308. Range Sum Query 2D - Mutable

Given a 2D matrix matrix, find the sum of the elements inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2).

The above rectangle (with the red border) is defined by (row1, col1) = (2, 1) and (row2, col2) = (4, 3), which contains sum = 8.

Example:

Given matrix = [
  [3, 0, 1, 4, 2],
  [5, 6, 3, 2, 1],
  [1, 2, 0, 1, 5],
  [4, 1, 0, 1, 7],
  [1, 0, 3, 0, 5]
]

sumRegion(2, 1, 4, 3) -> 8
update(3, 2, 2)
sumRegion(2, 1, 4, 3) -> 10

Note:

1. The matrix is only modifiable by the update function.
2. You may assume the number of calls to update and sumRegion function is distributed evenly.
3. You may assume that row1 ≤ row2 and col1 ≤ col2.

Solution:

We use int[][] colSum to store the prefix sum of each column.

colSum[i][j] denotes the sum of first i elements in column j.

To update an element, we find the corresponding column and update all the prefix sums that rely on this element.



Code:

public class NumMatrix {

    public int[][] colSum;
    public int[][] matrix;
    public NumMatrix(int[][] matrix) {
        this.matrix = matrix;
        if (matrix == null || matrix.length == 0) {
            return;
        }
        if (matrix[0] == null || matrix[0].length == 0) {
            return;
        }
        int m = matrix.length;
        int n = matrix[0].length;
        colSum = new int[m + 1][n];
        for (int i = 1; i <= m; i++) {
            for (int j = 0; j < n; j++) {
                colSum[i][j] = colSum[i - 1][j] + matrix[i - 1][j];
            }
        }
    }
    
    public void update(int row, int col, int val) {
        for (int i = row + 1; i < colSum.length; i++) {
            colSum[i][col] = colSum[i][col] - matrix[row][col] + val;
        }
        matrix[row][col] = val;
    }
    
    public int sumRegion(int row1, int col1, int row2, int col2) {
        int sum = 0;
        for (int j = col1; j <= col2; j++) {
            sum += colSum[row2 + 1][j] - colSum[row1][j]; 
        }
        return sum;
    }
}

/**
 * Your NumMatrix object will be instantiated and called as such:
 * NumMatrix obj = new NumMatrix(matrix);
 * obj.update(row,col,val);
 * int param_2 = obj.sumRegion(row1,col1,row2,col2);
 */