[leetcode] 308. Range Sum Query 2D - Mutable 解题报告

题目链接: https://leetcode.com/problems/range-sum-query-2d-mutable/

Given a 2D matrix matrix, find the sum of the elements inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2).

The above rectangle (with the red border) is defined by (row1, col1) = (2, 1) and (row2, col2) = (4, 3), which contains sum = 8.

Example:

Given matrix = [
  [3, 0, 1, 4, 2],
  [5, 6, 3, 2, 1],
  [1, 2, 0, 1, 5],
  [4, 1, 0, 1, 7],
  [1, 0, 3, 0, 5]
]

sumRegion(2, 1, 4, 3) -> 8
update(3, 2, 2)
sumRegion(2, 1, 4, 3) -> 10

Note:

1. The matrix is only modifiable by the update function.
2. You may assume the number of calls to update and sumRegion function is distributed evenly.
3. You may assume that row1 ≤ row2 and col1 ≤ col2.

思路: 按照直接的求前n项和的思路来做这道题也可以过, 但是显然这道题期望的并不是这样的答案. 期望的应该是二叉索引树, 在另一篇博客我已经很详细的讲了. 这里就不再重复讲二叉索引树的原理了.

代码如下:

class NumMatrix {
public:
    void add(int val, int x, int y)
    {
        while(y < sum[x].size())
        {
            sum[x][y] += val;
            y += (y&-y);
        }
    }
    
    int getSum(int x, int y)
    {
        int ans = 0;
        while(y > 0)
        {
            ans += sum[x][y];
            y -= (y&-y);
        }
        return ans;
    }

    NumMatrix(vector<vector<int>> &matrix):vec(matrix) {
        if(matrix.size()==0) return;
        int m = matrix.size(), n = matrix[0].size();
        sum.resize(m, vector<int>(n+1, 0));
        for(int i =0; i < m; i++)
            for(int j =1; j <= n; j++)
                add(matrix[i][j-1], i, j);
    }

    void update(int row, int col, int val) {
        int d = val - vec[row][col];
        vec[row][col] = val;
        add(d, row, col+1);
    }

    int sumRegion(int row1, int col1, int row2, int col2) {
        int ans = 0;
        for(int i = row1; i <= row2; i++)
            ans += (getSum(i, col2+1) - getSum(i, col1));
        return ans;
    }
private:
    vector<vector<int>> sum;
    vector<vector<int>> &vec;
};


// Your NumMatrix object will be instantiated and called as such:
// NumMatrix numMatrix(matrix);
// numMatrix.sumRegion(0, 1, 2, 3);
// numMatrix.update(1, 1, 10);
// numMatrix.sumRegion(1, 2, 3, 4);