Length of the longest substring with every character appearing even number of times

Difficulty Level : Medium
Last Updated : 11 Nov, 2020

Given a numerical string S of length N, the task is to find the length of the longest substring of S where each element occurs even number of times.

Examples:

Input: S = “324425”
Output: 4
Explanation: Two substrings consisting of even frequent elements only are “44” and “2442”. Since “2442” is the longer of the two, print 4 as the required answer.

Input: S = “223015150”
Output: 6
Explanation: Three substrings consisting of even frequent elements only are “22”, “1515” and “015150”. Since “015150” is the longest among the three, print 4 as the required answer.

Naive Approach: The simplest approach is to generate all possible substrings of even length from the given string and for each substring, check if it contains characters with even frequencies only or not. Print the length of the longest of all such substrings.
Time Complexity: O(N³)
Auxiliary Space: O(N)

Efficient Approach: To optimize the above approach the idea is to use Bit Masking. Follow the steps below to solve the problem:

Traverse the string from left to right.
While traversing, use a bitmask variable, say mask, to keep track of the occurrence of each element from index 0 to the current index, whether it is even or odd. The i^th (0 ≤ i ≤ 9) bit in the mask is 0 if the digit i has occurred even number of times up to the current index, and 1 if it has occurred an odd number of times.
Use a variable val to store the value of digit present at the current index.
To update the occurrence of val, take Bitwise XOR of mask with 1 << val.
Use a Hash table ind to keep track of the index of each bitmask.
After updating the value of mask at the current index, check if it is present in ind or not:
1. If the value of the mask is already present in ind, it means that each element from index ind[mask] + 1 to current index occurs even number of times. Therefore, update the answer if the length of this segment from index ind[mask] + 1 to the current index is greater than the answer.
2. Otherwise, assign the value of the current index to ind[mask].
Finally, print the length of the required substring after completing the above steps.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to find length of the
// longest substring with each element
// occurring even number of times
int lenOfLongestReqSubstr(string s, int N)
{
    // Initialize unordered_map
    unordered_map<int, int> ind;
 
    int mask = 0;
    ind[0] = -1;
 
    // Stores the length of the
    // longest required substring
    int ans = 0;
 
    // Traverse the string
    for (int i = 0; i < N; i++) {
 
        // Stores the value of the
        // digit present at current index
        int val = s[i] - '0';
 
        // Bitwise XOR of the mask with
        // 1 left-shifted by val
        mask ^= (1 << val);
 
        // Check if the value of mask is
        // already present in ind or not
        if (ind.find(mask) != ind.end()) {
 
            // Update the final answer
            ans = max(ans, i - ind[mask]);
        }
 
        // Otherwise
        else
            ind[mask] = i;
    }
 
    // Return the answer
    return ans;
}
 
// Driver Code
int main()
{
    // Given string
    string s = "223015150";
 
    // Length of the given string
    int N = s.length();
 
    // Function Call
    cout << lenOfLongestReqSubstr(s, N);
 
    return 0;
}

Java

// Java program for the 
// above approach
import java.util.*;
class GFG{
 
// Function to find length of the
// longest subString with each element
// occurring even number of times
static int lenOfLongestReqSubstr(String s,
                                 int N)
{
  // Initialize unordered_map
  HashMap<Integer,
          Integer> ind = 
          new HashMap<>();
 
  int mask = 0;
  ind.put(0, -1);
 
  // Stores the length of the
  // longest required subString
  int ans = 0;
 
  // Traverse the String
  for (int i = 0; i < N; i++)
  {
    // Stores the value of the
    // digit present at current 
    // index
    int val = s.charAt(i) - '0';
 
    // Bitwise XOR of the mask 
    // with 1 left-shifted by val
    mask ^= (1 << val);
 
    // Check if the value of mask is
    // already present in ind or not
    if (ind.containsKey(mask))
    {
      // Update the final answer
      ans = Math.max(ans, 
                     i - ind.get(mask));
    }
 
    // Otherwise
    else
      ind.put(mask, i);
  }
 
  // Return the answer
  return ans;
}
 
// Driver Code
public static void main(String[] args)
{
  // Given String
  String s = "223015150";
 
  // Length of the given String
  int N = s.length();
 
  // Function Call
  System.out.print(
  lenOfLongestReqSubstr(s, N));
}
}
 
// This code is contributed by Rajput-Ji

Python3

# Python3 program for the 
# above approach
 
# Function to find length of 
# the longest substring with 
# each element occurring even 
# number of times
def lenOfLongestReqSubstr(s, N):
 
    # Initialize unordered_map
    ind = {}
 
    mask = 0
    ind[0] = -1
 
    # Stores the length of the
    # longest required substring
    ans = 0
 
    # Traverse the string
    for i in range(N):
 
        # Stores the value of the
        # digit present at current
        # index
        val = ord(s[i]) - ord('0')
 
        # Bitwise XOR of the mask
        # with 1 left-shifted by val
        mask ^= (1 << val)
 
        # Check if the value of mask 
        # is already present in ind 
        # or not
        if (mask in ind):
           
            # Update the final answer
            ans = max(ans, 
                      i - ind[mask])
 
        # Otherwise
        else:
            ind[mask] = i
 
    # Return the answer
    return ans
 
# Driver Code
if __name__ == "__main__":
 
    # Given string
    s = "223015150"
 
    #:Length of the given 
    # string
    N = len(s)
 
    # Function Call
    print(lenOfLongestReqSubstr(s, N))
     
# This code is contributed by Chitranayal

C#

// C# program for the 
// above approach
using System;
using System.Collections.Generic;
class GFG{
 
// Function to find length of the
// longest subString with each element
// occurring even number of times
static int lenOflongestReqSubstr(String s,
                                 int N)
{
  // Initialize unordered_map
  Dictionary<int,
             int> ind = 
             new Dictionary<int, 
                            int>();
 
  int mask = 0;
  ind.Add(0, -1);
 
  // Stores the length of the
  // longest required subString
  int ans = 0;
 
  // Traverse the String
  for (int i = 0; i < N; i++)
  {
    // Stores the value of the
    // digit present at current 
    // index
    int val = s[i] - '0';
 
    // Bitwise XOR of the mask 
    // with 1 left-shifted by val
    mask ^= (1 << val);
 
    // Check if the value of mask is
    // already present in ind or not
    if (ind.ContainsKey(mask))
    {
      // Update the readonly answer
      ans = Math.Max(ans, 
                     i - ind[mask]);
    }
 
    // Otherwise
    else
      ind.Add(mask, i);
  }
 
  // Return the answer
  return ans;
}
 
// Driver Code
public static void Main(String[] args)
{
  // Given String
  String s = "223015150";
 
  // Length of the given String
  int N = s.Length;
 
  // Function Call
  Console.Write(
  lenOflongestReqSubstr(s, N));
}
}
 
// This code is contributed by 29AjayKumar

Output:

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

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