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本节结尾的正确性证明中,

使用反证法,只分析 n >= 3 的情况。

这句是否应该改为 “只分析 n >= 4 的情况”,因为 n == 3 时,由于题目要求至少将 n 切分为两个正整数,所以此时应该切分为 1 * 2 ,切分方案里是包含 1 的 😁;

此外,对于这句描述:

假设最优切分方案中存在 >= 4 的因子 x ,那么一定可以将其继续划分为 2(x-2) ,从而获得更大的乘积。

最后半句改为“从而获得更大或可替代的乘积”是否更好,因为当切分方案中存在 4 作为因子时,将其划分为 2 * 2,乘积相对划分前是相等的。不过这处改动不影响“所有因子 <= 3” 的结论,因为因子 4 是可以被替代的。

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本节结尾的正确性证明中,

"使用反证法,只分析 n >= 3 的情况。"

这句是否应该改为 “只分析 n >= 4 的情况”,因为 n == 3 时,由于题目要求至少将 n 切分为两个正整数,所以此时应该切分为 1 * 2 ,切分方案里是包含 1 的 😁;
此外,对于这句描述:

“假设最优切分方案中存在 >= 4 的因子 x ,那么一定可以将其继续划分为 2(x-2) ,从而获得更大的乘积。”

最后半句改为“从而获得更大或可替代的乘积”是否更好,因为当切分方案中存在 4 作为因子时,将其划分为 2 * 2,乘积相对划分前是相等的。不过这处改动不影响“所有因子 <= 3” 的结论,因为因子 4 是可以被替代的。
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