二维矩阵上的树状数组

例题 https://leetcode-cn.com/problems/range-sum-query-2d-mutable/

一般的树状数组tree[i]记录的是以i为右端点，长度为lowbit(i)的区间和，实现单点修改区间查询。
树状数组也可以实现矩阵上的单点修改区间查询

    int lowbit(int x) {
        return x & -x;
    }

    void modify(int x0, int y0, int val) {
        for (int x = x0; x <= n; x += lowbit(x)) {
            for (int y = y0; y <= n; y += lowbit(y)) {
                tree[x][y] += val;
            }
        }
    }

    long query(int row, int col) {
        long ret = 0;
        for (int x = row; x > 0; x -= lowbit(x)) {
            for (int y = col; y > 0; y -= lowbit(y)) {
                ret += tree[x][y];
            }
        }

        return ret;
    }