We say that a sequence of numbers is a palindrome if it is read the same backward or forward. For example, the sequence: 6, 15, 6, 3, 47, 3, 6, 15, 6 is a palindrome.

Implement the following function:
def construct_a_longest_palindrome (numbers_bank)

When given numbers_bank, a non-empty list of integers, it will create and return a list containing a longest possible palindrome made only with numbers from numbers_bank

Notes:
1. The longest palindrome might NOT contain all of the numbers in the sequence.
2. If no multi-number palindromes can be constructed, the function may return just one number (as a single number, alone, is a palindrome).
3. If there is more than one possible longest palindrome, your function can return any one of them.

For example, if numbers_bank=(3, 47, 6, 6, 5, 6, 15, 3, 22, 1, 6, 15). Then the call construct_a_longest_palindrome (numbers_bank) could return: [6, 15, 6, 3, 47, 3, 6, 15, 6] (Which is a palindrome of length 9, and there is no palindrome made only with numbers from numbers_bank that is longer than 9).

Implementation requirements:

1. You may use one Array Queue, one ArrayStack, and one ChaniningHashTableMap.
2. Your function has to run in expected (average) linear time. That is, if numbers_bank is a list with n numbers, your function should run in O(n) average case.
3. Besides the queue, stack, hash table, and the list that is created and returned, you may use only constant additional space. That is, besides the queue, stack, hash table, and the returned list, you may use variables to store an integer, a double, etc. However, you may not use an additional data structure (such as another list, stack, queue, etc.) to store non-constant number of elements.

Check the explanation

Explanation:

Code

##a simple line of code is to first of all

import java.io.*;

import java.util.*;

public class Main

{

##in line with the question, the first implementation requirement is to use ##one Array Queue, one ArrayStack, and one ChaniningHashTableMap.

public static List<Integer> construct_a_longest_pallindrome(int a[]){

Map <Integer,Integer> map = new HashMap<>();

List<Integer> ans1 = new ArrayList<>();

List<Integer> ans2 = new ArrayList<>();

for(int i=0;i<a.length;i++){

if(map.containsKey(a[i])){

map.put(a[i],map.get(a[i])+1);

}else

map.put(a[i],1);

}

int pos1 = 0;

int pos2 = 0;

for(Integer key : map.keySet()){

int val = map.get(key);

while(val % 2 == 0){

ans1.add(key);

ans2.add(key);

val = val-2;

}

if(val == 0)

map.remove(key);

else

map.put(key,1);

}

if(map.isEmpty() == false){

ans1.add(map.keySet().iterator().next());

}

Collections.reverse(ans2);

ans1.addAll(ans2);

return ans1;

}

  public static void main(String[] args) {

      Scanner sc = new Scanner(System.in);

      System.out.println("Enter the size of array");

      int n = sc.nextInt();

      int arr[] = new int[n];

      for(int i=0;i<n;i++){

      arr[i] = sc.nextInt();

      }

      System.out.println(construct_a_longest_pallindrome(arr));

  }

}

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