next_permutation、prev_permutation以及is_permutation使用

next_permutation、prev_permutation以及is_permutation均爲全排列相關的函數，調用時需要加入頭文件#include <algorithm>

next_permutation

next_permutation的函數原型：

//default
template <class BidirectionalIterator>
	bool next_permutation (BidirectionalIterator first, BidirectionalIterator last);

//custom 
template <class BidirectionalIterator, class Compare>
	bool next_permutation (BidirectionalIterator first, BidirectionalIterator last, Compare comp);

next就是下一個的意思，其中文直譯過來就是下一個全排列，因此在使用next_permutation函數的時候切記要對全排列的對象進行升序排列，不然結果只會出現比當前排列大的排列，依據ASCII計算。
next_permutation(a, b)表示只對[a, b)區間的數據進行全排列，其餘位置不變化

#include <iostream>
#include <algorithm>
#include <vector>
using namespace std;
#define SORT

int main()
{
	vector<int> V = {3, 2, 1 };
#ifdef SORT
	sort(V.begin(), V.end());//sort
#endif
	do
	{
		for (int i = 0; i < V.size(); i++)
		{
			cout << V[i] << " ";
		}
		cout << endl;
	} while (next_permutation(V.begin(), V.end()));
	return 0;
}
//result
/*
#define SORT
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1
*/

/*
沒有進行sort排序
3 2 1
*/

prev_permutation

prev_permutation和next_permutation功能一樣，唯一的區別是next_permutation下一個全排列，而prev_permutation是上一個全排列，所以運用prev_permutation的時候必須降序排列，不然只會出現比結果小的排列

#include <iostream>
#include <algorithm>
#include <vector>
using namespace std;

//#define SORT
#define RSORT

int main()
{
	vector<int> V = {3, 4, 2, 1};
#ifdef SORT
	sort(V.begin(), V.end());
#else
	sort(V.rbegin(), V.rend());
#endif
	do
	{
		for (int i = 0; i < V.size(); i++)
		{
			cout << V[i] << " ";
		}
		cout << endl;
	} while (prev_permutation(V.begin() + 1, V.end() - 1));
	return 0;
}
//result
/*
#define RSORT
4 3 2 1
4 2 3 1
*/

/*
#define RSORT
1 2 3 4
*/

is_permutation

template <class ForwardIterator1, class ForwardIterator2>
   bool is_permutation (ForwardIterator1 first1, ForwardIterator1 last1,
                        ForwardIterator2 first2);
                        
template <class ForwardIterator1, class ForwardIterator2, class BinaryPredicate>
   bool is_permutation (ForwardIterator1 first1, ForwardIterator1 last1,
                        ForwardIterator2 first2, BinaryPredicate pred);

is_permutation用來判斷兩個全排列是否相等，哪怕順序不同，只要元素一樣就返回true

#include <iostream>
#include <algorithm>
#include <vector>
using namespace std;
int main()
{
	vector<int> V1 = { 3, 4, 2, 1 };
	vector<int> V2 = { 1, 3, 2, 4 };
	vector<int> V3 = { 1, 3, 2, 4, 1};
	vector<float> V4 = { 1.0, 3.0, 2.0, 4.0 };
	vector<float> V5 = { 1.0000001, 3.0, 2.0, 4.0 };
	if (is_permutation(V1.begin(), V1.end(), V2.begin()))
	{
		cout << "V1 and V2 is equal" << endl;
	}
	if (is_permutation(V1.begin(), V1.end(), V3.begin()))
	{
		cout << "V1 and V3 is equal" << endl;
	}
	if (is_permutation(V1.begin(), V1.end(), V4.begin()))
	{
		cout << "V1 and V4 is equal" << endl;
	}
	if (is_permutation(V1.begin(), V1.end(), V5.begin()))
	{
		cout << "V1 and V5 is equal" << endl;
	}
	return 0;
}

//result
/*
V1 and V2 is equal
V1 and V3 is equal
V1 and V4 is equal
*/

is_permutation單純的比較值的大小，但是需要注意的是序列1重複的必須在序列2中展現，也就是count sequence1[i] <= count sequence2[i]。