Leetcode Permutation Sequence

超时算法—排序dfs：

class Solution {
public:
string s;
string s1;
int count;
    string getPermutation(int n, int k) 
    {
        s="123456789";
        count=0;
        s1="";
        dfs(0,n,k);
        return s1;
    }
    void dfs(int depth,int n,int k)
    {
        if(depth==n&&count<=k)
        {
            count++;
            if(count==k)
            {
                s1=s.substr(0,n);
                return;
            }
        }
        if(depth<n)
        {
            dfs(depth+1,n,k);
            for(int i=depth+1;i<n;i++)
            {
                string s2=s;
                swap(s[depth],s[i]);
                sort(s.begin()+depth+1,s.begin()+n);
                dfs(depth+1,n,k);
                s=s2;
            }
        }
    }
};

 超时算法—组合dfs

class Solution {
public:
string s1;
bool used[9];
int count;
char c[9];
    string getPermutation(int n, int k) 
    {
        for(int i=0;i<9;i++)
        {
            used[i]=false;
            c[i]='0';
        }        
        count=0;
        s1="";
        dfs(0,n,k);
        return s1;
    }
    void dfs(int depth,int n,int k)
    {
        if(depth==n&&count<k)
        {
            count++;
            if(count==k)
            {
                for(int i=0;i<n;i++)
                s1+=c[i];
                return;
            }
        }
        if(depth<n)
        {
            for(int i=0;i<n;i++)
            {
                if(!used[i])
                {
                 used[i]=true;
                 c[depth]='0'+i+1;
                 dfs(depth+1,n,k);
                 used[i]=false;
                }
            }           
        }
    }
};

 纯数学算法

class Solution {
public:
    string getPermutation(int n, int k) 
    {
        string      result;
        vector<int> num(n);
        int         i, d(1), q;
        for(i=1;i<=n;++i){
            num[i-1]  = i;
            d        *= i;  //d=n!
        }
        for(i=n;i>=1;--i){
            d       = d/i;
            q       = (k-1)/d;
            k       = k-q*d;
            result.push_back('0'+num[q]);
            num.erase(num.begin()+q);
        }
        return result;
    }
};