Hacktoberfest-2k22/60. Permutation Sequence.cpp at main · shreyansh-35/Hacktoberfest-2k22 · GitHub

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//backtracking
//TLE
//126 / 200 test cases passed.
class Solution {
public:
    string ans;

    void backtrack(int n, int k, string& s, vector<bool>& used, int& seq){
        if(s.size() == n){
            // cout << s << ", " << seq << endl;
            if(seq == k){
                ans = s;
            }
            ++seq;
        }else{
            for(int i = 0; i < n; ++i){
                if(!used[i]){
                    s += (i+1+'0');
                    used[i] = true;
                    backtrack(n, k, s, used, seq);
                    s.pop_back();
                    used[i] = false;
                }
                if(ans != "") break;
            }
        }
    }

    string getPermutation(int n, int k) {
        string s = "";
        vector<bool> used(n, false);
        int seq = 1;
        backtrack(n, k, s, used, seq);
        return ans;
    }
};

//backtracking + math
//Runtime: 4 ms, faster than 48.53% of C++ online submissions for Permutation Sequence.
//Memory Usage: 5.9 MB, less than 83.89% of C++ online submissions for Permutation Sequence.
class Solution {
public:
    string ans;

    vector<int> facts;

    void backtrack(int n, int k, string& s, vector<bool>& used, int& seq){
        if(s.size() == n){
            // cout << s << ", " << seq << endl;
            if(seq == k){
                ans = s;
            }
            ++seq;
        }else if(seq + facts[n-s.size()-1] < k){
            //skip the permutations formed by the remaining n-s.size() chars
            seq += facts[n-s.size()-1];
        }else{
            for(int i = 0; i < n; ++i){
                if(!used[i]){
                    s += (i+1+'0');
                    used[i] = true;
                    backtrack(n, k, s, used, seq);
                    s.pop_back();
                    used[i] = false;
                }
                if(ans != "") break;
            }
        }
    }

    string getPermutation(int n, int k) {
        string s = "";
        vector<bool> used(n, false);
        int seq = 1;

        facts = vector<int>(n);
        facts[0] = 1;
        for(int i = 2; i <= n; ++i){
            facts[i-1] = facts[i-2] * i;
        }

        backtrack(n, k, s, used, seq);
        return ans;
    }
};

//math
//https://leetcode.com/problems/permutation-sequence/discuss/22507/%22Explain-like-I'm-five%22-Java-Solution-in-O(n)
//Runtime: 0 ms, faster than 100.00% of C++ online submissions for Permutation Sequence.
//Memory Usage: 5.9 MB, less than 86.08% of C++ online submissions for Permutation Sequence.
//time: O(N)
class Solution {
public:
    string getPermutation(int n, int k) {
        string ans = "";

        vector<int> nums(n);
        iota(nums.begin(), nums.end(), 1);

        int fact = 1;
        for(int i = 1; i <= n; ++i){
            fact *= i;
        }

        --k; //1-based -> 0-based
        for(int i = 0; i < n; ++i){
            //there could be (n-1)! permutations if we exclude one char
            fact /= (n-i);
            //the kth permutation belongs to what group
            int groupid = k/fact;
            ans += (nums[groupid] + '0');
            nums.erase(nums.begin()+groupid);
            //there are "groupid" groups before the visited group
            k -= fact * groupid;
        }

        return ans;
    }
};