leetcode 60. Permutation Sequence

首先暴力解法，求出所以的排列， 排序，求第k个

class Solution {
public:
    
    void getP(vector<int> num, vector<string> & result, string s)
    {
        if(num.empty())
        {
            result.push_back(s);
            return ;
        }
            
        int t;
        for(int i=0;i<num.size();i++)
        {
            t=num[i];
            num.erase(num.begin()+i);
            getP(num, result, s+to_string(t));
         
            num.insert(num.begin()+i,t);
           
        }
    }
    string getPermutation(int n, int k) {
        vector<int> num;
        for(int i=1;i<=n;i++)
        {
            num.push_back(i);
        }
        vector<string> result;
        string temp;
        getP(num,result,temp);
      
        sort(result.begin(),result.end());
        return result[k-1];
    }
};

　　超时。。。

考虑数学归纳法：

n个数有n！个排列组合.  

    string getPermutation(int n, int k) {
        /*
        vector<int> num;
        for(int i=1;i<=n;i++)
        {
            num.push_back(i);
        }
        vector<string> result;
        string temp;
        getP(num,result,temp);
      
        sort(result.begin(),result.end());
        return result[k-1];
        */
         
         vector<int> factorial = vector<int>(n + 1, 1);
        for (int i = 1; i < n + 1; ++i) {
            factorial[i] = factorial[i - 1] * i;
        }
        vector<int> nums;
        for (int i = 1; i < n + 1; ++i) {
            nums.push_back(i);
        }
        
       vector<int> perm;
        for (int i = 0; i < n; ++i) {
            int rank = (k - 1) / factorial[n - i - 1];
            k = (k - 1) % factorial[n - i - 1] + 1;
            // append and remove nums[rank]
            perm.push_back(nums[rank]);
            nums.erase(std::remove(nums.begin(), nums.end(), nums[rank]), nums.end());
        }
        // transform a vector<int> to a string
        std::stringstream result;
        std::copy(perm.begin(), perm.end(), std::ostream_iterator<int>(result, ""));

        return result.str();
    
    }
};