算法：C++排列组合

题目：给定1-n数字，排列组合。

解法：递归。第一个数字有n种选择，第二个数字有n-1种选择，依次递归排列输出。用数组表示n个数字，用过的数字置0。

实现语言：C++

#include <iostream>
using namespace std;

/************************************************************************/
/*
	num : 需要排列的数组
	count : 数组总数
	numC： 已经排列的数组
	iUse：已经排列的个数
	iNull：置0的个数
	sum: 总排列数
*/
/************************************************************************/
template <class T>
void ComBineNum(T *num, const int count, T *numC, int iUse, int* sum)
{
	int iNull = 0;
	T *newNum = new T[count];
	for (int i = 0; i < count; ++i){
		memcpy(newNum, num, count);
		if (newNum[i] == 0){
			++iNull;
			if (iNull == count){
				for (int i = 0; i < count; ++i){
					cout << numC[i];
				}
				cout << endl;
				++(*sum);
				return;
			}
			continue;
		}
		numC[count - iUse] = newNum[i];
		newNum[i] = 0;
		ComBineNum(newNum, count, numC, iUse - 1, sum);
	}
	delete[] newNum;
}

int main()
{
	int sum = 0;
	const int count = 4;
	char num[count], pNum[count];
	for (int i = 0; i < count; ++i){
		num[i] = i + '1';
	}
	ComBineNum<char>(num, count, pNum, count, &sum);
	cout << "sum :" << sum << endl;

	sum = 1;
	for (int i = 1; i <= count; ++i){
		sum *= i;
	}
	cout << "sum :" << sum << endl;

	return 0;
}

输出：

template <class T>
void Swap(T& a, T& b)
{
	T c = a;
	a = b;
	b = c;
}

template <class T>
void Perm(T list[], int k, int m, int* count)
{
	if (k == m){
		for (int i = 0; i < m; ++ i){
			cout << list[i];
		}
		cout << endl;
		++(*count);
	}
	else{
		for (int i = k; i < m; ++i){
			Swap(list[k], list[i]);
			Perm(list, k + 1, m, count);
			Swap(list[i], list[k]);
		}
	}
}

int main()
{
	const int m = 4;
	int count = 0;
	int list[m];
	for (int i = 0; i < m; ++i){
		list[i] = i + 1;
	}

	Perm(list, 0, m, &count);
	cout << count;
	return 0;
}

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