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.

 

Analyse: Binary Search!!!

Runtime: 16ms. 

 1 class Solution {
 2 public:
 3     bool searchMatrix(vector<vector<int>>& matrix, int target) {
 4         if(matrix.size() == 0) return false;
 5         
 6         int m = matrix.size(), n = matrix[0].size();
 7         int low = 0, high = m * n - 1;
 8         
 9         while(low <= high){
10             int mid = (low + high) / 2;
11             int val = matrix[mid / n][mid % n];
12             
13             if(val < target) low = mid + 1;
14             else if(val > target) high = mid - 1;
15             else return true;
16         }
17         return false;
18     }
19 };

 

posted @ 2015-07-24 10:47  amazingzoe  阅读(115)  评论(0)  编辑  收藏  举报