fix diff-array cheatsheet, progress

Author: yennanliu

data/progress.txt

@@ -1,3 +1,4 @@
+20241202: 370(todo),1109(todo)
 20241130: 34,767
 20241126: 722,380
 20241125: 33,81

doc/cheatsheet/difference_array.md

@@ -1,14 +1,182 @@
 # Difference Array 
 
+- The main applicable scenario is to frequently query the cumulative sum of a certain interval when the original array will not be modified
+
 ## 0) Concept
-- [fucking algorithm - Difference Array](https://labuladong.gitee.io/algo/2/18/22/)
+- [fucking algorithm - Difference Array](https://labuladong.online/algo/data-structure/diff-array/)
 
 ### 0-1) Types
+	- LC 1109
+	- LC 370
+	- LC 1094
 
 ### 0-2) Pattern
 
+```java
+
+// java
+// https://labuladong.online/algo/data-structure/diff-array/
+
+class PrefixSum {
+    // 前缀和数组
+    private int[] preSum;
+
+    // 输入一个数组，构造前缀和
+    public PrefixSum(int[] nums) {
+        // preSum[0] = 0，便于计算累加和
+        preSum = new int[nums.length + 1];
+        // 计算 nums 的累加和
+        for (int i = 1; i < preSum.length; i++) {
+            preSum[i] = preSum[i - 1] + nums[i - 1];
+        }
+    }
+    
+    // 查询闭区间 [left, right] 的累加和
+    public int sumRange(int left, int right) {
+        return preSum[right + 1] - preSum[left];
+    }
+}
+```
+
 ## 1) General form
 
+```java
+
+// java
+// https://labuladong.online/algo/data-structure/diff-array/
+
+// 差分数组工具类
+class Difference {
+    // 差分数组
+    private int[] diff;
+    
+    // 输入一个初始数组，区间操作将在这个数组上进行
+    public Difference(int[] nums) {
+        assert nums.length > 0;
+        diff = new int[nums.length];
+        // 根据初始数组构造差分数组
+        diff[0] = nums[0];
+        for (int i = 1; i < nums.length; i++) {
+            diff[i] = nums[i] - nums[i - 1];
+        }
+    }
+
+    // 给闭区间 [i, j] 增加 val（可以是负数）
+    public void increment(int i, int j, int val) {
+        diff[i] += val;
+        if (j + 1 < diff.length) {
+            diff[j + 1] -= val;
+        }
+    }
+
+    // 返回结果数组
+    public int[] result() {
+        int[] res = new int[diff.length];
+        // 根据差分数组构造结果数组
+        res[0] = diff[0];
+        for (int i = 1; i < diff.length; i++) {
+            res[i] = res[i - 1] + diff[i];
+        }
+        return res;
+    }
+}
+```
+
 ### 1-1) Basic OP
 
 ## 2) LC Example
+
+## Range Addition
+
+```java
+// java
+// LC 370 
+class Solution {
+    public int[] getModifiedArray(int length, int[][] updates) {
+        // nums 初始化为全 0
+        int[] nums = new int[length];
+        // 构造差分解法
+        Difference df = new Difference(nums);
+        
+        for (int[] update : updates) {
+            int i = update[0];
+            int j = update[1];
+            int val = update[2];
+            df.increment(i, j, val);
+        }
+        
+        return df.result();
+    }
+}
+```
+
+### Corporate Flight Bookings
+
+```java
+// java
+// LC 1109
+
+class Solution {
+    public int[] corpFlightBookings(int[][] bookings, int n) {
+        // nums 初始化为全 0
+        int[] nums = new int[n];
+        // 构造差分解法
+        Difference df = new Difference(nums);
+
+        for (int[] booking : bookings) {
+            // 注意转成数组索引要减一哦
+            int i = booking[0] - 1;
+            int j = booking[1] - 1;
+            int val = booking[2];
+            // 对区间 nums[i..j] 增加 val
+            df.increment(i, j, val);
+        }
+        // 返回最终的结果数组
+        return df.result();
+    }
+}
+```
+
+
+### Car Pooling
+
+```java
+// java
+// LC 1094
+// https://leetcode.com/problems/car-pooling/description/
+
+class Solution {
+    public boolean carPooling(int[][] trips, int capacity) {
+        // 最多有 1001 个车站
+        int[] nums = new int[1001];
+
+        // 构造差分解法
+        Difference df = new Difference(nums);
+
+        for (int[] trip : trips) {
+            // 乘客数量
+            int val = trip[0];
+
+            // 第 trip[1] 站乘客上车
+            int i = trip[1];
+
+            // 第 trip[2] 站乘客已经下车，
+            // 即乘客在车上的区间是 [trip[1], trip[2] - 1]
+            int j = trip[2] - 1;
+
+            // 进行区间操作
+            df.increment(i, j, val);
+        }
+
+        int[] res = df.result();
+
+        // 客车自始至终都不应该超载
+        for (int i = 0; i < res.length; i++) {
+            if (capacity < res[i]) {
+                return false;
+            }
+        }
+        return true;
+    }
+}
+```