Longest Happy Prefix in C++

Suppose we have a string s, we have to find the longest happy prefix of s. A string is called a happy prefix if is a non-empty prefix which is also a suffix (excluding itself). If there is no such happy prefix, then simply return blank string.

So, if the input is like "madam", then the output will be "m", it has 4 prefixes excluding itself. These are "m", "ma", "mad", "mada" and 4 suffixes like "m", "am", "dam", "adam". The largest prefix which is also suffix is given by "m".

To solve this, we will follow these steps −

• Define a function lps(), this will take s,

• n := size of s

• Define an array ret of size n

• j := 0, i := 1

• while i < n, do −

  • if s[i] is same as s[j], then

    • ret[i] := j + 1

    • (increase i by 1)

    • (increase j by 1)

  • otherwise when s[i] is not equal to s[j], then −

    • if j > 0, then −

      • j := ret[j - 1]

    • Otherwise

      • (increase i by 1)

• return ret

• From the main method do the following −

• n := size of s

• if n is same as 1, then −

  • return blank string

• Define an array v = lps(s)

• x := v[n - 1]

• ret := blank string

• for initialize i := 0, when i < x, update (increase i by 1), do −

  • ret := ret + s[i]

• return ret

Let us see the following implementation to get better understanding −

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
class Solution {
   public:
   vector <int> lps(string s){
      int n = s.size();
      vector<int> ret(n);
      int j = 0;
      int i = 1;
      while (i < n) {
         if (s[i] == s[j]) {
            ret[i] = j + 1;
            i++;
            j++;
         }
         else if (s[i] != s[j]) {
            if (j > 0)
               j = ret[j - 1];
            else {
               i++;
            }
         }
      }
      return ret;
   }
   string longestPrefix(string s) {
      int n = s.size();
      if (n == 1)
      return "";
      vector<int> v = lps(s);
      int x = v[n - 1];
      string ret = "";
      for (int i = 0; i < x; i++) {
         ret += s[i];
      }
      return ret;
   }
};
main(){
   Solution ob;
   cout << (ob.longestPrefix("madam"));
}

Input

"madam"

Output

m