304. Range Sum Query 2D

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
sumRegion(1, 1, 2, 2) -> 11
sumRegion(1, 2, 2, 4) -> 12

Note:

1. You may assume that the matrix does not change.
2. There are many calls to sumRegion function.
3. You may assume that row1 ≤ row2 and col1 ≤ col2.

 本题比较简单，有一个难点就是，做二维和数组的时候，可以做出长度+1的二维数组，这样就不用考虑0的情况了，代码如下：

public class NumMatrix {
    int[][] sum;
    public NumMatrix(int[][] matrix) {
        if(matrix==null||matrix.length==0||matrix[0].length==0) return;
        sum = new int[matrix.length+1][matrix[0].length+1];
        for(int i=0;i<matrix.length;i++){
            for(int j=0;j<matrix[0].length;j++){
                sum[i+1][j+1] = sum[i+1][j]+sum[i][j+1]-sum[i][j]+matrix[i][j];
            }
        }
    }
    
    public int sumRegion(int row1, int col1, int row2, int col2) {
        return sum[row2+1][col2+1]-sum[row1][col2+1]-sum[row2+1][col1]+sum[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);
 */