Hello Codeforces. Recently I solved problems from VKOSHP XXII on CF and found something weird.

I've got 2 solutions of problem I — Wheel of Fortune

1st solution:

#include<bits/stdc++.h>

using namespace std;

const int N = 1e5;
string s[N + 10];

bool recur(vector<int> positions, set<char> letters) {
    int m = (int)positions.size();
    if(m == 1) 
        return 1;
    
    set<char> oldl = letters;
    for(int i = 0;i < m;i++) {

        set<char> newl;
        for(char c : s[ positions[ i ] ]) {
            if(letters.count( c ))
                newl.insert(c);
        }
        letters = newl;
    }
    if(letters.empty()) return 0;

    char letter = *letters.begin();

    unordered_map<string, vector<int>> mp;

    for(int i = 0;i < m;i++) {
        string pt = "";
        for(char c : s[ positions[ i ] ]) {
            pt += (c == letter ? letter : '#');
        }
        
        mp[ pt ].push_back( positions[ i ] );
    }

    oldl.erase(letter);
    for(auto c : mp) {
        if(!recur(c.second, oldl)) return 0;
    }

    return 1;
}

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);cout.tie(0);

    int l, n;
    cin >> l >> n;
    vector<int> pos(n);
    set<char> letters;
    for(int i = 0;i < n;i++) {
        cin >> s[ i ];
        pos[ i ] = i;
    }
    for(char c = 'a';c <= 'z';c++) 
        letters.insert(c);
    
    cout << (recur(pos, letters) ? "YES" : "NO");
}

and 2nd:

#include<bits/stdc++.h>

using namespace std;

const int N = 1e5;
string s[N + 10];
string words[N + 10];    // <== new line   

bool recur(vector<int> positions, set<char> letters) {
    int m = (int)positions.size();
    if(m == 1) 
        return 1;
    
    set<char> oldl = letters;
    for(int i = 0;i < m;i++) {
        words[ i ] = s[ positions[ i ] ]; // <== new line
        set<char> newl;
        for(char c : s[ positions[ i ] ]) {
            if(letters.count( c ))
                newl.insert(c);
        }
        letters = newl;
    }
    if(letters.empty()) return 0;

    char letter = *letters.begin();

    unordered_map<string, vector<int>> mp;

    for(int i = 0;i < m;i++) {
        string pt = "";
        for(char c : s[ positions[ i ] ]) {
            pt += (c == letter ? letter : '#');
        }
        
        mp[ pt ].push_back( positions[ i ] );
    }

    oldl.erase(letter);
    for(auto c : mp) {
        if(!recur(c.second, oldl)) return 0;
    }

    return 1;
}

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);cout.tie(0);

    int l, n;
    cin >> l >> n;
    vector<int> pos(n);
    set<char> letters;
    for(int i = 0;i < n;i++) {
        cin >> s[ i ];
        pos[ i ] = i;
    }
    for(char c = 'a';c <= 'z';c++) 
        letters.insert(c);
    
    cout << (recur(pos, letters) ? "YES" : "NO");
}

1st solution gives TLE on test 52, but in solution 2 I just added an array words which I'm not using at all but it gets AC (P.S. in 2nd code I marked the lines which aren't in 1st one).

So here in confusion I asking anybody explain me the reason of this jump in execution time of my code