[leetcode]Search a 2D Matrix

Search a 2D Matrix

Write an efficient algorithm that searches for a value in an m x n matrix. This matrix has the following properties:

 

• Integers in each row are sorted from left to right.
• The first integer of each row is greater than the last integer of the previous row.

 

For example,

Consider the following matrix:

[
  [1,   3,  5,  7],
  [10, 11, 16, 20],
  [23, 30, 34, 50]
]

Given target = 3, return true.

算法思路：

本题肯定要用二分查找的，如果是一维数组就完美了，可惜是二维，不过没关系，可以将二维数组抽象成一维。继续按照一维来操作。

代码如下：

public class Solution {
    public boolean searchMatrix(int[][] matrix, int target) {
        if(matrix == null || matrix.length == 0 || matrix[0].length == 0) return false;
        int height = matrix.length;
        int width = matrix[0].length;
        int begin = 0, end = height * width - 1;
        while(begin <= end){
            int mid = (begin + end) >> 1;
            int i = mid / width;
            int j = mid % width;
            if(matrix[i][j] == target){
                return true;
            }else if(matrix[i][j] < target){
                begin = mid + 1;
            }else{
                end = mid - 1;
            }
        }
        return false;        
    }
}