算法精粹(algorithm-essentials)

感谢soulmachine@github提供内容
## First Missing Positive


### 描述

Given an unsorted integer array, find the first missing positive integer.

For example,
Given `[1,2,0]` return `3`,
and `[3,4,-1,1]` return `2`.

Your algorithm should run in `O(n)` time and uses constant space.


### 分析

本质上是桶排序(bucket sort),每当 `A[i]!= i+1` 的时候,将`A[i]`与`A[A[i]-1]`交换,直到无法交换为止,终止条件是 `A[i]== A[A[i]-1]`。


### 代码

{% if book.java %}
{% codesnippet "./code/first-missing-positive."+book.suffix, language=book.suffix %}{% endcodesnippet %}
{% endif %}

{% if book.cpp %}
```cpp
// First Missing Positive
// 时间复杂度O(n),空间复杂度O(1)
class Solution {
public:
int firstMissingPositive(vector& nums) {
bucket_sort(nums);

for (int i = 0; i < nums.size(); ++i)
if (nums[i] != (i + 1))
return i + 1;
return nums.size() + 1;
}
private:
static void bucket_sort(vector& A) {
const int n = A.size();
for (int i = 0; i < n; i++) {
while (A[i] != i + 1) {
if (A[i] <= 0 || A[i] > n || A[i] == A[A[i] - 1])
break;
swap(A[i], A[A[i] - 1]);
}
}
}
};
```
{% endif %}


### 相关题目

* [Sort Colors](../quick-sort/sort-colors.md)