304. 二维区域和检索 - 矩阵不可变

class NumMatrix 
{
    vector<vector<int>> s;
public:
    NumMatrix(vector<vector<int>>& matrix) 
    {
        if(matrix.empty() || matrix[0].empty()) return;
        int m = matrix.size();
        int n = matrix[0].size();
        s = vector<vector<int>>(m + 1,vector<int>(n + 1,0));
        for(int i = 1;i <= m;i ++)
        {
            for(int j = 1;j <= n;j ++)
            {
                //根据表格分析可得
                //s[2,2] = s[1,2] + s[2,1] - s[1,1] + matrix[1,1];
                s[i][j] = s[i - 1][j] + s[i][j - 1] - s[i - 1][j - 1] + matrix[i - 1][j - 1];
            }
        }
    }
    
    //(x1,y1),(x2,y2)这一子矩阵中所有数的和：s[x2,y2] - s[x1 - 1,y2] - s[x2,y1 - 1] + s[x1 - 1,y1 - 1]
    //由于下标从1开始，所以横纵坐标都加上1
    int sumRegion(int row1, int col1, int row2, int col2) 
    {
        return s[row2 + 1][col2 + 1] - s[row2 + 1][col1] - s[row1][col2 + 1] + s[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);
 */