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

思路：二维前缀和，查询时可以把区域划分为四块， O ( n m ) O(nm) O(nm)初始化， O ( 1 ) O(1) O(1)查询。

class NumMatrix {
public:
    vector<vector<int>> sum;
    NumMatrix(vector<vector<int>>& matrix) {
        int n=matrix.size();
        if(!n)
            return;
        int m=matrix[0].size();
        vector<vector<int>> tmp_sum(n+1,vector<int>(m+1));
        for(int i=1;i<=n;i++)
        {
            tmp_sum[i][1]=matrix[i-1][0];
            for(int j=2;j<=m;j++)
                tmp_sum[i][j]=tmp_sum[i][j-1]+matrix[i-1][j-1];
            for(int j=1;j<=m;j++)
                tmp_sum[i][j]+=tmp_sum[i-1][j];
        }
        sum=move(tmp_sum);
    }
    
    int sumRegion(int row1, int col1, int row2, int col2) {
        return sum[row2+1][col2+1]-sum[row1][col2+1]-sum[row2+1][col1]+sum[row1][col1];
    }
};

/**
 * Your NumMatrix object will be instantiated and called as such:
 * NumMatrix* obj = new NumMatrix(matrix);
 * int param_1 = obj->sumRegion(row1,col1,row2,col2);
 */