算法精粹(algorithm-essentials)

感谢soulmachine@github提供内容
## Search a 2D Matrix


### 描述

Write an efficient algorithm that searches for a value in an `m × 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.


### 分析

二分查找。


### 代码

{% if book.java %}
{% codesnippet "./code/search-a-2d-matrix."+book.suffix, language=book.suffix %}{% endcodesnippet %}
{% endif %}

{% if book.cpp %}
```cpp
// Search a 2D Matrix
// 时间复杂度O(logn),空间复杂度O(1)
class Solution {
public:
bool searchMatrix(const vector>& matrix, int target) {
if (matrix.empty()) return false;
const size_t m = matrix.size();
const size_t n = matrix.front().size();

int first = 0;
int last = m * n;

while (first < last) {
int mid = first + (last - first) / 2;
int value = matrix[mid / n][mid % n];

if (value == target)
return true;
else if (value < target)
first = mid + 1;
else
last = mid;
}

return false;
}
};
```
{% endif %}


### 相关题目

* [Search a 2D Matrix II](search-a-2d-matrix-ii.md)