# Maximum length palindrome that can be created with characters in range L and R

• Difficulty Level : Medium
• Last Updated : 21 Jun, 2022

Given a string str and Q queries. Each query consists of two numbers L and R. The task is to find the maximum length palindrome that can be created with characters in the range [L, R]
Examples:

Input: str = “amim”, Q[] = {{1, 4}, {3, 4}
Output:

In range [1, 4], only two palindromes “mam” and “mim” can be formed.
In range [3, 4], only “i” or “m” can be created using the characters in range.
Input: str = “aaaaa”, Q[] = {{1, 5}, {5, 5}
Output:

Approach: Let prefix[i][j] be an array which denotes the frequency of character char(j+97) in range 1 to i. For any range L to R, count the even frequencies and the odd frequencies. Since odd-1 is even, it can also contribute to the palindromic string. Also keep a mark for an odd frequency character, which can be inserted in the middle. Hence the length of the longest palindrome possible will be the sum of all even and the sum of odd-1 frequencies, adding 1 if there exists an odd frequency character.
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;``#define N 4` `// Function to return the length of the``// longest palindrome that can be formed``// using the characters in the range [l, r]``int` `performQueries(``int` `l, ``int` `r, ``int` `prefix[N][26])``{` `    ``// 0-based indexing``    ``l--;``    ``r--;` `    ``// Marks if there is an``    ``// odd frequency character``    ``bool` `flag = ``false``;` `    ``// Length of the longest palindrome``    ``// possible from characters in range``    ``int` `count = 0;` `    ``// Traverse for all characters``    ``// and count their frequencies``    ``for` `(``int` `i = 0; i < 26; i++) {` `        ``// Find the frequency in range 1 - r``        ``int` `cnt = prefix[r][i];` `        ``// Exclude the frequencies in range 1 - (l - 1)``        ``if` `(l > 0)``            ``cnt -= prefix[l - 1][i];` `        ``// If frequency is odd, then add 1 less than``        ``// the original frequency to make it even``        ``if` `(cnt % 2 == 1) {``            ``flag = ``true``;``            ``count += cnt - 1;``        ``}``        ``// Else completely add if even``        ``else``            ``count += cnt;``    ``}` `    ``// If any odd frequency character``    ``// is present then add 1``    ``if` `(flag)``        ``count += 1;` `    ``return` `count;``}` `// Function to pre-calculate the frequencies``// of the characters to reduce complexity``void` `preCalculate(string s, ``int` `prefix[N][26])``{``    ``int` `n = s.size();` `    ``// Iterate and increase the count``    ``for` `(``int` `i = 0; i < n; i++) {``        ``prefix[i][s[i] - ``'a'``]++;``    ``}` `    ``// Create a prefix type array``    ``for` `(``int` `i = 1; i < n; i++) {``        ``for` `(``int` `j = 0; j < 26; j++)``            ``prefix[i][j] += prefix[i - 1][j];``    ``}``}` `// Driver code``int` `main()``{``    ``string s = ``"amim"``;` `    ``// Pre-calculate prefix array``    ``int` `prefix[N][26];``    ``memset``(prefix, 0, ``sizeof` `prefix);``    ``preCalculate(s, prefix);` `    ``int` `queries[][2] = { { 1, 4 }, { 3, 4 } };``    ``int` `q = ``sizeof``(queries) / ``sizeof``(queries[0]);` `    ``// Perform queries``    ``for` `(``int` `i = 0; i < q; i++) {``        ``cout << performQueries(queries[i][0],``                               ``queries[i][1], prefix)``             ``<< endl;``    ``}` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``class` `GFG``{``    ` `static` `int` `N = ``4` `;` `// Function to return the length of the``// longest palindrome that can be formed``// using the characters in the range [l, r]``static` `int` `performQueries(``int` `l, ``int` `r, ``int` `prefix[][])``{` `    ``// 0-based indexing``    ``l--;``    ``r--;` `    ``// Marks if there is an``    ``// odd frequency character``    ``boolean` `flag = ``false``;` `    ``// Length of the longest palindrome``    ``// possible from characters in range``    ``int` `count = ``0``;` `    ``// Traverse for all characters``    ``// and count their frequencies``    ``for` `(``int` `i = ``0``; i < ``26``; i++)``    ``{` `        ``// Find the frequency in range 1 - r``        ``int` `cnt = prefix[r][i];` `        ``// Exclude the frequencies in range 1 - (l - 1)``        ``if` `(l > ``0``)``            ``cnt -= prefix[l - ``1``][i];` `        ``// If frequency is odd, then add 1 less than``        ``// the original frequency to make it even``        ``if` `(cnt % ``2` `== ``1``)``        ``{``            ``flag = ``true``;``            ``count += cnt - ``1``;``        ``}``        ` `        ``// Else completely add if even``        ``else``            ``count += cnt;``    ``}` `    ``// If any odd frequency character``    ``// is present then add 1``    ``if` `(flag)``        ``count += ``1``;` `    ``return` `count;``}` `// Function to pre-calculate the frequencies``// of the characters to reduce complexity``static` `void` `preCalculate(String s, ``int` `prefix[][])``{``    ``int` `n = s.length();` `    ``// Iterate and increase the count``    ``for` `(``int` `i = ``0``; i < n; i++)``    ``{``        ``prefix[i][s.charAt(i) - ``'a'``]++;``    ``}` `    ``// Create a prefix type array``    ``for` `(``int` `i = ``1``; i < n; i++)``    ``{``        ``for` `(``int` `j = ``0``; j < ``26``; j++)``            ``prefix[i][j] += prefix[i - ``1``][j];``    ``}``}` `// Driver code``public` `static` `void` `main(String args[])``{``    ``String s = ``"amim"``;` `    ``// Pre-calculate prefix array``    ``int` `prefix[][] = ``new` `int``[N][``26``];``    ``preCalculate(s, prefix);` `    ``int` `queries[][] = { { ``1``, ``4` `}, { ``3``, ``4` `} };``    ``int` `q = queries.length;` `    ``// Perform queries``    ``for` `(``int` `i = ``0``; i < q; i++)``    ``{``        ``System.out.println( performQueries(queries[i][``0``],``                            ``queries[i][``1``], prefix) );``    ``}``}``}` `// This code is contributed by Arnab Kundu`

## Python3

 `# Python3 implementation of the approach``N ``=` `4` `# Function to return the length of the``# longest palindrome that can be formed``# using the characters in the range [l, r]``def` `performQueries(l, r, prefix):` `    ``# 0-based indexing``    ``l ``-``=` `1``    ``r ``-``=` `1` `    ``# Marks if there is an``    ``# odd frequency character``    ``flag ``=` `False` `    ``# Length of the longest palindrome``    ``# possible from characters in range``    ``count ``=` `0` `    ``# Traverse for all characters``    ``# and count their frequencies``    ``for` `i ``in` `range``(``26``):` `        ``# Find the frequency in range 1 - r``        ``cnt ``=` `prefix[r][i]` `        ``# Exclude the frequencies in range 1 - (l - 1)``        ``if` `(l > ``0``):``            ``cnt ``-``=` `prefix[l ``-` `1``][i]` `        ``# If frequency is odd, then add 1 less than``        ``# the original frequency to make it even``        ``if` `(cnt ``%` `2` `=``=` `1``):``            ``flag ``=` `True``            ``count ``+``=` `cnt ``-` `1``        ` `        ``# Else completely add if even``        ``else``:``            ``count ``+``=` `cnt``    ` `    ``# If any odd frequency character``    ``# is present then add 1``    ``if` `(flag):``        ``count ``+``=` `1` `    ``return` `count` `# Function to pre-calculate the frequencies``# of the characters to reduce complexity``def` `preCalculate(s, prefix):` `    ``n ``=` `len``(s)` `    ``# Iterate and increase the count``    ``for` `i ``in` `range``(n):``        ``prefix[i][``ord``(s[i]) ``-` `ord``(``'a'``)] ``+``=` `1``    `  `    ``# Create a prefix type array``    ``for` `i ``in` `range``(``1``, n):``        ``for` `j ``in` `range``(``26``):``            ``prefix[i][j] ``+``=` `prefix[i ``-` `1``][j]``    ` `# Driver code``s ``=` `"amim"` `# Pre-calculate prefix array``prefix ``=` `[[``0` `for` `i ``in` `range``(``26``)]``             ``for` `i ``in` `range``(N)]` `preCalculate(s, prefix)` `queries ``=` `[[``1``, ``4``] , [``3``, ``4``]]``q ``=` `len``(queries)` `# Perform queries``for` `i ``in` `range``(q):``    ``print``(performQueries(queries[i][``0``],``                         ``queries[i][``1``],``                         ``prefix))``    ` `# This code is contributed``# by mohit kumar`

## C#

 `// C# implementation of the approach``using` `System;` `class` `GFG``{``    ` `static` `int` `N = 4 ;` `// Function to return the length of the``// longest palindrome that can be formed``// using the characters in the range [l, r]``static` `int` `performQueries(``int` `l, ``int` `r, ``int``[,] prefix)``{` `    ``// 0-based indexing``    ``l--;``    ``r--;` `    ``// Marks if there is an``    ``// odd frequency character``    ``bool` `flag = ``false``;` `    ``// Length of the longest palindrome``    ``// possible from characters in range``    ``int` `count = 0;` `    ``// Traverse for all characters``    ``// and count their frequencies``    ``for` `(``int` `i = 0; i < 26; i++)``    ``{` `        ``// Find the frequency in range 1 - r``        ``int` `cnt = prefix[r, i];` `        ``// Exclude the frequencies in range 1 - (l - 1)``        ``if` `(l > 0)``            ``cnt -= prefix[l - 1, i];` `        ``// If frequency is odd, then add 1 less than``        ``// the original frequency to make it even``        ``if` `(cnt % 2 == 1)``        ``{``            ``flag = ``true``;``            ``count += cnt - 1;``        ``}``        ` `        ``// Else completely add if even``        ``else``            ``count += cnt;``    ``}` `    ``// If any odd frequency character``    ``// is present then add 1``    ``if` `(flag)``        ``count += 1;` `    ``return` `count;``}` `// Function to pre-calculate the frequencies``// of the characters to reduce complexity``static` `void` `preCalculate(``string` `s, ``int``[,] prefix)``{``    ``int` `n = s.Length;` `    ``// Iterate and increase the count``    ``for` `(``int` `i = 0; i < n; i++)``    ``{``        ``prefix[i, s[i] - ``'a'``]++;``    ``}` `    ``// Create a prefix type array``    ``for` `(``int` `i = 1; i < n; i++)``    ``{``        ``for` `(``int` `j = 0; j < 26; j++)``            ``prefix[i, j] += prefix[i - 1, j];``    ``}``}` `// Driver code``public` `static` `void` `Main()``{``    ``string` `s = ``"amim"``;` `    ``// Pre-calculate prefix array``    ``int``[,] prefix = ``new` `int``[N, 26];``    ``preCalculate(s, prefix);` `    ``int``[,] queries = { { 1, 4 }, { 3, 4 } };``    ``int` `q = queries.Length;` `    ``// Perform queries``    ``for` `(``int` `i = 0; i < q; i++)``    ``{``        ``Console.WriteLine( performQueries(queries[i, 0],``                            ``queries[i, 1], prefix) );``    ``}``}``}` `// This code is contributed by Code_Mech`

## Javascript

 ``

Output:

```3
1```

Time Complexity: O(26*N), as we are using nested loops to traverse 26*N times. Where N is the length of the string.

Auxiliary Space: O(26*N), as we are using extra space for the prefix matrix. Where N is the length of the string.

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