前缀和与差分：区间操作的利器

// 构建
int n = nums.length;
int[] prefix = new int[n + 1];
for (int i = 0; i < n; i++) {
    prefix[i + 1] = prefix[i] + nums[i];
}

// 查询 [l, r] 的和（0-indexed）
int rangeSum = prefix[r + 1] - prefix[l];

public int subarraySum(int[] nums, int k) {
    Map<Integer, Integer> count = new HashMap<>();
    count.put(0, 1);          // prefix = 0 出现 1 次
    int prefix = 0, ans = 0;
    for (int num : nums) {
        prefix += num;
        ans += count.getOrDefault(prefix - k, 0);
        count.merge(prefix, 1, Integer::sum);
    }
    return ans;
}

int[][] prefix = new int[m + 1][n + 1];
for (int i = 1; i <= m; i++) {
    for (int j = 1; j <= n; j++) {
        prefix[i][j] = matrix[i-1][j-1]
                     + prefix[i-1][j]
                     + prefix[i][j-1]
                     - prefix[i-1][j-1];
    }
}

int sum = prefix[r2+1][c2+1]
        - prefix[r1][c2+1]
        - prefix[r2+1][c1]
        + prefix[r1][c1];

int[] diff = new int[n + 1];

// 对 [l, r] 加 val
diff[l] += val;
diff[r + 1] -= val;

// 还原
int[] result = new int[n];
result[0] = diff[0];
for (int i = 1; i < n; i++) {
    result[i] = result[i - 1] + diff[i];
}

public int[] corpFlightBookings(int[][] bookings, int n) {
    int[] diff = new int[n + 1];
    for (int[] b : bookings) {
        diff[b[0] - 1] += b[2];
        diff[b[1]]     -= b[2];
    }
    int[] ans = new int[n];
    ans[0] = diff[0];
    for (int i = 1; i < n; i++) {
        ans[i] = ans[i - 1] + diff[i];
    }
    return ans;
}

int[] preXor = new int[n + 1];
for (int i = 0; i < n; i++) {
    preXor[i + 1] = preXor[i] ^ nums[i];
}
// 区间 [l, r] 异或
int xorLR = preXor[r + 1] ^ preXor[l];