【中等】二维区域和检索-矩阵不可变

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