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 }