Maximum length prefix of one string that occurs as subsequence in another

Given two strings s and t. The task is to find maximum length of some prefix of the string S which occur in string t as subsequence.

Examples :

```Input : s = "digger"
t = "biggerdiagram"
Output : 3
digger
biggerdiagram
Prefix "dig" of s is longest subsequence in t.

Input : s = "geeksforgeeks"
t = "agbcedfeitk"
Output : 4
```

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

A simple solutions is to consider all prefixes on by one and check if current prefix of s[] is a subsequence of t[] or not. Finally return length of the largest prefix.

An efficient solution is based on the fact that to find a prefix of length n, we must first find the prefix of length n – 1 and then look for s[n-1] in t. Similarly, to find a prefix of length n – 1, we must first find the prefix of length n – 2 and then look for s[n – 2] and so on.
Thus, we keep a counter which stores the current length of prefix found. We initialize it with 0 and begin with the first letter of s and keep iterating over t to find the occurrence of the first letter. As soon as we encounter the first letter of s we update the counter and look for second letter. We keep updating the counter and looking for next letter, until either the string s is found or there are no more letters in t.

Below is the implementation of this approach:

 `// C++ program to find maximum  ` `// length prefix of one string  ` `// occur as subsequence in another ` `// string. ` `#include ` `using` `namespace` `std; ` ` `  `// Return the maximum length  ` `// prefix which is subsequence. ` `int` `maxPrefix(``char` `s[], ``char` `t[]) ` `{ ` `    ``int` `count = 0; ` ` `  `    ``// Iterating string T. ` `    ``for` `(``int` `i = 0; i < ``strlen``(t); i++) ` `    ``{ ` `        ``// If end of string S. ` `        ``if` `(count == ``strlen``(s)) ` `            ``break``; ` ` `  `        ``// If character match,  ` `        ``// increment counter. ` `        ``if` `(t[i] == s[count]) ` `            ``count++; ` `    ``} ` ` `  `    ``return` `count; ` `} ` ` `  `// Driven Code ` `int` `main() ` `{ ` `    ``char` `S[] = ``"digger"``; ` `    ``char` `T[] = ``"biggerdiagram"``; ` ` `  `    ``cout << maxPrefix(S, T)  ` `         ``<< endl; ` ` `  `    ``return` `0; ` `} `

 `// Java program to find maximum ` `// length prefix of one string  ` `// occur as subsequence in another ` `// string. ` `public` `class` `GFG {      ` `     `  `    ``// Return the maximum length  ` `    ``// prefix which is subsequence. ` `    ``static` `int` `maxPrefix(String s,  ` `                         ``String t) ` `    ``{ ` `        ``int` `count = ``0``; ` `     `  `        ``// Iterating string T. ` `        ``for` `(``int` `i = ``0``; i < t.length(); i++) ` `        ``{ ` `            ``// If end of string S. ` `            ``if` `(count == t.length()) ` `                ``break``; ` `     `  `            ``// If character match,   ` `            ``// increment counter. ` `            ``if` `(t.charAt(i) == s.charAt(count)) ` `                ``count++; ` `        ``} ` `     `  `        ``return` `count; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``String S = ``"digger"``; ` `        ``String T = ``"biggerdiagram"``; ` `     `  `        ``System.out.println(maxPrefix(S, T)); ` `    ``} ` `} ` `// This code is contributed by Sumit Ghosh `

 `# Python 3 program to find maximum  ` `# length prefix of one string occur ` `# as subsequence in another string. ` ` `  ` `  `# Return the maximum length  ` `# prefix which is subsequence. ` `def` `maxPrefix(s, t) : ` `    ``count ``=` `0` ` `  `    ``# Iterating string T. ` `    ``for` `i ``in` `range``(``0``,``len``(t)) : ` `         `  `        ``# If end of string S. ` `        ``if` `(count ``=``=` `len``(s)) : ` `            ``break` ` `  `        ``# If character match,  ` `        ``# increment counter. ` `        ``if` `(t[i] ``=``=` `s[count]) : ` `            ``count ``=` `count ``+` `1` `             `  ` `  `    ``return` `count ` ` `  ` `  `# Driver Code ` `S ``=` `"digger"` `T ``=` `"biggerdiagram"` ` `  `print``(maxPrefix(S, T)) ` ` `  ` `  `# This code is contributed ` `# by Nikita Tiwari. `

 `// C# program to find maximum  ` `// length prefix of one string ` `// occur as subsequence in  ` `// another string. ` `using` `System; ` ` `  `class` `GFG  ` `{      ` `     `  `    ``// Return the maximum length prefix  ` `    ``// which is subsequence. ` `    ``static` `int` `maxPrefix(String s,  ` `                         ``String t) ` `    ``{ ` `        ``int` `count = 0; ` `     `  `        ``// Iterating string T. ` `        ``for` `(``int` `i = 0; i < t.Length; i++) ` `        ``{ ` `            ``// If end of string S. ` `            ``if` `(count == t.Length) ` `                ``break``; ` `     `  `            ``// If character match,  ` `            ``// increment counter. ` `            ``if` `(t[i] == s[count]) ` `                ``count++; ` `        ``} ` `     `  `        ``return` `count; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``String S = ``"digger"``; ` `        ``String T = ``"biggerdiagram"``; ` `     `  `        ``Console.Write(maxPrefix(S, T)); ` `    ``} ` `} ` ` `  `// This code is contributed by nitin mittal `

 ` `

Output :

```3
```

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Improved By : nitin mittal, nidhi_biet

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