0304-range-sum-query-2d-immutable.java

class NumMatrix {
    int[][] preSum;

    public NumMatrix(int[][] matrix) {
        int m = matrix.length;
        int n = matrix[0].length;
        preSum = new int[m + 1][n + 1];

        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                preSum[i + 1][j + 1] = preSum[i + 1][j] + preSum[i][j + 1] - preSum[i][j] + matrix[i][j]; 
            }
        }
    }
    
    public int sumRegion(int row1, int col1, int row2, int col2) {
        return preSum[row2 + 1][col2 + 1] - preSum[row2 + 1][col1] - preSum[row1][col2 + 1] + preSum[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);
 */