h-9 items-center"><div class="flex items-center rounded bg-token-sidebar-surface-primary px-2 font-sans text-xs text-token-text-secondary dark:bg-token-main-surface-secondary"><span class="" data-state="closed"><button class="flex gap-1 items-center select-none px-4 py-1" aria-label="复制"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-xs"><path fill-rule="evenodd" clip-rule="evenodd" d="M7 5C7 3.34315 8.34315 2 10 2H19C20.6569 2 22 3.34315 22 5V14C22 15.6569 20.6569 17 19 17H17V19C17 20.6569 15.6569 22 14 22H5C3.34315 22 2 20.6569 2 19V10C2 8.34315 3.34315 7 5 7H7V5ZM9 7H14C15.6569 7 17 8.34315 17 10V15H19C19.5523 15 20 14.5523 20 14V5C20 4.44772 19.5523 4 19 4H10C9.44772 4 9 4.44772 9 5V7ZM5 9C4.44772 9 4 9.44772 4 10V19C4 19.5523 4.44772 20 5 20H14C14.5523 20 15 19.5523 15 19V10C15 9.44772 14.5523 9 14 9H5Z" fill="currentColor"></path></svg>复制</button></span><span class="" data-state="closed"><button class="flex select-none items-center gap-1"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-xs"><path d="M2.5 5.5C4.3 5.2 5.2 4 5.5 2.5C5.8 4 6.7 5.2 8.5 5.5C6.7 5.8 5.8 7 5.5 8.5C5.2 7 4.3 5.8 2.5 5.5Z" fill="currentColor" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round"></path><path d="M5.66282 16.5231L5.18413 19.3952C5.12203 19.7678 5.09098 19.9541 5.14876 20.0888C5.19933 20.2067 5.29328 20.3007 5.41118 20.3512C5.54589 20.409 5.73218 20.378 6.10476 20.3159L8.97693 19.8372C9.72813 19.712 10.1037 19.6494 10.4542 19.521C10.7652 19.407 11.0608 19.2549 11.3343 19.068C11.6425 18.8575 11.9118 18.5882 12.4503 18.0497L20 10.5C21.3807 9.11929 21.3807 6.88071 20 5.5C18.6193 4.11929 16.3807 4.11929 15 5.5L7.45026 13.0497C6.91175 13.5882 6.6425 13.8575 6.43197 14.1657C6.24513 14.4392 6.09299 14.7348 5.97903 15.0458C5.85062 15.3963 5.78802 15.7719 5.66282 16.5231Z" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"></path><path d="M14.5 7L18.5 11" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"></path></svg>编辑</button></span></div></div></div><div class="overflow-y-auto p-4" dir="ltr"><code class="!whitespace-pre language-java"><span><span class="hljs-keyword">import</span> java.util.*;
<span class="hljs-keyword">public</span> <span class="hljs-keyword">class</span> <span class="hljs-title class_">BooleanExpressionParser</span> {
<span class="hljs-keyword">static</span> <span class="hljs-keyword">class</span> <span class="hljs-title class_">TreeNode</span> {
String value;
TreeNode left;
TreeNode right;
TreeNode(String value) {
<span class="hljs-built_in">this</span>.value = value;
<span class="hljs-built_in">this</span>.left = <span class="hljs-literal">null</span>;
<span class="hljs-built_in">this</span>.right = <span class="hljs-literal">null</span>;
}
}
<span class="hljs-comment">// 解析切分好的token数组，返回二叉树</span>
<span class="hljs-keyword">public</span> <span class="hljs-keyword">static</span> TreeNode <span class="hljs-title function_">parse</span><span class="hljs-params">(List<String> tokens)</span> {
Stack<TreeNode> operands = <span class="hljs-keyword">new</span> <span class="hljs-title class_">Stack</span><>(); <span class="hljs-comment">// 操作数栈</span>
Stack<String> operators = <span class="hljs-keyword">new</span> <span class="hljs-title class_">Stack</span><>(); <span class="hljs-comment">// 运算符栈</span>
<span class="hljs-type">int</span> <span class="hljs-variable">index</span> <span class="hljs-operator">=</span> <span class="hljs-number">0</span>;
<span class="hljs-keyword">while</span> (index < tokens.size()) {
<span class="hljs-type">String</span> <span class="hljs-variable">token</span> <span class="hljs-operator">=</span> tokens.get(index);
<span class="hljs-keyword">if</span> (token.equals(<span class="hljs-string">"("</span>)) {
<span class="hljs-comment">// 递归解析括号内的表达式</span>
operators.push(token);
} <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (token.equals(<span class="hljs-string">")"</span>)) {
<span class="hljs-comment">// 遇到右括号，开始构建树</span>
<span class="hljs-keyword">while</span> (!operators.peek().equals(<span class="hljs-string">"("</span>)) {
processOperator(operands, operators.pop());
}
operators.pop(); <span class="hljs-comment">// 移除 '('</span>
} <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (token.equals(<span class="hljs-string">"!"</span>) || token.equals(<span class="hljs-string">"&"</span>) || token.equals(<span class="hljs-string">"|"</span>)) {
<span class="hljs-comment">// 操作符，处理运算符优先级</span>
<span class="hljs-keyword">while</span> (!operators.isEmpty() && precedence(operators.peek()) >= precedence(token)) {
processOperator(operands, operators.pop());
}
operators.push(token);
} <span class="hljs-keyword">else</span> {
<span class="hljs-comment">// 变量，直接入栈</span>
operands.push(<span class="hljs-keyword">new</span> <span class="hljs-title class_">TreeNode</span>(token));
}
index++;
}
<span class="hljs-comment">// 处理剩余的操作符</span>
<span class="hljs-keyword">while</span> (!operators.isEmpty()) {
processOperator(operands, operators.pop());
}
<span class="hljs-keyword">return</span> operands.isEmpty() ? <span class="hljs-literal">null</span> : operands.pop();
}
<span class="hljs-comment">// 处理栈顶的运算符</span>
<span class="hljs-keyword">private</span> <span class="hljs-keyword">static</span> <span class="hljs-keyword">void</span> <span class="hljs-title function_">processOperator</span><span class="hljs-params">(Stack<TreeNode> operands, String operator)</span> {
<span class="hljs-type">TreeNode</span> <span class="hljs-variable">node</span> <span class="hljs-operator">=</span> <span class="hljs-keyword">new</span> <span class="hljs-title class_">TreeNode</span>(operator);
<span class="hljs-comment">// 对于 '!' 操作符，只有右子树</span>
<span class="hljs-keyword">if</span> (operator.equals(<span class="hljs-string">"!"</span>)) {
node.right = operands.pop();
} <span class="hljs-keyword">else</span> {
node.right = operands.pop();
node.left = operands.pop();
}
operands.push(node);
}
<span class="hljs-comment">// 运算符的优先级：'!' > '&' > '|'</span>
<span class="hljs-keyword">private</span> <span class="hljs-keyword">static</span> <span class="hljs-type">int</span> <span class="hljs-title function_">precedence</span><span class="hljs-params">(String operator)</span> {
<span class="hljs-keyword">if</span> (operator.equals(<span class="hljs-string">"!"</span>)) {
<span class="hljs-keyword">return</span> <span class="hljs-number">3</span>;
} <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (operator.equals(<span class="hljs-string">"&"</span>)) {
<span class="hljs-keyword">return</span> <span class="hljs-number">2</span>;
} <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (operator.equals(<span class="hljs-string">"|"</span>)) {
<span class="hljs-keyword">return</span> <span class="hljs-number">1</span>;
}
<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;
}
<span class="hljs-comment">// 打印二叉树，用于测试</span>
<span class="hljs-keyword">public</span> <span class="hljs-keyword">static</span> <span class="hljs-keyword">void</span> <span class="hljs-title function_">printTree</span><span class="hljs-params">(TreeNode node, String indent)</span> {
<span class="hljs-keyword">if</span> (node != <span class="hljs-literal">null</span>) {
System.out.println(indent + node.value);
printTree(node.left, indent + <span class="hljs-string">" "</span>);
printTree(node.right, indent + <span class="hljs-string">" "</span>);
}
}
<span class="hljs-comment">// 测试</span>
<span class="hljs-keyword">public</span> <span class="hljs-keyword">static</span> <span class="hljs-keyword">void</span> <span class="hljs-title function_">main</span><span class="hljs-params">(String[] args)</span> {
<span class="hljs-comment">// 输入是一个已经切分好的token数组</span>
List<String> tokens = Arrays.asList(<span class="hljs-string">"x1"</span>, <span class="hljs-string">"&"</span>, <span class="hljs-string">"("</span>, <span class="hljs-string">"x2"</span>, <span class="hljs-string">"|"</span>, <span class="hljs-string">"!"</span>, <span class="hljs-string">"x3"</span>, <span class="hljs-string">")"</span>);
<span class="hljs-type">TreeNode</span> <span class="hljs-variable">root</span> <span class="hljs-operator">=</span> parse(tokens);
printTree(root, <span class="hljs-string">""</span>);
}
}
</span></code></div></div></pre><h3 data-start="3090" data-end="3098">代码解析</h3><ol data-start="3100" data-end="3619"><li data-start="3100" data-end="3371"><p data-start="3103" data-end="3146"><strong data-start="3103" data-end="3112">parse</strong>：接受已经切分好的 token 列表，然后逐步解析这些 token。</p><ul data-start="3150" data-end="3371"><li data-start="3150" data-end="3208">使用两个栈：<code data-start="3158" data-end="3168">operands</code> 用于存储操作数（布尔变量或子表达式），<code data-start="3188" data-end="3199">operators</code> 用于存储操作符。</li><li data-start="3212" data-end="3275">遇到左括号 <code data-start="3220" data-end="3223">(</code> 时，将其压入 <code data-start="3231" data-end="3242">operators</code> 栈中；遇到右括号 <code data-start="3252" data-end="3255">)</code> 时，弹出操作符并处理，直到遇到左括号。</li><li data-start="3279" data-end="3330">遇到操作符时，比较当前操作符与栈顶操作符的优先级，如果当前操作符优先级更低，则先处理栈中的操作符。</li><li data-start="3334" data-end="3371">遇到布尔变量时，直接创建一个树节点并压入 <code data-start="3357" data-end="3367">operands</code> 栈中。</li></ul></li><li data-start="3373" data-end="3503"><p data-start="3376" data-end="3503"><strong data-start="3376" data-end="3395">processOperator</strong>：这个方法用于从 <code data-start="3404" data-end="3414">operands</code> 栈中弹出两个操作数，并根据操作符创建新的树节点，然后将新节点压入 <code data-start="3448" data-end="3458">operands</code> 栈中。如果是 <code data-start="3466" data-end="3469">!</code> 操作符，只处理右子树；如果是 <code data-start="3485" data-end="3488">&</code> 或 <code data-start="3491" data-end="3494">|</code>，则处理左右子树。</p></li><li data-start="3505" data-end="3577"><p data-start="3508" data-end="3577"><strong data-start="3508" data-end="3522">precedence</strong>：这是一个简单的优先级比较方法，用于决定操作符的优先级。<code data-start="3550" data-end="3553">!</code> 的优先级最高，其次是 <code data-start="3565" data-end="3568">&</code>，最后是 <code data-start="3573" data-end="3576">|</code>。</p></li><li data-start="3579" data-end="3619"><p data-start="3582" data-end="3619"><strong data-start="3582" data-end="3595">printTree</strong>：打印二叉树，用于验证构建出来的树结构是否正确。</p></li></ol><h3 data-start="3621" data-end="3627">测试</h3><p data-start="3629" data-end="3702">对于输入的 tokens 列表 <code data-start="3645" data-end="3690">["x1", "&", "(", "x2", "|", "!", "x3", ")"]</code>，程序会输出以下二叉树：</p><pre class="!overflow-visible" data-start="3704" data-end="3744"><div class="contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary dark:bg-gray-950"><div class="flex items-center text-token-text-secondary px-4 py-2 text-xs font-sans justify-between rounded-t-[5px] h-9 bg-token-sidebar-surface-primary dark:bg-token-main-surface-secondary select-none">markdown</div><div class="sticky top-9 md:top-[5.75rem]"><div class="absolute bottom-0 right-2 flex h-9 items-center"><div class="flex items-center rounded bg-token-sidebar-surface-primary px-2 font-sans text-xs text-token-text-secondary dark:bg-token-main-surface-secondary"><span class="" data-state="closed"><button class="flex gap-1 items-center select-none px-4 py-1" aria-label="复制"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-xs"><path fill-rule="evenodd" clip-rule="evenodd" d="M7 5C7 3.34315 8.34315 2 10 2H19C20.6569 2 22 3.34315 22 5V14C22 15.6569 20.6569 17 19 17H17V19C17 20.6569 15.6569 22 14 22H5C3.34315 22 2 20.6569 2 19V10C2 8.34315 3.34315 7 5 7H7V5ZM9 7H14C15.6569 7 17 8.34315 17 10V15H19C19.5523 15 20 14.5523 20 14V5C20 4.44772 19.5523 4 19 4H10C9.44772 4 9 4.44772 9 5V7ZM5 9C4.44772 9 4 9.44772 4 10V19C4 19.5523 4.44772 20 5 20H14C14.5523 20 15 19.5523 15 19V10C15 9.44772 14.5523 9 14 9H5Z" fill="currentColor"></path></svg>复制</button></span><span class="" data-state="closed"><button class="flex select-none items-center gap-1"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-xs"><path d="M2.5 5.5C4.3 5.2 5.2 4 5.5 2.5C5.8 4 6.7 5.2 8.5 5.5C6.7 5.8 5.8 7 5.5 8.5C5.2 7 4.3 5.8 2.5 5.5Z" fill="currentColor" stroke="currentColor" stroke-linecap="round" stroke-linejoin="round"></path><path d="M5.66282 16.5231L5.18413 19.3952C5.12203 19.7678 5.09098 19.9541 5.14876 20.0888C5.19933 20.2067 5.29328 20.3007 5.41118 20.3512C5.54589 20.409 5.73218 20.378 6.10476 20.3159L8.97693 19.8372C9.72813 19.712 10.1037 19.6494 10.4542 19.521C10.7652 19.407 11.0608 19.2549 11.3343 19.068C11.6425 18.8575 11.9118 18.5882 12.4503 18.0497L20 10.5C21.3807 9.11929 21.3807 6.88071 20 5.5C18.6193 4.11929 16.3807 4.11929 15 5.5L7.45026 13.0497C6.91175 13.5882 6.6425 13.8575 6.43197 14.1657C6.24513 14.4392 6.09299 14.7348 5.97903 15.0458C5.85062 15.3963 5.78802 15.7719 5.66282 16.5231Z" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"></path><path d="M14.5 7L18.5 11" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round"></path></svg>编辑</button></span></div></div></div><div class="overflow-y-auto p-4" dir="ltr"><code class="!whitespace-pre"><span>&
x1
|
<span class="hljs-code"> x2
!
x3
</span></span></code></div></div></pre><h3 data-start="3746" data-end="3752">总结</h3><p data-start="3754" data-end="3849" data-is-last-node="">这个实现方法利用了栈和优先级来处理运算符，确保正确处理操作符的优先级，并通过栈将表达式转换为二叉树。由于输入已经是切分好的 token 数组，这使得处理更加直接，避免了复杂的字符串解析操作。</p></div></div></div></div></div></div></div></div></article><div class="mx-auto flex flex-1 gap-4 text-base md:gap-5 lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><p class="flex items-center text-xs text-gray-500"><svg width="24" height="24" viewBox="0 0 24 24" fill="none" xmlns="http://www.w3.org/2000/svg" class="icon-xs mr-2"><path fill-rule="evenodd" clip-rule="evenodd" d="M12 4C9.79086 4 8 5.79086 8 8H16C16 5.79086 14.2091 4 12 4ZM6 10C5.44772 10 5 10.4477 5 11V19C5 19.5523 5.44772 20 6 20H18C18.5523 20 19 19.5523 19 19V11C19 10.4477 18.5523 10 18 10H6ZM6 8C6 4.68629 8.68629 2 12 2C15.3137 2 18 4.68629 18 8C19.6569 8 21 9.34315 21 11V19C21 20.6569 19.6569 22 18 22H6C4.34315 22 3 20.6569 3 19V11C3 9.34315 4.34315 8 6 8ZM10 14C10 12.8954 10.8954 12 12 12C13.1046 12 14 12.8954 14 14C14 14.7403 13.5978 15.3866 13 15.7324V17C13 17.5523 12.5523 18 12 18C11.4477 18 11 17.5523 11 17V15.7324C10.4022 15.3866 10 14.7403 10 14Z" fill="currentColor"></path></svg>超出此点的消息将只对您显示</p></div></div></div></div><div class="md:pt-0 dark:border-white/20 md:border-transparent md:dark:border-transparent w-full isolate has-[[data-has-thread-error]]:[box-shadow:var(--sharp-edge-bottom-shadow)] has-[[data-has-thread-error]]:pt-2"><div><div class="m-auto text-base px-3 md:px-4 w-full md:px-5 lg:px-4 xl:px-5"><div class="mx-auto flex flex-1 gap-4 text-base md:gap-5 lg:gap-6 md:max-w-3xl lg:max-w-[40rem] xl:max-w-[48rem]"><div class="flex justify-center empty:hidden"></div><form class="w-full" type="button" aria-haspopup="dialog" aria-expanded="false" aria-controls="radix-:r1:" data-state="closed"><div class="relative z-[1] flex h-full max-w-full flex-1 flex-col"><div class="absolute bottom-full left-0 right-0 z-20"></div><div class="group relative z-[1] flex w-full items-center" style="--force-hide-label: block;"><div class="w-full"><div id="composer-background" class="flex w-full cursor-text flex-col rounded-3xl border border-token-border-light px-3 py-1 duration-150 ease-in-out contain-inline-size motion-safe:transition-[color,background-color,border-color,text-decoration-color,fill,stroke,box-shadow] dark:border-none dark:shadow-none shadow-[0_9px_9px_0px_rgba(0,0,0,0.01),_0_2px_5px_0px_rgba(0,0,0,0.06)] has-[:focus]:shadow-[0_2px_12px_0px_rgba(0,0,0,0.04),_0_9px_9px_0px_rgba(0,0,0,0.01),_0_2px_5px_0px_rgba(0,0,0,0.06)] bg-token-main-surface-primary dark:bg-[#303030]" style="view-transition-name: var(--vt-composer);"><div class="flex min-h-[44px] items-start pl-1"><div class="min-w-0 max-w-full flex-1"><div class="_prosemirror-parent_1r7mb_1 text-token-text-primary max-h-[25dvh] max-h-52 overflow-auto default-browser"><textarea class="block h-10 w-full resize-none border-0 bg-transparent px-0 py-2 text-token-text-primary placeholder:text-token-text-tertiary" placeholder="给 ChatGPT 发送消息" data-virtualkeyboard="true" style="display: none;"></textarea><script nonce="">window.__oai_logHTML?window.__oai_logHTML():window.__oai_SSR_HTML=window.__oai_SSR_HTML||Date.now();requestAnimationFrame((function(){window.__oai_logTTI?window.__oai_logTTI():window.__oai_SSR_TTI=window.__oai_SSR_TTI||Date.now()}))</script><div contenteditable="true" translate="no" class="ProseMirror" id="prompt-textarea" data-virtualkeyboard="true"><p data-placeholder="给 ChatGPT 发送消息" class="placeholder"><br class="ProseMirror-trailingBreak"></p></div></div></div><div class="w-[32px] pt-1"><span aria-hidden="true" class="pointer-events-none invisible fixed left-0 top-0 block">O</span></div></div><div class="mb-2 mt-1 flex items-center justify-between sm:mt-5"><div class="flex gap-x-1.5 text-token-text-primary"><div style="view-transition-name: var(--vt-composer-attach-file-action);"><div class="relative"><div class="relative"><div class="flex flex-col"><input multiple="" tabindex="-1" class="hidden" type="file" style="display: none;"><span class="hidden"></span><button type="button" id="radix-:r2q:" aria-haspopup="menu" aria-expanded="false" data-state="closed" class="text-token-text-primary border border-transparent inline-flex items-center justify-center gap-1 rounded-lg text-sm dark:transparent dark:bg-transparent leading-none outline-none cursor-pointer hover:bg-token-main-surface-secondary dark:hover:bg-token-main-surface-secondary focus-visible:bg-token-main-surface-secondary radix-state-active:text-token-text-secondary radix-disabled:cursor-auto radix-disabled:bg-transparent radix-disabled:text-token-text-tertiary dark:radix-disabled:bg-transparent m-0 h-0 w-0 border-none bg-transparent p-0"></button><span class="flex" data-state="closed"><button aria-disabled="false" aria-label="上传文件等" class="flex items-center justify-center h-9 rounded-full border border-token-border-light text-token-text-secondary w-9 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Safari/537.36\",\"is_punch_out_user\",\"is_paid\",\"auth_status\",\"logged_in\",\"ip\",\"2a12:a301:1000::2087\",\"userAgent\",\"statsigEnvironment\",{\"_1262\":1263},\"tier\",\"production\",{\"_1247\":58,\"_1248\":1265,\"_1238\":1266,\"_1257\":1258,\"_59\":60,\"_1267\":1268,\"_1259\":1252,\"_1237\":12},{\"_1250\":70,\"_1251\":1252,\"_1253\":25,\"_1254\":25,\"_1255\":1256},{\"_1240\":1241,\"_1242\":1241,\"_1243\":1241},\"privateAttributes\",{\"_15\":16},\"authStatus\",\"userRegion\",\"Tokyo\",\"cfConnectingIp\",\"cfIpLatitude\",\"35.68930\",\"cfIpLongitude\",\"139.68990\",\"cfIpCity\",\"isNoAuthEnabled\",\"isIos\",\"isAndroidChrome\",\"isElectron\",\"windowStyle\",\"cspScriptNonce\",\"a02edb2c-06db-4978-945d-2ac4de5e3f7b\",\"routes/share.$shareId.($action)\",{\"_1287\":1288,\"_1289\":1290,\"_1567\":25,\"_1568\":25,\"_1569\":1570,\"_2026\":2027},\"sharedConversationId\",\"67ae2667-adf4-8002-b72c-40c0f01d749e\",\"serverResponse\",{\"_1291\":7,\"_7\":1292},\"type\",{\"_538\":1293,\"_1294\":1295,\"_1296\":1297,\"_1298\":1299,\"_1448\":1449,\"_1450\":1433,\"_1451\":1288,\"_1452\":25,\"_1453\":1454,\"_1362\":1363,\"_1455\":1456,\"_1457\":70,\"_1458\":1459,\"_1543\":25,\"_1544\":1545,\"_1546\":1547,\"_1558\":1559,\"_1565\":25,\"_1566\":70},\"布尔表达式解析器\",\"create_time\",1739466343.680858,\"update_time\",1739466368.708411,\"mapping\",{\"_1300\":1301,\"_1304\":1305,\"_1328\":1329,\"_1349\":1350,\"_1367\":1368,\"_1390\":1391,\"_1404\":1405,\"_1419\":1420,\"_1433\":1434},\"aaa14198-77f9-493c-b743-8152676ff430\",{\"_11\":1300,\"_1302\":1303},\"children\",[1304],\"7d4dc734-a7ba-461a-bc60-bafd1860d912\",{\"_11\":1304,\"_1306\":1307,\"_1326\":1300,\"_1302\":1327},\"message\",{\"_11\":1304,\"_1308\":1309,\"_1314\":1315,\"_46\":1319,\"_1320\":70,\"_1321\":40,\"_1312\":1322,\"_1325\":1044},\"author\",{\"_1310\":1311,\"_1312\":1313},\"role\",\"system\",\"metadata\",{},\"content\",{\"_1316\":542,\"_1317\":1318},\"content_type\",\"parts\",[617],\"finished_successfully\",\"end_turn\",\"weight\",{\"_1323\":70,\"_1324\":1288},\"is_visually_hidden_from_conversation\",\"shared_conversation_id\",\"recipient\",\"parent\",[1328],\"248da6d4-b818-49ee-a588-767850054a97\",{\"_11\":1328,\"_1306\":1330,\"_1326\":1304,\"_1302\":1348},{\"_11\":1328,\"_1308\":1331,\"_1294\":1333,\"_1314\":1334,\"_46\":1319,\"_1321\":35,\"_1312\":1337,\"_1325\":1044},{\"_1310\":9,\"_1312\":1332},{},1739462316.329153,{\"_1316\":542,\"_1317\":1335},[1336],\"基于java，实现一个布尔表达式解析器。表达式允许的字符包括：\\n- 与运算 \u0026\\n- 或运算 |\\n- 取非运算 ! \\n- 空格\\n- 布尔变量 x_{i} ，如 x_1, x_20 \\n表达式形如 x1 \u0026 (x2 | ! x3) \\n\\n请实现一个函数，能够将字符串表达式解析为一个二叉树。\",{\"_1338\":1339,\"_1342\":1343,\"_1344\":-5,\"_1345\":1346,\"_1347\":-5,\"_1324\":1288},\"serialization_metadata\",{\"_1340\":1341},\"custom_symbol_offsets\",[],\"request_id\",\"91160552ae122f7f-IAD\",\"message_source\",\"timestamp_\",\"absolute\",\"message_type\",[1349],\"7a556f19-a932-4898-8ffb-e81bb6ef5880\",{\"_11\":1349,\"_1306\":1351,\"_1326\":1328,\"_1302\":1366},{\"_11\":1349,\"_1308\":1352,\"_1294\":1355,\"_1314\":1356,\"_46\":1319,\"_1321\":35,\"_1312\":1359,\"_1325\":1044},{\"_1310\":1353,\"_1312\":1354},\"assistant\",{},1739462385.811449,{\"_1316\":1357,\"_1358\":617},\"model_editable_context\",\"model_set_context\",{\"_1347\":-5,\"_1360\":1361,\"_1362\":1363,\"_1364\":1328,\"_1342\":1343,\"_1345\":1346,\"_1324\":1288,\"_1365\":70},\"model_slug\",\"gpt-4o\",\"default_model_slug\",\"auto\",\"parent_id\",\"is_redacted\",[1367],\"65167b6e-0fe9-4ff0-ab18-1f096e6de947\",{\"_11\":1367,\"_1306\":1369,\"_1326\":1349,\"_1302\":1389},{\"_11\":1367,\"_1308\":1370,\"_1294\":1372,\"_1314\":1373,\"_46\":1319,\"_1320\":70,\"_1321\":35,\"_1312\":1376,\"_1325\":1044},{\"_1310\":1353,\"_1312\":1371},{},1739462385.811573,{\"_1316\":542,\"_1317\":1374},[1375],\"要实现一个布尔表达式解析器并将其解析为二叉树，可以通过递归下降解析（Recursive Descent Parsing）的方法来构建这个解析器。首先，我们定义一个二叉树节点类，然后利用递归来解析布尔表达式。\\n\\n### 步骤：\\n\\n1. **定义二叉树节点**：每个节点表示一个布尔表达式的操作符或布尔变量。\\n2. **递归解析**：首先从左到右解析表达式，处理括号、操作符（\u0026、|、!）和变量。\\n3. **操作符优先级**：根据布尔操作符的优先级，`!` 优先级最高，其次是 `\u0026`，最后是 `|`。\\n4. **构建二叉树**：每个操作符都会成为一个节点，它的左右子节点代表操作数。\\n\\n### Java代码实现：\\n\\n```java\\nimport java.util.*;\\n\\npublic class BooleanExpressionParser {\\n\\n static class TreeNode {\\n String value;\\n TreeNode left;\\n TreeNode right;\\n\\n TreeNode(String value) {\\n this.value = value;\\n this.left = null;\\n this.right = null;\\n }\\n }\\n\\n // 解析布尔表达式为二叉树\\n public static TreeNode parse(String expression) {\\n // 清理输入，去除空格\\n expression = expression.replaceAll(\\\"\\\\\\\\s+\\\", \\\"\\\");\\n\\n // 使用递归下降解析\\n return parseOr(expression, new int[] {0});\\n }\\n\\n // 解析 OR 表达式\\n private static TreeNode parseOr(String expression, int[] index) {\\n TreeNode left = parseAnd(expression, index);\\n\\n while (index[0] \u003c expression.length() \u0026\u0026 expression.charAt(index[0]) == '|') {\\n index[0]++; // 跳过 '|'\\n TreeNode node = new TreeNode(\\\"|\\\");\\n node.left = left;\\n node.right = parseAnd(expression, index);\\n left = node; // 更新左子树\\n }\\n\\n return left;\\n }\\n\\n // 解析 AND 表达式\\n private static TreeNode parseAnd(String expression, int[] index) {\\n TreeNode left = parseNot(expression, index);\\n\\n while (index[0] \u003c expression.length() \u0026\u0026 expression.charAt(index[0]) == '\u0026') {\\n index[0]++; // 跳过 '\u0026'\\n TreeNode node = new TreeNode(\\\"\u0026\\\");\\n node.left = left;\\n node.right = parseNot(expression, index);\\n left = node; // 更新左子树\\n }\\n\\n return left;\\n }\\n\\n // 解析 NOT 表达式\\n private static TreeNode parseNot(String expression, int[] index) {\\n if (index[0] \u003c expression.length() \u0026\u0026 expression.charAt(index[0]) == '!') {\\n index[0]++; // 跳过 '!'\\n TreeNode node = new TreeNode(\\\"!\\\");\\n node.right = parseFactor(expression, index); // 取非操作只有右子树\\n return node;\\n }\\n return parseFactor(expression, index);\\n }\\n\\n // 解析基本的因子：布尔变量或括号\\n private static TreeNode parseFactor(String expression, int[] index) {\\n if (index[0] \u003c expression.length() \u0026\u0026 expression.charAt(index[0]) == '(') {\\n index[0]++; // 跳过 '('\\n TreeNode node = parseOr(expression, index); // 递归解析括号中的表达式\\n index[0]++; // 跳过 ')'\\n return node;\\n }\\n\\n return parseVariable(expression, index);\\n }\\n\\n // 解析布尔变量（例如 x1, x20）\\n private static TreeNode parseVariable(String expression, int[] index) {\\n int start = index[0];\\n while (index[0] \u003c expression.length() \u0026\u0026 (Character.isLetterOrDigit(expression.charAt(index[0])) || expression.charAt(index[0]) == '_')) {\\n index[0]++;\\n }\\n String variable = expression.substring(start, index[0]);\\n return new TreeNode(variable);\\n }\\n\\n // 打印二叉树，用于测试\\n public static void printTree(TreeNode node, String indent) {\\n if (node != null) {\\n System.out.println(indent + node.value);\\n printTree(node.left, indent + \\\" \\\");\\n printTree(node.right, indent + \\\" \\\");\\n }\\n }\\n\\n // 测试\\n public static void main(String[] args) {\\n String expression = \\\"x1 \u0026 (x2 | ! x3)\\\";\\n TreeNode root = parse(expression);\\n printTree(root, \\\"\\\");\\n }\\n}\\n```\\n\\n### 解析器的工作原理：\\n\\n1. **parse**：接受一个字符串表示的布尔表达式，先去除所有空格，然后开始从 `parseOr` 开始解析。\\n2. **parseOr**：解析 OR (`|`) 操作，优先级最低。\\n3. **parseAnd**：解析 AND (`\u0026`) 操作。\\n4. **parseNot**：解析 NOT (`!`) 操作，优先级最高。\\n5. **parseFactor**：解析一个布尔因子，它可以是布尔变量（如 `x1`）或者括号内的表达式。\\n6. **parseVariable**：处理布尔变量的解析，如 `x1`, `x20` 等。\\n\\n### 测试\\n\\n对于表达式 `\\\"x1 \u0026 (x2 | !x3)\\\"`，程序会构建如下的二叉树：\\n\\n```\\n\u0026\\n├── x1\\n└── |\\n ├── x2\\n └── !\\n └── x3\\n```\\n\\n### 输出\\n\\n```\\n\u0026\\n x1\\n |\\n x2\\n !\\n x3\\n```\\n\\n这个实现是一个基本的递归下降解析器，能够处理布尔表达式中的 `\u0026`、`|` 和 `!` 操作符，支持括号和布尔变量。你可以根据需求对其进行扩展和优化，例如支持更多的错误检查和优化解析过程。\",{\"_1377\":1378,\"_1384\":70,\"_1385\":1386,\"_1387\":1388,\"_1347\":-5,\"_1360\":1361,\"_1362\":1363,\"_1364\":1349,\"_1342\":1343,\"_1345\":1346,\"_1324\":1288},\"finish_details\",{\"_1291\":1379,\"_1380\":1381},\"stop\",\"stop_tokens\",[1382,1383],200002,200007,\"is_complete\",\"citations\",[],\"content_references\",[],[1390],\"486a666e-6495-4fd4-baa8-7cd1b61978ad\",{\"_11\":1390,\"_1306\":1392,\"_1326\":1367,\"_1302\":1403},{\"_11\":1390,\"_1308\":1393,\"_1294\":1395,\"_1314\":1396,\"_46\":1319,\"_1321\":35,\"_1312\":1399,\"_1325\":1044},{\"_1310\":9,\"_1312\":1394},{},1739463300.16271,{\"_1316\":542,\"_1317\":1397},[1398],\"能否不依赖编译原理的知识背景，只通过基本的数据结构与算法知识解决？\",{\"_1338\":1400,\"_1342\":1402,\"_1344\":-5,\"_1345\":1346,\"_1347\":-5,\"_1324\":1288},{\"_1340\":1401},[],\"91161d554aad0fdb-LAX\",[1404],\"6777da8e-e075-4919-9a1a-e47a1fbc826d\",{\"_11\":1404,\"_1306\":1406,\"_1326\":1390,\"_1302\":1418},{\"_11\":1404,\"_1308\":1407,\"_1294\":1409,\"_1314\":1410,\"_46\":1319,\"_1320\":70,\"_1321\":35,\"_1312\":1413,\"_1325\":1044},{\"_1310\":1353,\"_1312\":1408},{},1739463370.815039,{\"_1316\":542,\"_1317\":1411},[1412],\"当然可以！如果不依赖编译原理的知识，我们可以通过栈和递归来实现一个解析器，使用基本的数据结构（栈）和算法（递归）来逐步解析表达式，并构建一个二叉树。\\n\\n下面是一个更简单的实现方法，不依赖于编译原理的知识，使用的是常见的栈和递归算法来解析布尔表达式并构建二叉树。\\n\\n### 关键思想\\n\\n1. **栈的使用**：我们可以使用栈来处理运算符的优先级，确保正确地处理操作顺序（例如，`!` 优先于 `\u0026`，`\u0026` 优先于 `|`）。\\n2. **递归的使用**：遇到括号时，我们通过递归来解析括号内的表达式，避免过于复杂的状态管理。\\n\\n### 代码实现\\n\\n```java\\nimport java.util.*;\\n\\npublic class BooleanExpressionParser {\\n\\n static class TreeNode {\\n String value;\\n TreeNode left;\\n TreeNode right;\\n\\n TreeNode(String value) {\\n this.value = value;\\n this.left = null;\\n this.right = null;\\n }\\n }\\n\\n // 解析布尔表达式为二叉树\\n public static TreeNode parse(String expression) {\\n expression = expression.replaceAll(\\\"\\\\\\\\s+\\\", \\\"\\\"); // 去除空格\\n return parseExpression(expression);\\n }\\n\\n // 解析布尔表达式\\n private static TreeNode parseExpression(String expression) {\\n Stack\u003cTreeNode\u003e operands = new Stack\u003c\u003e();\\n Stack\u003cCharacter\u003e operators = new Stack\u003c\u003e();\\n int index = 0;\\n\\n while (index \u003c expression.length()) {\\n char ch = expression.charAt(index);\\n\\n if (ch == '(') {\\n // 递归解析括号内的表达式\\n int end = findClosingParenthesis(expression, index);\\n operands.push(parseExpression(expression.substring(index + 1, end)));\\n index = end + 1; // 更新索引\\n } else if (ch == '!') {\\n // 取非操作，立即应用\\n index++;\\n operands.push(new TreeNode(\\\"!\\\"));\\n } else if (ch == '\u0026' || ch == '|') {\\n // 操作符处理\\n operators.push(ch);\\n index++;\\n } else if (ch == 'x') {\\n // 变量处理，如 x1, x20\\n int start = index;\\n while (index \u003c expression.length() \u0026\u0026 (Character.isDigit(expression.charAt(index)) || expression.charAt(index) == '_')) {\\n index++;\\n }\\n String variable = expression.substring(start, index);\\n operands.push(new TreeNode(variable));\\n } else {\\n index++; // 忽略不需要的字符\\n }\\n\\n // 处理运算符优先级\\n while (!operators.isEmpty() \u0026\u0026 (operators.peek() == '!' || operators.peek() == '\u0026' || operators.peek() == '|')) {\\n char op = operators.peek();\\n if (op == '!') {\\n TreeNode operand = operands.pop();\\n TreeNode node = new TreeNode(\\\"!\\\");\\n node.right = operand;\\n operands.push(node);\\n operators.pop();\\n } else if (op == '\u0026' || op == '|') {\\n TreeNode right = operands.pop();\\n TreeNode left = operands.pop();\\n TreeNode node = new TreeNode(String.valueOf(op));\\n node.left = left;\\n node.right = right;\\n operands.push(node);\\n operators.pop();\\n }\\n }\\n }\\n return operands.isEmpty() ? null : operands.pop();\\n }\\n\\n // 找到匹配的右括号\\n private static int findClosingParenthesis(String expression, int index) {\\n int count = 1;\\n int i = index + 1;\\n while (i \u003c expression.length() \u0026\u0026 count \u003e 0) {\\n if (expression.charAt(i) == '(') {\\n count++;\\n } else if (expression.charAt(i) == ')') {\\n count--;\\n }\\n i++;\\n }\\n return i - 1; // 返回右括号的索引\\n }\\n\\n // 打印二叉树，用于测试\\n public static void printTree(TreeNode node, String indent) {\\n if (node != null) {\\n System.out.println(indent + node.value);\\n printTree(node.left, indent + \\\" \\\");\\n printTree(node.right, indent + \\\" \\\");\\n }\\n }\\n\\n // 测试\\n public static void main(String[] args) {\\n String expression = \\\"x1 \u0026 (x2 | ! x3)\\\";\\n TreeNode root = parse(expression);\\n printTree(root, \\\"\\\");\\n }\\n}\\n```\\n\\n### 关键点：\\n\\n1. **括号处理**：当遇到左括号 `(` 时，我们递归解析括号内的子表达式，直到遇到右括号 `)` 为止。这是通过 `findClosingParenthesis` 方法来找到匹配的右括号实现的。\\n2. **运算符优先级**：在解析运算符时，我们使用栈来保存操作符。对于每个操作符，首先检查栈顶的操作符优先级，按照优先级（`!` \u003e `\u0026` \u003e `|`）构建二叉树节点。\\n3. **操作数和运算符**：对于变量（如 `x1`），我们直接从字符串中提取并构建二叉树节点；对于运算符（如 `\u0026`, `|`），我们在栈中存储操作符，并在遇到运算符时进行二叉树节点的合并。\\n\\n### 测试\\n\\n对于输入表达式 `\\\"x1 \u0026 (x2 | ! x3)\\\"`，程序构建的二叉树将是：\\n\\n```\\n\u0026\\n├── x1\\n└── |\\n ├── x2\\n └── !\\n └── x3\\n```\\n\\n### 输出\\n\\n```\\n\u0026\\n x1\\n |\\n x2\\n !\\n x3\\n```\\n\\n### 总结\\n\\n这个实现方法不依赖编译原理知识，而是通过栈和递归的基本算法来处理运算符优先级和括号结构。它足够简单，适合没有编译原理背景的开发者理解和实现。\",{\"_1377\":1414,\"_1384\":70,\"_1385\":1416,\"_1387\":1417,\"_1347\":-5,\"_1360\":1361,\"_1362\":1363,\"_1364\":1390,\"_1342\":1402,\"_1345\":1346,\"_1324\":1288},{\"_1291\":1379,\"_1380\":1415},[1382,1383],[],[],[1419],\"85ff7d5a-9c75-469a-b98b-41dc5510b3b9\",{\"_11\":1419,\"_1306\":1421,\"_1326\":1404,\"_1302\":1432},{\"_11\":1419,\"_1308\":1422,\"_1294\":1424,\"_1314\":1425,\"_46\":1319,\"_1321\":35,\"_1312\":1428,\"_1325\":1044},{\"_1310\":9,\"_1312\":1423},{},1739463467.670899,{\"_1316\":542,\"_1317\":1426},[1427],\"我简化一下问题，如果输入不是表达式字符串，而是已经切分好的token数组，如 [\\\"x1\\\", \\\"\u0026\\\", \\\"(\\\", \\\"x2\\\", \\\"|\\\", \\\"!\\\", \\\"x3\\\", \\\")\\\"] ，重新实现一下这个函数\",{\"_1338\":1429,\"_1342\":1431,\"_1344\":-5,\"_1345\":1346,\"_1347\":-5,\"_1324\":1288},{\"_1340\":1430},[],\"9116216e1c010fdb-IAD\",[1433],\"511d6fb9-6d30-4c33-b884-0c944373e301\",{\"_11\":1433,\"_1306\":1435,\"_1326\":1419,\"_1302\":1447},{\"_11\":1433,\"_1308\":1436,\"_1294\":1438,\"_1314\":1439,\"_46\":1319,\"_1320\":70,\"_1321\":35,\"_1312\":1442,\"_1325\":1044},{\"_1310\":1353,\"_1312\":1437},{},1739463533.09751,{\"_1316\":542,\"_1317\":1440},[1441],\"好的，如果输入是一个已经切分好的 token 数组，那么问题就变得更简单了，我们可以直接基于这些 token 逐步构建二叉树，而不需要解析原始字符串。\\n\\n### 关键点：\\n1. **使用栈**：由于我们需要处理优先级和括号的结构，栈可以帮助我们管理运算符和操作数。\\n2. **递归解析**：递归会处理括号内的子表达式，并根据优先级构建相应的二叉树。\\n\\n### 代码实现\\n\\n```java\\nimport java.util.*;\\n\\npublic class BooleanExpressionParser {\\n\\n static class TreeNode {\\n String value;\\n TreeNode left;\\n TreeNode right;\\n\\n TreeNode(String value) {\\n this.value = value;\\n this.left = null;\\n this.right = null;\\n }\\n }\\n\\n // 解析切分好的token数组，返回二叉树\\n public static TreeNode parse(List\u003cString\u003e tokens) {\\n Stack\u003cTreeNode\u003e operands = new Stack\u003c\u003e(); // 操作数栈\\n Stack\u003cString\u003e operators = new Stack\u003c\u003e(); // 运算符栈\\n\\n int index = 0;\\n while (index \u003c tokens.size()) {\\n String token = tokens.get(index);\\n\\n if (token.equals(\\\"(\\\")) {\\n // 递归解析括号内的表达式\\n operators.push(token);\\n } else if (token.equals(\\\")\\\")) {\\n // 遇到右括号，开始构建树\\n while (!operators.peek().equals(\\\"(\\\")) {\\n processOperator(operands, operators.pop());\\n }\\n operators.pop(); // 移除 '('\\n } else if (token.equals(\\\"!\\\") || token.equals(\\\"\u0026\\\") || token.equals(\\\"|\\\")) {\\n // 操作符，处理运算符优先级\\n while (!operators.isEmpty() \u0026\u0026 precedence(operators.peek()) \u003e= precedence(token)) {\\n processOperator(operands, operators.pop());\\n }\\n operators.push(token);\\n } else {\\n // 变量，直接入栈\\n operands.push(new TreeNode(token));\\n }\\n index++;\\n }\\n\\n // 处理剩余的操作符\\n while (!operators.isEmpty()) {\\n processOperator(operands, operators.pop());\\n }\\n\\n return operands.isEmpty() ? null : operands.pop();\\n }\\n\\n // 处理栈顶的运算符\\n private static void processOperator(Stack\u003cTreeNode\u003e operands, String operator) {\\n TreeNode node = new TreeNode(operator);\\n\\n // 对于 '!' 操作符，只有右子树\\n if (operator.equals(\\\"!\\\")) {\\n node.right = operands.pop();\\n } else {\\n node.right = operands.pop();\\n node.left = operands.pop();\\n }\\n\\n operands.push(node);\\n }\\n\\n // 运算符的优先级：'!' \u003e '\u0026' \u003e '|'\\n private static int precedence(String operator) {\\n if (operator.equals(\\\"!\\\")) {\\n return 3;\\n } else if (operator.equals(\\\"\u0026\\\")) {\\n return 2;\\n } else if (operator.equals(\\\"|\\\")) {\\n return 1;\\n }\\n return 0;\\n }\\n\\n // 打印二叉树，用于测试\\n public static void printTree(TreeNode node, String indent) {\\n if (node != null) {\\n System.out.println(indent + node.value);\\n printTree(node.left, indent + \\\" \\\");\\n printTree(node.right, indent + \\\" \\\");\\n }\\n }\\n\\n // 测试\\n public static void main(String[] args) {\\n // 输入是一个已经切分好的token数组\\n List\u003cString\u003e tokens = Arrays.asList(\\\"x1\\\", \\\"\u0026\\\", \\\"(\\\", \\\"x2\\\", \\\"|\\\", \\\"!\\\", \\\"x3\\\", \\\")\\\");\\n TreeNode root = parse(tokens);\\n printTree(root, \\\"\\\");\\n }\\n}\\n```\\n\\n### 代码解析\\n\\n1. **parse**：接受已经切分好的 token 列表，然后逐步解析这些 token。\\n - 使用两个栈：`operands` 用于存储操作数（布尔变量或子表达式），`operators` 用于存储操作符。\\n - 遇到左括号 `(` 时，将其压入 `operators` 栈中；遇到右括号 `)` 时，弹出操作符并处理，直到遇到左括号。\\n - 遇到操作符时，比较当前操作符与栈顶操作符的优先级，如果当前操作符优先级更低，则先处理栈中的操作符。\\n - 遇到布尔变量时，直接创建一个树节点并压入 `operands` 栈中。\\n\\n2. **processOperator**：这个方法用于从 `operands` 栈中弹出两个操作数，并根据操作符创建新的树节点，然后将新节点压入 `operands` 栈中。如果是 `!` 操作符，只处理右子树；如果是 `\u0026` 或 `|`，则处理左右子树。\\n\\n3. **precedence**：这是一个简单的优先级比较方法，用于决定操作符的优先级。`!` 的优先级最高，其次是 `\u0026`，最后是 `|`。\\n\\n4. **printTree**：打印二叉树，用于验证构建出来的树结构是否正确。\\n\\n### 测试\\n\\n对于输入的 tokens 列表 `[\\\"x1\\\", \\\"\u0026\\\", \\\"(\\\", \\\"x2\\\", \\\"|\\\", \\\"!\\\", \\\"x3\\\", \\\")\\\"]`，程序会输出以下二叉树：\\n\\n```\\n\u0026\\n x1\\n |\\n x2\\n !\\n x3\\n```\\n\\n### 总结\\n\\n这个实现方法利用了栈和优先级来处理运算符，确保正确处理操作符的优先级，并通过栈将表达式转换为二叉树。由于输入已经是切分好的 token 数组，这使得处理更加直接，避免了复杂的字符串解析操作。\",{\"_1377\":1443,\"_1384\":70,\"_1385\":1445,\"_1387\":1446,\"_1347\":-5,\"_1360\":1361,\"_1362\":1363,\"_1364\":1419,\"_1342\":1431,\"_1345\":1346,\"_1324\":1288},{\"_1291\":1379,\"_1380\":1444},[1382,1383],[],[],[],\"moderation_results\",[],\"current_node\",\"conversation_id\",\"is_archived\",\"safe_urls\",[],\"disabled_tool_ids\",[],\"is_public\",\"linear_conversation\",[1460,1462,1470,1480,1487,1499,1509,1521,1531],{\"_11\":1300,\"_1302\":1461},[1304],{\"_11\":1304,\"_1306\":1463,\"_1326\":1300,\"_1302\":1469},{\"_11\":1304,\"_1308\":1464,\"_1314\":1466,\"_46\":1319,\"_1320\":70,\"_1321\":40,\"_1312\":1468,\"_1325\":1044},{\"_1310\":1311,\"_1312\":1465},{},{\"_1316\":542,\"_1317\":1467},[617],{\"_1323\":70,\"_1324\":1288},[1328],{\"_11\":1328,\"_1306\":1471,\"_1326\":1304,\"_1302\":1479},{\"_11\":1328,\"_1308\":1472,\"_1294\":1333,\"_1314\":1474,\"_46\":1319,\"_1321\":35,\"_1312\":1476,\"_1325\":1044},{\"_1310\":9,\"_1312\":1473},{},{\"_1316\":542,\"_1317\":1475},[1336],{\"_1338\":1477,\"_1342\":1343,\"_1344\":-5,\"_1345\":1346,\"_1347\":-5,\"_1324\":1288},{\"_1340\":1478},[],[1349],{\"_11\":1349,\"_1306\":1481,\"_1326\":1328,\"_1302\":1486},{\"_11\":1349,\"_1308\":1482,\"_1294\":1355,\"_1314\":1484,\"_46\":1319,\"_1321\":35,\"_1312\":1485,\"_1325\":1044},{\"_1310\":1353,\"_1312\":1483},{},{\"_1316\":1357,\"_1358\":617},{\"_1347\":-5,\"_1360\":1361,\"_1362\":1363,\"_1364\":1328,\"_1342\":1343,\"_1345\":1346,\"_1324\":1288,\"_1365\":70},[1367],{\"_11\":1367,\"_1306\":1488,\"_1326\":1349,\"_1302\":1498},{\"_11\":1367,\"_1308\":1489,\"_1294\":1372,\"_1314\":1491,\"_46\":1319,\"_1320\":70,\"_1321\":35,\"_1312\":1493,\"_1325\":1044},{\"_1310\":1353,\"_1312\":1490},{},{\"_1316\":542,\"_1317\":1492},[1375],{\"_1377\":1494,\"_1384\":70,\"_1385\":1496,\"_1387\":1497,\"_1347\":-5,\"_1360\":1361,\"_1362\":1363,\"_1364\":1349,\"_1342\":1343,\"_1345\":1346,\"_1324\":1288},{\"_1291\":1379,\"_1380\":1495},[1382,1383],[],[],[1390],{\"_11\":1390,\"_1306\":1500,\"_1326\":1367,\"_1302\":1508},{\"_11\":1390,\"_1308\":1501,\"_1294\":1395,\"_1314\":1503,\"_46\":1319,\"_1321\":35,\"_1312\":1505,\"_1325\":1044},{\"_1310\":9,\"_1312\":1502},{},{\"_1316\":542,\"_1317\":1504},[1398],{\"_1338\":1506,\"_1342\":1402,\"_1344\":-5,\"_1345\":1346,\"_1347\":-5,\"_1324\":1288},{\"_1340\":1507},[],[1404],{\"_11\":1404,\"_1306\":1510,\"_1326\":1390,\"_1302\":1520},{\"_11\":1404,\"_1308\":1511,\"_1294\":1409,\"_1314\":1513,\"_46\":1319,\"_1320\":70,\"_1321\":35,\"_1312\":1515,\"_1325\":1044},{\"_1310\":1353,\"_1312\":1512},{},{\"_1316\":542,\"_1317\":1514},[1412],{\"_1377\":1516,\"_1384\":70,\"_1385\":1518,\"_1387\":1519,\"_1347\":-5,\"_1360\":1361,\"_1362\":1363,\"_1364\":1390,\"_1342\":1402,\"_1345\":1346,\"_1324\":1288},{\"_1291\":1379,\"_1380\":1517},[1382,1383],[],[],[1419],{\"_11\":1419,\"_1306\":1522,\"_1326\":1404,\"_1302\":1530},{\"_11\":1419,\"_1308\":1523,\"_1294\":1424,\"_1314\":1525,\"_46\":1319,\"_1321\":35,\"_1312\":1527,\"_1325\":1044},{\"_1310\":9,\"_1312\":1524},{},{\"_1316\":542,\"_1317\":1526},[1427],{\"_1338\":1528,\"_1342\":1431,\"_1344\":-5,\"_1345\":1346,\"_1347\":-5,\"_1324\":1288},{\"_1340\":1529},[],[1433],{\"_11\":1433,\"_1306\":1532,\"_1326\":1419,\"_1302\":1542},{\"_11\":1433,\"_1308\":1533,\"_1294\":1438,\"_1314\":1535,\"_46\":1319,\"_1320\":70,\"_1321\":35,\"_1312\":1537,\"_1325\":1044},{\"_1310\":1353,\"_1312\":1534},{},{\"_1316\":542,\"_1317\":1536},[1441],{\"_1377\":1538,\"_1384\":70,\"_1385\":1540,\"_1387\":1541,\"_1347\":-5,\"_1360\":1361,\"_1362\":1363,\"_1364\":1419,\"_1342\":1431,\"_1345\":1346,\"_1324\":1288},{\"_1291\":1379,\"_1380\":1539},[1382,1383],[],[],[],\"has_user_editable_context\",\"continue_conversation_url\",\"https://chatgpt.com/share/67ae2667-adf4-8002-b72c-40c0f01d749e/continue\",\"model\",{\"_1548\":1361,\"_1549\":1550,\"_538\":1551,\"_1552\":1553,\"_1554\":1555},\"slug\",\"max_tokens\",128000,\"GPT-4o\",\"description\",\"Newest 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