C++ 递归位置排列算法及其应用

废话不多说，我们先看一下位置排序的算法：

#include <iostream>
using namespace std;

	int n = 0;
	int m = 2;
	int l = 0;
	int a[100];

	void solve(int l);

int main()
{

	cout<<"请输入位数 n "<<endl;
	cin>>n;

	solve(l);
	return 0;
}

void solve(int l)
{
	if(l>=n)
	{
		for(int i = 0 ; i<n; i++)
		{
			cout<<a[i];
		}
		cout << endl;
		return;
	}
	for(int i = 0 ;i < m;i++)
	{
		a[l] = i;
		solve(l+1);

	}
}

执行结果例如以下：

请输入位数 n 

4

0000

0001

0010

0011

0100

0101

0110

0111

1000

1001

1010

1011

1100

1101

1110

1111

我们能够把这个算法应用到这样一个样例中：

递归求一个集合的全部子集：

代码例如以下：

#include <iostream>
#include<vector>
#include <stdio.h>

using namespace std;

void solve(int l);

int n, m;
int mat[100];
vector<string>   collection;

int main()
{
    string   firstElement;
    string   element;

    int     mcount          = 1;

    cout << "Please input the element , end by #end" << endl;
    cin  >>  firstElement;

    while(firstElement != "#end")
    {
        element = firstElement;

         cout << "The element "<<mcount<< " you input is  "+ element<< endl;

         collection.push_back(element);

	 //cout << collection[mcount-1];

         cout << "Please input the next element , end by #end" << endl;
         cin >>  firstElement;
    }
	n = collection.size();
    	m = 2;
    	solve(0);
    return 0;
}

void solve(int l)//l=0
{
    int i;
    if(l >= n)//n=4
    {
	printf("{");
        for(i=0; i<n; ++i)
        {
            if(mat[i] == 1)
            {
                cout<< collection[i] << " ";
            }
        }
        printf("}\n");
        return;
    }
    for(i=0; i<m; ++i)//m=2
    {
        mat[l] = i;
        solve(l+1);
    }
}

执行结果例如以下：

Please input the element , end by #end

a

The element 1 you input is  a

Please input the next element , end by #end

b

The element 1 you input is  b

Please input the next element , end by #end

c

The element 1 you input is  c

Please input the next element , end by #end

#end

{}

{c }

{b }

{b c }

{a }

{a c }

{a b }

{a b c }