[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.

二分查找，时间复杂度O(logm)+O(logn)。

 1 class Solution {
 2 public:
 3     bool searchMatrix(vector<vector<int>>& matrix, int target) {
 4         if(matrix.size()==0 || matrix[0].size()==0) return false;
 5         int m=matrix.size(),n=matrix[0].size();
 6         int left=0,right=m-1;
 7         while(left<=right)
 8         {
 9             int mid = (left+right)/2;
10             if(matrix[mid][0]==target) return true;
11             else if(matrix[mid][0]<target)
12             {
13                 left = mid+1;
14             }
15             else
16             {
17                 right = mid-1;
18             }
19         }
20         int pos = right;
21         if(pos<0) return false;
22         left=0;
23         right = n-1;
24         while(left<=right)
25         {
26             int mid = (left+right)/2;
27             if(matrix[pos][mid]==target) return true;
28             else if(matrix[pos][mid]<target)
29             {
30                 left = mid+1;
31             }
32             else
33             {
34                 right = mid-1;
35             }
36         }
37         return false;
38     }
39 };

这题也可以从右上角遍历，时间复杂度O(m)+O(n)。

 1 class Solution {
 2 public:
 3     bool searchMatrix(vector<vector<int>>& matrix, int target) {
 4         if(matrix.size()==0 || matrix[0].size()==0) return false;
 5         int m=matrix.size(),n=matrix[0].size();
 6         int row=0,col=n-1;
 7         while(row<m && col>=0)
 8         {
 9             if(matrix[row][col]==target) return true;
10             else if(matrix[row][col]<target) row++;
11             else col--;
12         }
13         return false;
14     }
15 };