# Longest Substring that can be made a palindrome by swapping of characters

Given a numeric string **S**, the task is to find the longest non-empty substring that can be made palindrome.

**Examples:**

Input:S = “3242415”Output:5Explanation:“24241” is the longest such substring which can be converted to the palindromic string “24142”.

Input:S = “213123”Output:6Explanation:“213123” such substring which can be converted to the palindromic string “231132”.

**Naive Approach:** The simplest approach to solve this problem is to generate all possible substrings and for each substring check if it can be made a palindrome or not by counting the characters in each substring and check if only one or no odd frequent character is present or not.

**Time Complexity:** O(N^{3})**Auxiliary Space:** O(1)

**Efficient Approach: **To optimize the above approach, the idea to solve this problem is to use Bitmasking and Dynamic Programming. A palindrome can be formed if the count of each included number (except maybe one) is even. Follow the steps below to solve the problem:

- Initialize an integer variable, say
**mask**. A bit in our**mask is 0**if the count for the corresponding number is**even**, and 1 if it’s**odd**. - Traverse through the string and while traversing the string, track
**odd/even counts**in the variable**mask**. - If the same
**mask**is encountered again, the subarray between the**first position**(exclusive) and the**current position**(inclusive) with the same mask has all numbers with the even count. - Let the size of the substring be stored in a variable, say
**res**. - Initialize an array, say
**dp[]**, to track the smallest (first) position of each mask of size 1024, since the input only contains 10 digits (“0123456789”), and there can be only 2^10 or 1024 variations of bit masks. - The size of the substring can be calculated by subtracting it from the current position. Note that the position for
**zero mask**is**-1,**as the first character is to be included. - Also, check all masks that are different from the current one by
**one bit**. In other words, if**two masks are different**by one bit, that means that there is one**odd count**in the substring. - Print
**res**as the length of longest such substring.

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 the Longest` `// substring that can be made a` `// palindrome by swapping of characters` `int` `longestSubstring(string s)` `{` ` ` ` ` `// Initialize dp array of size 1024` ` ` `int` `dp[1024];` ` ` `// Initializeing dp array with length of s` ` ` `fill(dp, dp + 1024, s.size());` ` ` `// Initializing mask and res` ` ` `int` `res = 0, mask = 0;` ` ` `dp[0] = -1;` ` ` `// Traverse the string` ` ` `for` `(` `int` `i = 0; i < s.size(); ++i)` ` ` `{` ` ` `// Find the mask of the current character` ` ` `mask ^= 1 << (s[i] - 48);` ` ` `// Finding the length of the longest` ` ` `// substring in s which is a` ` ` `// palindrome for even count` ` ` `res = max(res, i - dp[mask]);` ` ` `// Finding the length of the longest` ` ` `// substring in s which is a` ` ` `// palindrome for one odd count` ` ` `for` `(` `int` `j = 0; j <= 9; ++j)` ` ` `// Finding maximum length of` ` ` `// substring having one odd count` ` ` `res = max(res, i - dp[mask ^ (1 << j)]);` ` ` `// dp[mask] is minimum of` ` ` `// current i and dp[mask]` ` ` `dp[mask] = min(dp[mask], i);` ` ` `}` ` ` `// Return longest length of the substring` ` ` `// which forms a palindrome with swaps` ` ` `return` `res;` `}` `// Driver Code` `int` `main()` `{` ` ` ` ` `// Input String` ` ` `string s = ` `"3242415"` `;` ` ` `// Function Call` ` ` `cout << longestSubstring(s);` ` ` `return` `0;` `}` `// This code is contributed by subhammahato348.` |

## Java

`// Java program for the above approach` `import` `java.io.*;` `import` `java.util.*;` `class` `GFG {` ` ` `// Function to find the Longest` ` ` `// substring that can be made a` ` ` `// palindrome by swapping of characters` ` ` `public` `static` `int` `longestSubstring(String s)` ` ` `{` ` ` `// Initialize dp array of size 1024` ` ` `int` `dp[] = ` `new` `int` `[` `1024` `];` ` ` `// Initializeing dp array with length of s` ` ` `Arrays.fill(dp, s.length());` ` ` `// Initializing mask and res` ` ` `int` `res = ` `0` `, mask = ` `0` `;` ` ` `dp[` `0` `] = -` `1` `;` ` ` `// Traverse the string` ` ` `for` `(` `int` `i = ` `0` `; i < s.length(); ++i) {` ` ` `// Find the mask of the current character` ` ` `mask ^= ` `1` `<< (s.charAt(i) - ` `'0'` `);` ` ` `// Finding the length of the longest` ` ` `// substring in s which is a` ` ` `// palindrome for even count` ` ` `res = Math.max(res, i - dp[mask]);` ` ` `// Finding the length of the longest` ` ` `// substring in s which is a` ` ` `// palindrome for one odd count` ` ` `for` `(` `int` `j = ` `0` `; j <= ` `9` `; ++j)` ` ` `// Finding maximum length of` ` ` `// substring having one odd count` ` ` `res = Math.max(res,` ` ` `i - dp[mask ^ (` `1` `<< j)]);` ` ` `// dp[mask] is minimum of` ` ` `// current i and dp[mask]` ` ` `dp[mask] = Math.min(dp[mask], i);` ` ` `}` ` ` `// Return longest length of the substring` ` ` `// which forms a palindrome with swaps` ` ` `return` `res;` ` ` `}` ` ` `// Driver Code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `// Input String` ` ` `String s = ` `"3242415"` `;` ` ` `// Function Call` ` ` `System.out.println(longestSubstring(s));` ` ` `}` `}` |

## Python3

`# Python3 program for the above approach` `# Function to find the Longest` `# substring that can be made a` `# palindrome by swapping of characters` `def` `longestSubstring(s):` ` ` ` ` `# Initialize dp array of size 1024` ` ` `dp ` `=` `[` `1024` `for` `i ` `in` `range` `(` `1024` `)]` ` ` `# Initializeing dp array with length of s` ` ` `# Arrays.fill(dp, s.length());` ` ` `# Initializing mask and res` ` ` `res, mask ` `=` `0` `, ` `0` ` ` `dp[` `0` `] ` `=` `-` `1` ` ` `# Traverse the string` ` ` `for` `i ` `in` `range` `(` `len` `(s)):` ` ` ` ` `# Find the mask of the current character` ` ` `mask ^` `=` `1` `<< (` `ord` `(s[i]) ` `-` `ord` `(` `'0'` `))` ` ` `# Finding the length of the longest` ` ` `# substring in s which is a` ` ` `# palindrome for even count` ` ` `res ` `=` `max` `(res, i ` `-` `dp[mask])` ` ` `# Finding the length of the longest` ` ` `# substring in s which is a` ` ` `# palindrome for one odd count` ` ` `for` `j ` `in` `range` `(` `10` `):` ` ` ` ` `# Finding maximum length of` ` ` `# substring having one odd count` ` ` `res ` `=` `max` `(res, i ` `-` `dp[mask ^ (` `1` `<< j)])` ` ` `# dp[mask] is minimum of` ` ` `# current i and dp[mask]` ` ` `dp[mask] ` `=` `min` `(dp[mask], i)` ` ` `# Return longest length of the substring` ` ` `# which forms a palindrome with swaps` ` ` `return` `res` `# Driver Code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` ` ` `# Input String` ` ` `s ` `=` `"3242415"` ` ` `# Function Call` ` ` `print` `(longestSubstring(s))` `# This code is contributed by mohit kumar 29` |

## C#

`// C# program for the above approach` `using` `System;` `class` `GFG` `{` ` ` `// Function to find the Longest` ` ` `// substring that can be made a` ` ` `// palindrome by swapping of characters` ` ` `public` `static` `int` `longestSubstring(` `string` `s)` ` ` `{` ` ` `// Initialize dp array of size 1024` ` ` `int` `[]dp = ` `new` `int` `[1024];` ` ` `// Initializeing dp array with length of s` ` ` `for` `(` `int` `i = 0; i < 1024; ++i)` ` ` `{` ` ` `dp[i] = s.Length;` ` ` `}` ` ` `// Initializing mask and res` ` ` `int` `res = 0, mask = 0;` ` ` `dp[0] = -1;` ` ` `// Traverse the string` ` ` `for` `(` `int` `i = 0; i < s.Length; i++)` ` ` `{` ` ` `// Find the mask of the current character` ` ` `mask = mask ^ (1 << (s[i] - ` `'0'` `));` ` ` `// Finding the length of the longest` ` ` `// substring in s which is a` ` ` `// palindrome for even count` ` ` `res = Math.Max(res, i - dp[mask]);` ` ` `// Finding the length of the longest` ` ` `// substring in s which is a` ` ` `// palindrome for one odd count` ` ` `for` `(` `int` `j = 0; j < 10; j++)` ` ` `{` ` ` `// Finding maximum length of` ` ` `// substring having one odd count` ` ` `res = Math.Max(res,i - dp[mask ^ (1 << j)]);` ` ` `}` ` ` `// dp[mask] is minimum of` ` ` `// current i and dp[mask]` ` ` `dp[mask] = Math.Min(dp[mask], i);` ` ` `}` ` ` `// Return longest length of the substring` ` ` `// which forms a palindrome with swaps` ` ` `return` `res;` ` ` `}` ` ` `// Driver Code` ` ` `public` `static` `void` `Main(` `string` `[] args)` ` ` `{` ` ` `// Input String` ` ` `string` `s = ` `"3242415"` `;` ` ` `// Function Call` ` ` `Console.WriteLine(longestSubstring(s));` ` ` `}` `}` `// This code is contributed by AnkThon` |

## Javascript

`<script>` `// Javascript program for the above approach` `// Function to find the Longest` `// substring that can be made a` `// palindrome by swapping of characters` `function` `longestSubstring(s)` `{` ` ` ` ` `// Initialize dp array of size 1024` ` ` `let dp = ` `new` `Array(1024).fill(1);` ` ` `// Initializing mask and res` ` ` `let res = 0, mask = 0;` ` ` `dp[0] = -1;` ` ` `// Traverse the string` ` ` `for` `(let i = 0; i < s.length; ++i)` ` ` `{` ` ` ` ` `// Find the mask of the current character` ` ` `mask ^= 1 << (s[i] - ` `'0'` `);` ` ` `// Finding the length of the longest` ` ` `// substring in s which is a` ` ` `// palindrome for even count` ` ` `res = Math.max(res, i - dp[mask]);` ` ` `// Finding the length of the longest` ` ` `// substring in s which is a` ` ` `// palindrome for one odd count` ` ` `for` `(let j = 0; j <= 9; ++j)` ` ` ` ` `// Finding maximum length of` ` ` `// substring having one odd count` ` ` `res = Math.max(res,` ` ` `i - dp[mask ^ (1 << j)]);` ` ` `// dp[mask] is minimum of` ` ` `// current i and dp[mask]` ` ` `dp[mask] = Math.min(dp[mask], i);` ` ` `}` ` ` `// Return longest length of the substring` ` ` `// which forms a palindrome with swaps` ` ` `return` `res;` `}` `// Driver Code` `// Input String` `let s = ` `"3242415"` `;` `// Function Call` `document.write(longestSubstring(s));` `// This code is contributed by splevel62` ` ` `</script>` |

**Output:**

5

**Time Complexity:** O(10*N)**Auxiliary Space:** O(1024)

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