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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. 如果直接对矩阵元素进行二分查找的话,时间复杂度是O(m*n),其实很容易想到先通过查找找到对应可能存在于哪一行,然后再在那行中查找是否存在,采用最简单的直接查找这样时间复杂度仅有O(m+n),如果这两次查找再分别采用二分查找的话,时间复杂度更可以降低到O(logm+logn),下面是O(m+n)的代码: class Solution {
public:
bool searchMatrix(vector
> &matrix, int target) {
if(matrix.empty())
return false;
int m = matrix.size();
int n = matrix[0].size();
int i = 0, j=0;
while(i
=matrix[i][0]) i++; i--; if(i==-1) return false; while(j
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