LeetCode-304. Range Sum Query 2D - Immutable

Description:

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

和这个题型的第一题一样，只不过一维变成二维了，但是思路是一样的。先算出结果，避免重复计算。在算结果的时候也可以利用已经算好的结果来优化。sum[i][j]表示matrix[i][j]到matrix[0][0]的和，则一般的(i1, j1)到(i2, j2)的和为sum[i2][j2] - sum[i1-1][j2] - sum[i2][j1-1] + sum[i1-1][j1-1];边界(0,0)(0,x),(x,0)特殊考虑。在计算优化时也类似。

实现代码：

public class NumMatrix {

   /* 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]
]
*/
    private int[][] matrix;

    private int[][] sum;

    public NumMatrix(int[][] matrix) {
        if(matrix == null)
            this.matrix = new int[0][0];
        else
            this.matrix = matrix;
        if(this.matrix.length == 0)
            sum = new int[0][0];
        else
            sum = new int[this.matrix.length][this.matrix[0].length];
        //边界
        if(sum.length !=0 && sum[0].length != 0) {
            sum[0][0] = this.matrix[0][0];
            for(int i=1; i<sum.length; i++) {
                sum[i][0] = this.matrix[i][0] + sum[i-1][0];
            }

            for(int j=1; j<sum[0].length; j++) {
                sum[0][j] = this.matrix[0][j] + sum[0][j-1];
            }
        }
        //计算sum
        for(int i=1; i<sum.length; i++) {
            for(int j=1; j<sum[i].length; j++) {
                sum[i][j] = this.matrix[i][j] + sum[i-1][j] + sum[i][j-1] - sum[i-1][j-1];
                //System.out.println("("+i+","+j+"):"+sum[i][j]);
            }

        }

    }

    public int sumRegion(int row1, int col1, int row2, int col2) {
        if(row1 == 0 && col1 == 0)
            return sum[row2][col2];
        else if(row1 == 0 && col1 != 0)
            return sum[row2][col2] - sum[row2][col1-1];
        else if(row1 != 0 && col1 == 0)
            return sum[row2][col2] - sum[row1-1][col2];
        else
        　　return sum[row2][col2] - sum[row1-1][col2] - sum[row2][col1-1] + sum[row1-1][col1-1];
    }

}

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