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Check if string S2 can be obtained by appending subsequences of string S1
• Difficulty Level : Hard
• Last Updated : 04 Dec, 2020

Given two strings S1 and S2, the task is to check if it’s possible to generate string S2 by repeatedly appending subsequences of S1 to the end of an initially empty string. If possible, print “YES” and the minimum number of operations required. Otherwise, print “NO“.

Examples:

Input: S1 = “acebcd”, S2 = “acbcd”
Output:
YES

Explanation: Append subsequence “acbc” followed by “d” to obtain S2.

Input: S1 = “aceasd”, S2 = “asdxds”
Output: NO
Explanation: Since character ‘x’ is not present in S1, S2 cannot be obtained.

Approach: Follow the steps below to solve the problem:

• Iterate over characters of string S1 and store frequencies of each character in S1 in an array freq[].
• Traverse the string S2 and check if there is any character in S2 which is not present in S1. If any such character is found, print “NO”.
• Otherwise, iterate over characters in S1 and update indices of each character in a Set
• Traverse string S2 and for each character, check if it can be included in the current subsequence of S1 that can be appended.
• If found to be true, set the index of current character as that of the last character appended. Otherwise, increase count of subsequences and set the index of current character as that of the last character appended. Proceed to the next character.
• finally, print “YES” and the count of such subsequences as the required answer.

Below is the implementation of the above approach:

## C++

 `// C++ Program to implement``// the above approach``#include "bits/stdc++.h"``using` `namespace` `std;` `// Function for finding minimum``// number of operations``int` `findMinimumOperations(string s,``                          ``string s1)``{` `    ``// Stores the length of strings``    ``int` `n = s.length(), m = s1.length();` `    ``// Stores frequency of``    ``// characters in string s``    ``int` `frequency = { 0 };` `    ``// Update  frequencies of``    ``// character in s``    ``for` `(``int` `i = 0; i < n; i++)``        ``frequency[s[i] - ``'a'``]++;` `    ``// Traverse string s1``    ``for` `(``int` `i = 0; i < m; i++) {` `        ``// If any character in s1``        ``// is not present in s``        ``if` `(frequency[s1[i] - ``'a'``]``            ``== 0) {``            ``return` `-1;``        ``}``    ``}` `    ``// Stores the indices of``    ``// each character in s``    ``set<``int``> indices;` `    ``// Traverse string s``    ``for` `(``int` `i = 0; i < n; i++) {` `        ``// Store indices of characters``        ``indices[s[i] - ``'a'``].insert(i);``    ``}` `    ``int` `ans = 1;` `    ``// Stores index of last``    ``// appended characterr``    ``int` `last = (*indices[s1``                      ``- ``'a'``]``                     ``.begin());` `    ``// Traaverse string s1``    ``for` `(``int` `i = 1; i < m; i++) {` `        ``int` `ch = s1[i] - ``'a'``;` `        ``// Find the index of next``        ``// character that can be appended``        ``auto` `it = indices[ch].upper_bound(``            ``last);` `        ``// Check if the current``        ``// character be included``        ``// in the current subsequence``        ``if` `(it != indices[ch].end()) {``            ``last = (*it);``        ``}` `        ``// Otherwise``        ``else` `{` `            ``// Start a new subsequence``            ``ans++;` `            ``// Update index of last``            ``// character appended``            ``last = (*indices[ch].begin());``        ``}``    ``}``    ``return` `ans;``}` `// Driver Code``int` `main()``{` `    ``string S1 = ``"acebcd"``, S2 = ``"acbcde"``;``    ``int` `ans = findMinimumOperations(``        ``S1, S2);` `    ``// If S2 cannot be obtained``    ``// from subsequences of S1``    ``if` `(ans == -1) {``        ``cout << ``"NO\n"``;``    ``}``    ``// Otherwise``    ``else` `{``        ``cout << ``"YES\n"``             ``<< ans;``    ``}` `    ``return` `0;``}`

## Python3

 `# Python3 Program to implement``# the above approach``from` `bisect ``import` `bisect ,bisect_left,bisect_right` `# Function for finding minimum``# number of operations``def` `findMinimumOperations(s,s1):` `    ``#Stores the length of strings``    ``n ``=` `len``(s)``    ``m ``=` `len``(s1)` `    ``# Stores frequency of``    ``# characters in string s``    ``frequency ``=` `[``0``]``*``26` `    ``# Update  frequencies of``    ``# character in s``    ``for` `i ``in` `range``(n):``        ``frequency[``ord``(s[i]) ``-` `ord``(``'a'``)] ``+``=` `1` `    ``# Traverse string s1``    ``for` `i ``in` `range``(m):` `        ``# If any character in s1``        ``# is not present in s``        ``if` `(frequency[``ord``(s1[i]) ``-` `ord``(``'a'``)] ``=``=` `0``):``            ``return` `-``1` `    ``# Stores the indices of``    ``# each character in s``    ``indices ``=` `[[] ``for` `i ``in` `range``(``26``)]` `    ``# Traverse string s``    ``for` `i ``in` `range``(n):` `        ``# Store indices of characters``        ``indices[``ord``(s[i]) ``-` `ord``(``'a'``)].append(i)` `    ``ans ``=` `2` `    ``# Stores index of last``    ``# appended characterr``    ``last ``=``len``(indices[``ord``(s1[``0``])``-` `ord``(``'a'``)]) ``-` `1` `    ``# Traaverse string s1``    ``for` `i ``in` `range``(``1``,m):` `        ``ch ``=` `ord``(s1[i]) ``-` `ord``(``'a'``)` `        ``# Find the index of next``        ``# character that can be appended``        ``it ``=` `bisect_right(indices[ch],last)``        ``# print(it)` `        ``# Check if the current``        ``# character be included``        ``# in the current subsequence``        ``if` `(it !``=` `len``(indices[ch])):``            ``last ``=` `it``        ``# Otherwise``        ``else``:` `            ``# Start a new subsequence``            ``ans ``+``=` `1` `            ``# Update index of last``            ``# character appended``            ``last ``=` `len``(indices[ch])``    ``return` `ans` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:` `    ``S1 ``=` `"acebcd"``    ``S2 ``=` `"acbcde"``    ``ans ``=` `findMinimumOperations(S1, S2)` `    ``# If S2 cannot be obtained``    ``# from subsequences of S1``    ``if` `(ans ``=``=` `-``1``):``        ``print``(``"NO"``)``    ``# Otherwise``    ``else``:``        ``print``(``"YES"``)``        ``print``(ans)` `# This code is contributed by mohit kumar 29`
Output:
```YES
2```

Time Complexity: O(Mlog(N))
Auxiliary Space: O(N)

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