NumMatrix.cpp

class NumMatrix {
public:
    NumMatrix(vector<vector<int>>& matrix) {
        if (matrix.size() == 0 || matrix[0].size() == 0) return;
        dp = vector<vector<int>>(matrix.size() + 1,vector<int>(matrix[0].size()+1,0));
        for (int r = 0; r < matrix.size(); r++) {
            for (int c = 0; c < matrix[0].size(); c++) {
                dp[r + 1][c + 1] = dp[r + 1][c] + dp[r][c + 1] + matrix[r][c] - dp[r][c];
            }
        }
    }
    
    int sumRegion(int row1, int col1, int row2, int col2) {
        return dp[row2 + 1][col2 + 1] - dp[row1][col2 + 1] - dp[row2 + 1][col1] + dp[row1][col1];
    }
    
private:
    vector<vector<int>> dp;
};

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