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:4Explanation: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:6Explanation: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(N^{3})**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**(0 ≤ i ≤ 9) bit in the^{th}**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:- 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. - Otherwise, assign the value of the current index to
**ind[mask]**.

- If the value of the
- 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;` `}` |

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## 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` |

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## 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` |

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## 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` |

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**Output:**

6

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

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