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.

 

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题目标签：Array

　　题目给了我们一个有序的矩阵，让我们找target是否在矩阵中。首先我们分析，如果我们知道了target 在哪一行的话，直接用binary search 就可以了。所以第一步可以用binary search 来搜索第一列，确认target在哪一行。在用一次二分法对于那一行，找出target。

 

 

 

Java Solution:

Runtime beats 71.85% 

完成日期：07/23/2017

关键词：Array

关键点：用二分法两次

 

 

1 public class Solution  2 { 3     public boolean searchMatrix(int[][] matrix, int target)  4     { 5         if(matrix.length == 0 || matrix[0].length == 0) 6             return false; 7         if(target < matrix[0][0] || target > matrix[matrix.length-1][matrix[0].length-1]) 8             return false; 9         // first determine which row the target is in10         int top = 0;11         int bottom = matrix.length-1;12         13         while(top <= bottom)14         {15             int mid = top + (bottom - top) / 2;16             17             if(matrix[mid][0] == target)18                 return true;19             else if(matrix[mid][0] > target)20                 bottom = mid - 1;21             else22                 top = mid + 1;23         }24         25         int rowNum = bottom;26         27         // use binary search for this row28         int left = 0;29         int right = matrix[0].length-1;30         31         while(left <= right)32         {33             int mid = left + (right - left) / 2;34             35             if(matrix[rowNum][mid] == target)36                 return true;37             else if(matrix[rowNum][mid] < target)38                 left = mid + 1;39             else40                 right = mid - 1;41             42         }43     44         return false;45     }46 }

参考资料：

http://www.cnblogs.com/grandyang/p/4323301.html

 

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