先求前缀和数组，再根据四个角坐标计算矩形内元素的和。

class NumMatrix {
private:
    int sums[210][210];

public:
    NumMatrix(vector<vector<int>>& matrix) {
        if　(matrix.size() == 0 || matrix[0].size() == 0) return;

        for (int i = 0; i < matrix.size(); ++ i)
            for (int j = 0; j < matrix[0].size(); ++ j)
                sums[i + 1][j + 1] = matrix[i][j] - sums[i][j] + sums[i + 1][j] + sums[i][j + 1];
    }

    int sumRegion(int row1, int col1, int row2, int col2) {
        return sums[row2 + 1][col2 + 1] - sums[row2 + 1][col1] - sums[row1][col2 + 1] + sums[row1][col1];
    }
};