[LeetCode] Range Sum Query 2D - Immutable

Very similar to Range Sum Query - Immutable, but we now need to compute a 2d accunulated-sum. In fact, if you work in computer vision, you may know a name for such an array --- Integral Image.

To solve this problem, Stefan has already posted a very elegant solution.

The code is copied here.

class NumMatrix {
public:
    NumMatrix(vector<vector<int>> &matrix) {
        accu = matrix;
        for (int i = 0; i < matrix.size(); i++)
            for (int j = 0; j < matrix[0].size(); j++)
                accu[i][j] += a(i-1, j) + a(i, j-1) - a(i-1, j-1);
    }

    int sumRegion(int row1, int col1, int row2, int col2) {
        return a(row2, col2) - a(row1-1, col2) - a(row2, col1-1) + a(row1-1, col1-1);
    }
private:
    vector<vector<int>> accu;
    int a(int i, int j) {
        return i >= 0 && j >= 0 ? accu[i][j] : 0;
    }
};


// Your NumMatrix object will be instantiated and called as such:
// NumMatrix numMatrix(matrix);
// numMatrix.sumRegion(0, 1, 2, 3);
// numMatrix.sumRegion(1, 2, 3, 4);