Cantor expansion is a way to use the Full Permutation and the id in the Permutation.In this way to map the id and the permutation,we can create a easy hash.It can be said a the most easy hash.
\(ans=a_{0}\cdot (n-1)!+a_{1}\cdot(n-2)!+\cdot\cdot\cdot+a_{n-1}\cdot(n-(n-1))!+a_{n}\cdot(n-n)!\)
the \(a_{i}\)

is the num in the others.

deCantor expansion is a opposite progress.

#include<bits/stdc++.h>
using namespace std;
int f[]={1,1,2,6,24,120};
int a[5];
void contorExpanse(){//康拓展開
    int ans=0;
    for(int i=0;i<5;i++){
        int tmp=0;
        for(int j=i+1;j<5;j++){
            if(a[j]<a[i]) tmp++;//計數        }
        ans+=tmp*f[5-i-1];//當前計數*階乘    }
    cout
 
<<ans<<endl;
}
void anticontorExpanse(int n){
    //寫的非常混亂
    /*
        整理一下思路就是設計兩個動態陣列作為可選和結果
        從n->1開始，不斷的輾轉相除
        計算當前小於該數的個數，從可選中選擇，並刪除
        此時該數變成餘數，重複步驟
    */
    vector<int>k;
    for(int i=1;i<=5;i++) k.push_back(i);
    vector<int>contor;
    int tmp=n;
    for(int i=5;i>=1;i--){
        int cc=tmp/(f[i-1]);//計算當前的計數        contor.push_back(k[cc]);
        k.erase(k.begin()+cc);//刪除
        tmp=tmp%f[i-1];//變成餘數    }
    for(int i=0;i<contor.size();i++) cout<<contor[i]<<" ";
}
int main(){

    for(int i=0;i<5;i++) cin>>a[i];
    contorExpanse();


    int n;
    cin>>n;
    anticontorExpanse(n);

    return 0;
}