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);

	}
}

运行结果如下：

请输入位数 n 
4
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111

我们可以把这个算法应用到这样一个例子中：

递归求一个集合的所有子集：

代码如下：

#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);
    }
}

运行结果如下：

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 }