Longest prefix which is also suffix

Given a string s, find the length of the longest prefix, which is also a suffix. The prefix and suffix should not overlap.

Examples: 

Input : aabcdaabc
Output : 4
The string "aabc" is the longest
prefix which is also suffix.

Input : abcab
Output : 2

Input : aaaa
Output : 2

Simple Solution: Since overlapping prefixes and suffixes is not allowed, we break the string from the middle and start matching left and right strings. If they are equal return size of one string, else they try for shorter lengths on both sides.
Below is a solution to the above approach!

C++

// CPP program to find length of the
// longest prefix which is also suffix
#include <bits/stdc++.h>
using namespace std;

// Function to find largest prefix
// which is also a suffix
int largest_prefix_suffix(const std::string
                                      &str)
{

  int n = str.length();

  // if n is less than 2
  if(n < 2) {
    return 0;
  }

  int len = 0;
  int i = 1;

  // Iterate i till n
  while(i < n)
  {

    // If str[i] is equal to
    // str[len]
    if(str[i] == str[len])
    {
      ++len;
      ++i;
    }
    else
    {
      i = i - len + 1;
      len = 0;
    }
  }

  // Return len
  return len>n/2? len/2:len;

}

// Driver code
int main()
{

  string s = "blablabla";

  // Function Call
  cout << largest_prefix_suffix(s);
  return 0;
}

Java

// Java program to find length of the longest
// prefix which is also suffix
class GFG
{

   // Function to find largest prefix
   // which is also a suffix
   static int longestPrefixSuffix(String s)
   {
      int n = s.length();

      // If n is less than 2
      if(n < 2) {
          return 0;
      }

      int len = 0;
      int i = (n + 1)/2;

      // Iterate i till n
      while(i < n)
      {

        // If s.charAt(i) is equal to
        // s.charAt(len)
        if(s.charAt(i) == s.charAt(len))
        {
          ++len;
          ++i;
        }
        else
        {
          i = i - len + 1;
          len = 0;
        }
      }

      // Return len
      return len;

  }

    // Driver code
  public static void main (String[] args)
  {
    String s = "abcaabc";
    System.out.println(longestPrefixSuffix(s));
  }
}

// This code is contributed by Anant Agarwal.

Python3

# Python3 program to find length
# of the longest prefix which
# is also suffix
def longestPrefixSuffix(s) :
    n = len(s)

    for res in range(n // 2, 0, -1) :

        # Check for shorter lengths
        # of first half.
        prefix = s[0: res]
        suffix = s[n - res: n]

        if (prefix == suffix) :
            return res


    # if no prefix and suffix match
    # occurs
    return 0

# Driver Code
if __name__ == "__main__":
    s = "blablabla"
    print(longestPrefixSuffix(s))

# This code is contributed by Nikita Tiwari.

C#

// C# program to find length of the longest
// prefix which is also suffix
using System;

class GFG
{

    // Function to find largest prefix
    // which is also a suffix
    static int longestPrefixSuffix(String s)
    {
        int n = s.Length;

        // if n is less than 2
        if(n < 2) {
          return 0;
        }

        int len = 0;
        int i = (n + 1)/2;

        // Iterate i till n
        while(i < n)
        {

          // If str[i] is equal to
          // str[len]
          if(str[i] == str[len])
          {
            ++len;
            ++i;
          }
          else
          {
            i = i - len + 1;
            len = 0;
          }
        }

        // Return len
        return len;
    }

    // Driver code
    public static void Main ()
    {
        String s = "blablabla";

        Console.WriteLine(longestPrefixSuffix(s));
    }
}

// This code is contributed by vt_m.

Javascript

<script>

// JavaScript program to find length of the longest
// prefix which is also suffix

   // Function to find largest prefix
   // which is also a suffix
   function longestPrefixSuffix(s)
   {
      var n = s.length;

      // If n is less than 2
      if(n < 2) {
          return 0;
      }

      var len = 0;
      var i = (n + 1)/2;

      // Iterate i till n
      while(i < n)
      {

        // If s[i] is equal to
        // s[len]
        if(s[i] == s[len])
        {
          ++len;
          ++i;
        }
        else
        {
          i = i - len + 1;
          len = 0;
        }
      }

      // Return len
      return len;

  }

// Driver code
var s = "blablabla";
document.write(longestPrefixSuffix(s));

// This code contributed by shikhasingrajput

</script>

Output:

3

Efficient Solution: The idea is to use the preprocessing algorithm KMP search. In the preprocessing algorithm, we build lps array which stores the following values.

lps[i] = the longest proper prefix of pat[0..i] 
which is also a suffix of pat[0..i].

C++

// Efficient CPP program to find length of
// the longest prefix which is also suffix
#include<bits/stdc++.h>
using namespace std;

// Returns length of the longest prefix
// which is also suffix and the two do
// not overlap. This function mainly is
// copy computeLPSArray() of in below post
// https://www.geeksforgeeks.org/searching-for-patterns-set-2-kmp-algorithm/
int longestPrefixSuffix(string s)
{
    int n = s.length();

    int lps[n];
    lps[0] = 0; // lps[0] is always 0

    // length of the previous
    // longest prefix suffix
    int len = 0;

    // the loop calculates lps[i]
    // for i = 1 to n-1
    int i = 1;
    while (i < n)
    {
        if (s[i] == s[len])
        {
            len++;
            lps[i] = len;
            i++;
        }
        else // (pat[i] != pat[len])
        {
            // This is tricky. Consider
            // the example. AAACAAAA
            // and i = 7. The idea is
            // similar to search step.
            if (len != 0)
            {
                len = lps[len-1];

                // Also, note that we do
                // not increment i here
            }
            else // if (len == 0)
            {
                lps[i] = 0;
                i++;
            }
        }
    }

    int res = lps[n-1];

    // Since we are looking for
    // non overlapping parts.
    return (res > n/2)? res/2 : res;
}

// Driver program to test above function
int main()
{
    string s = "abcab";
    cout << longestPrefixSuffix(s);
    return 0;
}

Java

// Efficient Java program to find length of
// the longest prefix which is also suffix

class GFG
{
    // Returns length of the longest prefix
    // which is also suffix and the two do
    // not overlap. This function mainly is
    // copy computeLPSArray() of in below post
    // https://www.geeksforgeeks.org/searching-
    // for-patterns-set-2-kmp-algorithm/
    static int longestPrefixSuffix(String s)
    {
        int n = s.length();

        int lps[] = new int[n];

        // lps[0] is always 0
        lps[0] = 0;

        // length of the previous
        // longest prefix suffix
        int len = 0;

        // the loop calculates lps[i]
        // for i = 1 to n-1
        int i = 1;
        while (i < n)
        {
            if (s.charAt(i) == s.charAt(len))
            {
                len++;
                lps[i] = len;
                i++;
            }

             // (pat[i] != pat[len])
            else
            {
                // This is tricky. Consider
                // the example. AAACAAAA
                // and i = 7. The idea is
                // similar to search step.
                if (len != 0)
                {
                    len = lps[len-1];

                    // Also, note that we do
                    // not increment i here
                }

                // if (len == 0)
                else
                {
                    lps[i] = 0;
                    i++;
                }
            }
        }

        int res = lps[n-1];

        // Since we are looking for
        // non overlapping parts.
        return (res > n/2)? n/2 : res;
    }

    // Driver program
    public static void main (String[] args)
    {
        String s = "abcab";
        System.out.println(longestPrefixSuffix(s));
    }
}

// This code is contributed by Anant Agarwal.

Python3

# Efficient Python 3 program
# to find length of
# the longest prefix
# which is also suffix

# Returns length of the longest prefix
# which is also suffix and the two do
# not overlap. This function mainly is
# copy computeLPSArray() of in below post
# https://www.geeksforgeeks.org/searching-for-patterns-set-2-kmp-algorithm/
def longestPrefixSuffix(s) :
    n = len(s)
    lps = [0] * n   # lps[0] is always 0

    # length of the previous
    # longest prefix suffix
    l = 0

    # the loop calculates lps[i]
    # for i = 1 to n-1
    i = 1
    while (i < n) :
        if (s[i] == s[l]) :
            l = l + 1
            lps[i] = l
            i = i + 1

        else :

            # (pat[i] != pat[len])
            # This is tricky. Consider
            # the example. AAACAAAA
            # and i = 7. The idea is
            # similar to search step.
            if (l != 0) :
                l = lps[l-1]

                # Also, note that we do
                # not increment i here

            else :

                # if (len == 0)
                lps[i] = 0
                i = i + 1

    res = lps[n-1]

    # Since we are looking for
    # non overlapping parts.
    if(res > n/2) :
        return n//2
    else :
        return res


# Driver program to test above function
s = "abcab"
print(longestPrefixSuffix(s))


# This code is contributed
# by Nikita Tiwari.

C#

// Efficient C# program to find length of
// the longest prefix which is also suffix
using System;

class GFG {

    // Returns length of the longest prefix
    // which is also suffix and the two do
    // not overlap. This function mainly is
    // copy computeLPSArray() of in below post
    // https://www.geeksforgeeks.org/searching-
    // for-patterns-set-2-kmp-algorithm/
    static int longestPrefixSuffix(string s)
    {
        int n = s.Length;

        int []lps = new int[n];

        // lps[0] is always 0
        lps[0] = 0;

        // length of the previous
        // longest prefix suffix
        int len = 0;

        // the loop calculates lps[i]
        // for i = 1 to n-1
        int i = 1;
        while (i < n)
        {
            if (s[i] == s[len])
            {
                len++;
                lps[i] = len;
                i++;
            }

            // (pat[i] != pat[len])
            else
            {

                // This is tricky. Consider
                // the example. AAACAAAA
                // and i = 7. The idea is
                // similar to search step.
                if (len != 0)
                {
                    len = lps[len-1];

                    // Also, note that we do
                    // not increment i here
                }

                // if (len == 0)
                else
                {
                    lps[i] = 0;
                    i++;
                }
            }
        }

        int res = lps[n-1];

        // Since we are looking for
        // non overlapping parts.
        return (res > n/2) ? n/2 : res;
    }

    // Driver program
    public static void Main ()
    {
        string s = "abcab";

        Console.WriteLine(longestPrefixSuffix(s));
    }
}

// This code is contributed by vt_m.

PHP

<?php
// Efficient PHP program to find length of
// the longest prefix which is also suffix

// Returns length of the longest prefix
// which is also suffix and the two do
// not overlap. This function mainly is
// copy computeLPSArray() of in below post
// https://www.geeksforgeeks.org/searching-for-patterns-set-2-kmp-algorithm/
function longestPrefixSuffix($s)
{
    $n = strlen($s);

    $lps[$n] = NULL;

    // lps[0] is always 0
    $lps[0] = 0;

    // length of the previous
    // longest prefix suffix
    $len = 0;

    // the loop calculates lps[i]
    // for i = 1 to n-1
    $i = 1;
    while ($i < $n)
    {
        if ($s[$i] == $s[$len])
        {
            $len++;
            $lps[$i] = $len;
            $i++;
        }

        // (pat[i] != pat[len])
        else
        {

            // This is tricky. Consider
            // the example. AAACAAAA
            // and i = 7. The idea is
            // similar to search step.
            if ($len != 0)
            {
                $len = $lps[$len-1];

                // Also, note that we do
                // not increment i here
            }

            // if (len == 0)
            else
            {
                $lps[$i] = 0;
                $i++;
            }
        }
    }

    $res = $lps[$n-1];

    // Since we are looking for
    // non overlapping parts.
    return ($res > $n/2)? $n/2 : $res;
}

    // Driver Code
    $s = "abcab";
    echo longestPrefixSuffix($s);

// This code is contributed by nitin mittal
?>

Javascript

<script>

// Efficient javascript program to find length of
// the longest prefix which is also suffix{
// Returns length of the longest prefix
// which is also suffix and the two do
// not overlap. This function mainly is
// copy computeLPSArray() of in below post
// https://www.geeksforgeeks.org/searching-
// for-patterns-set-2-kmp-algorithm/
function longestPrefixSuffix(s)
{
    var n = s.length;

    var lps = Array.from({length: n}, (_, i) => 0);

    // lps[0] is always 0
    lps[0] = 0;

    // length of the previous
    // longest prefix suffix
    var len = 0;

    // the loop calculates lps[i]
    // for i = 1 to n-1
    var i = 1;
    while (i < n)
    {
        if (s.charAt(i) == s.charAt(len))
        {
            len++;
            lps[i] = len;
            i++;
        }

         // (pat[i] != pat[len])
        else
        {
            // This is tricky. Consider
            // the example. AAACAAAA
            // and i = 7. The idea is
            // similar to search step.
            if (len != 0)
            {
                len = lps[len-1];

                // Also, note that we do
                // not increment i here
            }

            // if (len == 0)
            else
            {
                lps[i] = 0;
                i++;
            }
        }
    }

    var res = lps[n-1];

    // Since we are looking for
    // non overlapping parts.
    return (res > n/2)? n/2 : res;
}

// Driver program
var s = "abcab";
document.write(longestPrefixSuffix(s));


// This code is contributed by 29AjayKumar


</script>

Output:

2

Please refer computeLPSArray() of KMP search for explanation.
Time Complexity : O(n) 
Auxiliary Space : O(n)

Solution using RegEx: 

Python3

# Python code to find length of the longest
# prefix which is also suffix
import re

s = "ABCABCABCABCABC" # Example input

print(len(re.findall(r'^(\w*).*\1$',s)[0]))

Output:

6

Efficient Solution: The idea is to traverse the suffix in reverse order and try to find a match in first half of the string (possible prefix). Here we take advantage of the property of a prefix substring – when traversed in reverse order, the prefix substring’s last character will always terminate at the string’s beginning.

Please note that we search for the prefix in the first half of the string alone because of the constraint given in the problem that the prefix and suffix are non-overlapping.

Algorithm :

        1. Maintain two pointers –  one which starts at the end of string(for suffix) and one which starts at the middle of string(for prefix)

        2. Keep on decrementing both the pointers provided they match and the prefix pointer is not exhausted( >0) .

        3. When a mismatch occurs, reset the suffix pointer back to end of string and repeat step 2.

        4. When prefix pointer reaches ‘-1’ (i.e. string is exhausted) the longest common suffix/prefix will be the substring from suffix pointer

            to end of the string.  Return the length of this substring. 

Implementation:

Python3

# Python3 program to find length
# of the longest prefix which
# is also suffix

# Returns length of the longest prefix
# which is also suffix and the two do
# not overlap.
def longestPrefixSuffix(s):

    n = len(s)

    if n == 0:
        return 0

    # end_suffix and end_prefix are used to keep track of the common suffix and prefix respectively.
    # For the prefix we search only in first half of string (0-->n//2-1) since
    # suffix and prefix do not overlap.
    end_suffix = n-1
    end_prefix = n // 2 - 1

    # Traverse each character of suffix from end to start and check for a match of prefix
    # in first half of array.
    while end_prefix >= 0:
        if s[end_prefix] != s[end_suffix]:
            if end_suffix != n-1:
                end_suffix = n-1  # reset end_suffix
            else:
                end_prefix -= 1
        else:
            end_suffix -= 1
            end_prefix -= 1

    # The longest common suffix and prefix is s[end+1:]
    return n-end_suffix-1


# Driver Code
if __name__ == "__main__":
    s = "ABCABCABCABCABC"
    print(longestPrefixSuffix(s))

# This code is contributed by Reshma Koshy.

Output

6

Time Complexity: O(n)

Auxiliary Space: O(1)