求全排列和组合

第一种方法耗费空间比较大，第二种方法更有技巧

方法一：

#include <iostream>
using namespace std;
#include <cstdio>
#include <cstdlib>

char  a[100];
bool vis[100];
int  ct[100];
int n;
int cst ;

void dfs(char a[],int i){
     if(i == n){
         for(int k = 0;k < n;k++)
         cout << a[ct[k]] << " ";
         cout << endl;
         cst ++;
         return ;       
     }
     for(int j = 0;j < n;j++){
         if(!vis[j]){
             vis[j] = 1;
             ct[j] = i;
             dfs(a,i+1);
             vis[j] = 0;
             ct[j] = 0;
         }
     }
}

int main(){
    while(cin >> n){
         for(int i = 0;i < n;i++)
         cin >> a[i];
         memset(vis, 0, sizeof(vis));
         cst = 0;
         dfs(a,0);
         cout << cst << endl;
    }
    system("pause");   
}

方法二：

#include <iostream>
using namespace std;
#include <cstdio>
#include <cstdlib>
#include <algorithm>

char  a[100];
int   n,cst;
void swap(int &a, int &b){
     a = a^b;
     b = a^b;
     a = a^b;
}   
void  dfs(char a[],int k,int n){
      if(k == n){
         for(int p = 0;p < n;p++)
         cout << a[p] << " ";
         cout << endl;
         cst ++;
         return ;       
      }
      for(int i = k;i < n;i++){
             swap(a[i],a[k]);
             dfs(a,k+1,n);
             swap(a[i],a[k]);  
      }    
}

int main(){
    while(cin >> n){
         cst = 0;
         for(int i = 0;i < n;i++)
         cin >> a[i];
         dfs(a,0,n);
         cout << cst << endl;
    }
    system("pause");   
}

update:11-2

支持不输出重复的组合，如【1,1,1】只输出一次，上面那个会输出多次[方法错误]

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

void perm(vector<int> ct,int n, int k, vector<vector<int> > &cnt){
     if(k >= ct.size()){
            cnt.push_back(ct);
            return ;
     }
     for(int i = k;i < ct.size();i++){
             if(ct[i] == ct[k] && i != k)
             continue;
             swap(ct[i],ct[k]);
             perm(ct,n,k+1,cnt);
             swap(ct[i],ct[k]);
     }    
}

int main(){
    int n,tmp;
    vector<int> ct;
    vector<vector<int> > cnt;
    while(cin >> n){
         ct.clear();
         cnt.clear();
         while(n--){
             cin >> tmp;
             ct.push_back(tmp);
         }
         perm(ct, n, 0, cnt);
        
         for(int i = 0;i < ct.size();i++)
         cout << ct[i] << " *" ;
         cout << endl;
        
         for(int i = 0;i < cnt.size();i++){
                for(int j = 0;j < cnt[i].size();j++){
                     cout << cnt[i][j] << " " ;       
                }
                cout << endl;
         }
    }
}

下面才是正确的代码：

参加链接：http://www.zhizhihu.com/html/y2011/3674.html

#include <iostream>
using namespace std;
#include <cstdio>
#include <cstdlib>
/* 求排列 */
int cnt;

bool isok(int s[],int k,int i){
     for(int j = k;j < i;j++)
     if(s[j] == s[i])
     return 1;
     return 0;
}

void dfs(int s[], int k, int n){
     if(k == n){
        for(int i = 0;i < n;i++)
        printf("%d ",s[i]);
        printf("\n");
        cnt++;
        return;
     }
     
     for(int i = k;i < n;i++){
         if(isok(s,k,i))
         continue;
         swap(s[i],s[k]);
         dfs(s,k+1,n);
         swap(s[i],s[k]);
     }
}

int main(){
    int s[100], n;
    while(scanf("%d",&n) != EOF){
         for(int i = 0;i < n;i++){
               scanf("%d",&s[i]);        
         }
         cnt = 0;
         dfs(s,0,n);
         printf("cnt = %d\n",cnt); 
    }
}

 

 组合的过程:

#include <iostream>
using namespace std;
#include <cstdio>
#include <cstdlib>
#include <vector>

int size;

void dfs(vector<int> s,vector<int>& st,int pos,int n){
     if(pos >= n){
           for(int i = 0;i < st.size();i++)
           printf("%d ",st[i]);
           printf("\n");
           size++;       
           return;
     }
     dfs(s,st,pos+1,n);
     st.push_back(s[pos]);
     dfs(s,st,pos+1,n);
     st.pop_back();
}

int  main(){
     int n,key;
     vector<int> s;
     vector<int> st;
     while(scanf("%d",&n) != EOF){
         for(int i = 0;i < n;i++){
            scanf("%d",&key);
            s.push_back(key);
         }
         st.clear();
         size = 0;
         dfs(s,st,0,n);
         printf("size = %d\n",size);
     }
     system("pause");
}