康托展开

http://zh.wikipedia.org/wiki/康托展开

http://www.nocow.cn/index.php/康托展开

http://blog.sina.com.cn/s/blog_4bf7b6580100l2zs.html

http://www.skymoon.biz/?p=86

http://www.cnblogs.com/1-2-3/archive/2011/04/25/generate-permutation-part2.html

 

 

#include<cstdio>
#include<cstring>
#include<iostream>
#include<string>
#include<algorithm>
using namespace std;

int  fac[] = {1,1,2,6,24,120,720,5040,40320}; //i的阶乘为fac[i]  

int cantor(int s[],int n)
{
    int num=0;
    for(int i=0;i<n;i++)
    { 
        int temp=0;
        for(int j=i+1;j<n;j++)
        { 
            if(s[j]<s[i])temp++;//判断几个数小于它
        } 
        num+=fac[n-1-i]*temp;
    } 
    return(num+1);
}

void uncantor(int s[], int n, int k)
{
    k--;
    bool vis[8]={0};

    for(int i=n-1;i>=0;i--)
    { 
        int x=k/fac[i];
        for(int j=0;j<=x;j++)
            if(vis[j]) x++;
        s[n-1-i]=x+1;
        vis[x]=1;
        k%=fac[i];
    }
}



int main()
{
    int s[]={1, 2, 3, 4};
    int n=sizeof(s)/sizeof(int);
    do
    {
        printf("%d\n", cantor(s, n));
    }while(next_permutation(s, s+n));

    for(int k=1;k<=24;k++)
    {
        uncantor(s, 4, k);
        for(int i=0;i<4;i++)
        {
            printf("%d ", s[i]);
        }
        printf("\n");
    }

    return 0;
}