Maximum even length sub-string that is permutation of a palindrome

Given a string str, the task is to find the maximum length of the sub-string of str that can be arranged into a Palindrome (i.e at least one of its permutation is a Palindrome). Note that the sub-string must be of even length.

Examples:

Input: str = “124565463”
Output: 6
“456546” is the valid sub-string

Input: str = “122313”
Output: 6

Approach: Use two variables: start (inclusive) and end (exclusive) to keep track of the starting and ending index of the current sub-string that is being considered in the given string. Also use a dictionary named count which keeps the record of how many times, a character occurs in the current sub-string. Now, there are two possible cases for a sub-string:

  1. If the length of the sub-string is odd, then it cannot be considered in the final solution.
  2. If the length of the sub-string is even, then it can be a possible solution only if each character in that sub-string occurs even number of times which can be done using the dictionary count. We check if each character occurs even number of times or not. If yes, then we include it as one of the possible solutions. Then we form the next sub-string by including the next character in the string which can be done by simply incrementing end and check recursively if a sub-string with greater length can be formed which satisfies the given conditions and return the maximum of all possible solutions.

Below is the implementation of the above approach:

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# Python3 code to find the maximum length of sub-string 
# (of even length) which can be arranged into a Palindrome
  
from collections import defaultdict
  
# function that returns true if the given 
# sub-string can be arranged into a Palindrome
def canBePalindrome(count):    
    for key in count:
        if count[key] % 2 != 0:
            return False            
    return True
      
# This function returns the maximum length of 
# the sub-string (of even length) which can be 
# arranged into a Palindrome
def maxPal(string, count, start, end):
      
    # If we reach end of the string
    if end == len(string):
  
        # if string is of even length
        if (end-start) % 2 == 0:
  
            # if string can be arranged into a
            # palindrome
            if canBePalindrome(count) == True:
                return end-start
                  
        return 0
          
    else:
          
        # Even length sub-string
        if (end-start) % 2 == 0:
              
            # Check if current sub-string can be 
            # arranged into a palindrome
            if canBePalindrome(count) == True:
                count[string[end]] += 1
                return max(end-start, maxPal(string, count, start, end + 1))
                  
            else:
                count[string[end]] += 1
                return maxPal(string, count, start, end + 1)
          
        # Odd length sub-string  
        else:
              
            count[string[end]] += 1
            length = maxPal(string, count.copy(), start, end + 1)
              
            count[string[end]] -= 1
            count[string[start]] -= 1
            return max(length, maxPal(string, count, start + 1, end))
              
# Driver code
string = '124565463'
start, end = 0, 0
count = defaultdict(lambda : 0)
  
print(maxPal(string, count, start, end))

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Output:

6


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