Leet Code : Permutation Sequence .cpp

class Solution {
public:
    string getPermutation(int n, int k) {
        string re(n,'0');
        int fac=factorial(n);
        vector<int> vecNum(n,0);
        for(int i=1;i<=vecNum.size();++i)vecNum[i-1]=i;
        --k;//  k=[0,(n-i)! ) ,inorder to get the right index 
        for(int i=0;i<n;++i)
        {
            fac=fac/(n-i); //fac=(n-i)!
            int index=k/fac;//index of the right number
            k=k%fac;
            re[i]+=vecNum[index];
            vecNum.erase(vecNum.begin()+index);//remove the used number and get a subsequence
        }
        return re;
    }
    
    int factorial(int i)
    {
        int re=1;
        if(!i)return re;
        else
        while(i)re=re*(i--);
        return re;
    }

};