CSES Solutions – Palindrome Reorder

Given a string S, your task is to reorder its letters in such a way that it becomes a palindrome (i.e., it reads the same forwards and backwards).

Examples:

Input: S = “AAAACACBA”
Output: AAACBCAAA
Explanation: We can reorder “AAAACACBA” to “AAACBCAAA” to get a palindrome string.

Input: S = “AAABBB”
Output: NO SOLUTION
Explanation: We cannot reorder “AAABBB” to get a palindrome string.

Approach: To solve the problem, follow the below idea:

We can construct the palindrome by recording the frequency of every character in the string S. If the character occurs even number of times in the string, then we can construct the palindromic string by placing equal number of characters at same distance from the middle of the string. Otherwise, if the character occurs odd number of times, then we can only have one occurrence in the middle and then distribute the remaining even number of characters equally at same distance from the middle of the string. Also, we can have at most one character that occurs odd number of times as that character will be placed in the middle.

Step-by-step algorithm:

• Count the frequency of all characters in the string S.
• If more than one character has odd frequency, then it is not possible to reorder the string to make it palindrome.
• Use two pointers, say left and right to keep track of the positions where we have to keep the next pair of same characters.
• If exactly one character has odd frequency, then place one such character at the middle of the string and now we will be left will all characters having even frequency which we can distribute equally with same distance from the middle of the string.
• If no character has odd frequency, then also we can distribute equally with same distance from the middle of the string.
• Finally, return the constructed palindromic string.

Below is the implementation of the algorithm:

C++

#include <bits/stdc++.h>
using namespace std;

// function to construct a palindromic string
string solve(string S)
{
    int N = S.length();
    string ans(N, ' ');

    // frequency array to count the occurrence of each
    // character
    int freq[26] = {};
    for (int i = 0; i < N; i++) {
        freq[S[i] - 'A'] += 1;
    }

    // Count the number of character having odd frequency
    int cnt = 0;
    for (int i = 0; i < 26; i++) {
        if (freq[i] % 2 != 0) {
            cnt += 1;
        }
    }

    // If more than one characters have odd frequency, then
    // no solution exists
    if (cnt > 1)
        return "NO SOLUTION";

    int left = 0, right = N - 1;
    for (int i = 0; i < N; i++) {
        if (freq[S[i] - 'A'] % 2 == 1) {
            ans[N / 2] = S[i];
            freq[S[i] - 'A'] -= 1;
        }
        while (freq[S[i] - 'A'] > 0) {
            ans[left++] = ans[right--] = S[i];
            freq[S[i] - 'A'] -= 2;
        }
    }
    return ans;
}

int main()
{
    // Sample Input
    string S = "AAAACACBA";
    cout << solve(S) << endl;
    return 0;
}

Java

import java.util.Arrays;

public class PalindromicString {

    // function to construct a palindromic string
    static String solve(String S) {
        int N = S.length();
        char[] ans = new char[N];

        // frequency array to count the occurrence of each character
        int[] freq = new int[26];
        for (int i = 0; i < N; i++) {
            freq[S.charAt(i) - 'A'] += 1;
        }

        // Count the number of characters having odd frequency
        int cnt = 0;
        for (int i = 0; i < 26; i++) {
            if (freq[i] % 2 != 0) {
                cnt += 1;
            }
        }

        // If more than one character has odd frequency, then no solution exists
        if (cnt > 1)
            return "NO SOLUTION";

        int left = 0, right = N - 1;
        for (int i = 0; i < 26; i++) {
            while (freq[i] > 1) {
                ans[left++] = ans[right--] = (char) ('A' + i);
                freq[i] -= 2;
            }
        }

        for (int i = 0; i < 26; i++) {
            if (freq[i] == 1) {
                ans[N / 2] = (char) ('A' + i);
                break;
            }
        }

        return new String(ans);
    }

    public static void main(String[] args) {
        // Sample Input
        String S = "AAAACACBA";
        System.out.println(solve(S));
    }
}

// This code is contributed by shivamgupta0987654321

JavaScript

// Function to construct a palindromic string
function solve(S) {
    const N = S.length;
    const ans = new Array(N);

    // Frequency array to count the occurrence of each character
    const freq = new Array(26).fill(0);
    for (let i = 0; i < N; i++) {
        freq[S.charCodeAt(i) - 65] += 1;
    }

    // Count the number of characters having odd frequency
    let cnt = 0;
    for (let i = 0; i < 26; i++) {
        if (freq[i] % 2 !== 0) {
            cnt += 1;
        }
    }

    // If more than one character has odd frequency, then no solution exists
    if (cnt > 1)
        return "NO SOLUTION";

    let left = 0, right = N - 1;
    for (let i = 0; i < 26; i++) {
        while (freq[i] > 1) {
            ans[left++] = ans[right--] = String.fromCharCode(65 + i);
            freq[i] -= 2;
        }
    }

    for (let i = 0; i < 26; i++) {
        if (freq[i] === 1) {
            ans[Math.floor(N / 2)] = String.fromCharCode(65 + i);
            break;
        }
    }

    return ans.join('');
}

// Sample Input
const S = "AAAACACBA";
console.log(solve(S));

Python3

# function to construct a palindromic string
def solve(S):
    N = len(S)
    ans = [' '] * N

    # frequency array to count the occurrence of each character
    freq = [0] * 26
    for i in range(N):
        freq[ord(S[i]) - ord('A')] += 1

    # Count the number of characters having odd frequency
    cnt = 0
    for i in range(26):
        if freq[i] % 2 != 0:
            cnt += 1

    # If more than one character has odd frequency, then no solution exists
    if cnt > 1:
        return "NO SOLUTION"

    left, right = 0, N - 1
    for i in range(N):
        if freq[ord(S[i]) - ord('A')] % 2 == 1:
            ans[N // 2] = S[i]
            freq[ord(S[i]) - ord('A')] -= 1
        while freq[ord(S[i]) - ord('A')] > 0:
            ans[left] = ans[right] = S[i]
            left += 1
            right -= 1
            freq[ord(S[i]) - ord('A')] -= 2

    return ''.join(ans)

# Sample Input
S = "AAAACACBA"
print(solve(S))

Output

AAACBCAAA

Time Complexity: O(N), where N is the length of input string S.
Auxiliary Space: O(1)