Largest palindromic number by permuting digits

Given N(very large), the task is to print the largest palindromic number obtained by permuting the digits of N. If it is not possible to make a palindromic number, then print an appropriate message. 

Examples :

Input : 313551
Output : 531135
Explanations : 531135 is the largest number 
which is a palindrome, 135531, 315513 and other 
numbers can also be formed but we need the highest 
of all of the palindromes. 

Input : 331
Output : 313

Input : 3444
Output : Palindrome cannot be formed 

Naive Approach: The naive approach will be to try all the permutations possible, and print the largest of such combinations, which is a palindrome. 

Efficient Approach:

An efficient approach will be to use the Greedy algorithm. Since the number is large, store the number in a string. Store the count of occurrences of every digit in the given number on a map. Check if it is possible to form a palindrome or not. If the digits of the given number can be rearranged to form a palindrome, then apply the greedy approach to obtain the number. Check for the occurrence of every digit (9 to 0), and place every available digit at the front and back. 

Initially, the front pointer will be at index 0, as the largest digit will be placed at first to make the number a large one. With every step, move the front pointer 1 position ahead. If the digit occurs an odd number of times, then place one digit in the middle and the rest of the even number of digits at front and back. Keep repeating the process (map[digit]/2) the number of times for a single digit. After placing a particular digit that occurs an even number of times at the front and back, move the front pointer one step ahead. The placing is done till map[digit] is 0. The char array will have the largest palindromic number possible after the completion of the placing of digits greedily. 

In the worst case, the time complexity will be O(10 * (length of string/2)), in case the number consists of the same digit at every position. 

Below is the implementation of the above idea: 

C++

// CPP program to print the largest palindromic
// number by permuting digits of a number
#include <bits/stdc++.h>
using namespace std;

// function to check if a number can be
// permuted to form a palindrome number
bool possibility(unordered_map<int, int> m,
                 int length, string s)
{
    // counts the occurrence of number which is odd
    int countodd = 0;
    for (int i = 0; i < length; i++) {

        // if occurrence is odd
        if (m[s[i] - '0'] & 1)
            countodd++;

        // if number exceeds 1
        if (countodd > 1)
            return false;
    }

    return true;
}

// function to print the largest palindromic number
// by permuting digits of a number
void largestPalindrome(string s)
{

    // string length
    int l = s.length();

    // map that marks the occurrence of a number
    unordered_map<int, int> m;
    for (int i = 0; i < l; i++)
        m[s[i] - '0']++;

    // check the possibility of a palindromic number
    if (possibility(m, l, s) == false) {
        cout << "Palindrome cannot be formed";
        return;
    }

    // string array that stores the largest
    // permuted palindromic number
    char largest[l];

    // pointer of front
    int front = 0;

    // greedily start from 9 to 0 and place the
    // greater number in front and odd in the
    // middle
    for (int i = 9; i >= 0; i--) {

        // if the occurrence of number is odd
        if (m[i] & 1) {

            // place one odd occurring number
            // in the middle
            largest[l / 2] = char(i + 48);

            // decrease the count
            m[i]--;

            // place the rest of numbers greedily
            while (m[i] > 0) {
                largest[front] = char(i + 48);
                largest[l - front - 1] = char(i + 48);
                m[i] -= 2;
                front++;
            }
        }
        else {

            // if all numbers occur even times,
            // then place greedily
            while (m[i] > 0) {

                // place greedily at front
                largest[front] = char(i + 48);
                largest[l - front - 1] = char(i + 48);

                // 2 numbers are placed, so decrease the count
                m[i] -= 2;

                // increase placing position
                front++;
            }
        }
    }

    // print the largest string thus formed
    for (int i = 0; i < l; i++)
        cout << largest[i];
}

// Driver Code
int main()
{
    string s = "313551";
    largestPalindrome(s);
    return 0;
}

Java

// JAVA program to print the
// largest palindromic number
// by permuting digits of a number
import java.util.*;
class GFG{

// Function to check if a number can be
// permuted to form a palindrome number
static boolean possibility(HashMap<Integer,
                                   Integer> m,
                           int length, String s)
{
  // counts the occurrence of number
  // which is odd
  int countodd = 0;

  for (int i = 0; i < length; i++)
  {
    // if occurrence is odd
    if (m.get(s.charAt(i) - '0') % 2 == 1)
      countodd++;

    // if number exceeds 1
    if (countodd > 1)
      return false;
  }

  return true;
}

// function to print the largest
// palindromic number by permuting
// digits of a number
static void largestPalindrome(String s)
{
  // String length
  int l = s.length();

  // map that marks the occurrence
  // of a number
  HashMap<Integer,
          Integer> m = new HashMap<>();

  for (int i = 0; i < l; i++)
    if(m.containsKey(s.charAt(i) - '0'))
      m.put(s.charAt(i) - '0',
      m.get(s.charAt(i) - '0') + 1);
  else
    m.put(s.charAt(i) - '0', 1);

  // check the possibility of a
  // palindromic number
  if (possibility(m, l, s) == false)
  {
    System.out.print("Palindrome cannot be formed");
    return;
  }

  // String array that stores
  // the largest permuted
  // palindromic number
  char []largest = new char[l];

  // pointer of front
  int front = 0;

  // greedily start from 9 to 0
  // and place the greater number
  // in front and odd in the middle
  for (int i = 9; i >= 0; i--)
  {
    // if the occurrence of
    // number is odd
    if (m.containsKey(i) &&
        m.get(i)%2==1)
    {
      // place one odd occurring
      // number in the middle
      largest[l / 2] = (char)(i + 48);

      // decrease the count
      m.put(i, m.get(i)-1);

      // place the rest of
      // numbers greedily
      while (m.get(i) > 0)
      {
        largest[front] = (char)(i + 48);
        largest[l - front - 1] =
                    (char)(i + 48);
        m.put(i, m.get(i) - 2);
        front++;
      }
    }
    else
    {
      // if all numbers occur even
      // times, then place greedily
      while (m.containsKey(i) &&
             m.get(i) > 0)
      {
        // place greedily at front
        largest[front] = (char)(i + 48);
        largest[l - front - 1] =
               (char)(i + 48);

        // 2 numbers are placed,
        // so decrease the count
        m.put(i, m.get(i) - 2);

        // increase placing position
        front++;
      }
    }
  }

  // print the largest String
  // thus formed
  for (int i = 0; i < l; i++)
    System.out.print(largest[i]);
}

// Driver Code
public static void main(String[] args)
{
  String s = "313551";
  largestPalindrome(s);
}
}

// This code is contributed by Rajput-Ji

Python3

# Python3 program to print the largest palindromic
# number by permuting digits of a number
from collections import defaultdict

# Function to check if a number can be
# permuted to form a palindrome number
def possibility(m, length, s):

    # counts the occurrence of
    # number which is odd
    countodd = 0
    for i in range(0, length):

        # if occurrence is odd
        if m[int(s[i])] & 1:
            countodd += 1

        # if number exceeds 1
        if countodd > 1:
            return False

    return True

# Function to print the largest palindromic
# number by permuting digits of a number
def largestPalindrome(s):

    # string length
    l = len(s)

    # map that marks the occurrence of a number
    m = defaultdict(lambda:0)
    for i in range(0, l):
        m[int(s[i])] += 1

    # check the possibility of a
    # palindromic number
    if possibility(m, l, s) == False:
        print("Palindrome cannot be formed")
        return

    # string array that stores the largest
    # permuted palindromic number
    largest = [None] * l

    # pointer of front
    front = 0

    # greedily start from 9 to 0 and place the
    # greater number in front and odd in the middle
    for i in range(9, -1, -1):

        # if the occurrence of number is odd
        if m[i] & 1:

            # place one odd occurring number
            # in the middle
            largest[l // 2] = chr(i + 48)

            # decrease the count
            m[i] -= 1

            # place the rest of numbers greedily
            while m[i] > 0:
                largest[front] = chr(i + 48)
                largest[l - front - 1] = chr(i + 48)
                m[i] -= 2
                front += 1

        else:

            # if all numbers occur even times,
            # then place greedily
            while m[i] > 0:

                # place greedily at front
                largest[front] = chr(i + 48)
                largest[l - front - 1] = chr(i + 48)

                # 2 numbers are placed,
                # so decrease the count
                m[i] -= 2

                # increase placing position
                front += 1

    # print the largest string thus formed
    for i in range(0, l):
        print(largest[i], end = "")

# Driver Code
if __name__ == "__main__":

    s = "313551"
    largestPalindrome(s)

# This code is contributed by Rituraj Jain

C#

// C# program to print the largest
// palindromic number by permuting
// digits of a number
using System;
using System.Collections.Generic;

class GFG{

// Function to check if a number can be
// permuted to form a palindrome number
static bool possibility(Dictionary<int, int> m,
                        int length, string s)
{

    // Counts the occurrence of number
    // which is odd
    int countodd = 0;

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

        // If occurrence is odd
        if ((m[s[i] - '0'] & 1) != 0)
            countodd++;

        // If number exceeds 1
        if (countodd > 1)
            return false;
    }
    return true;
}

// Function to print the largest palindromic
// number by permuting digits of a number
static void largestPalindrome(string s)
{

    // string length
    int l = s.Length;

    // Map that marks the occurrence of a number
    Dictionary<int,
               int> m = new Dictionary<int,
                                       int>();

    for(int i = 0; i < 10; i++)
        m[i] = 0;

    for(int i = 0; i < l; i++)
        m[s[i] - '0']++;

    // Check the possibility of a
    // palindromic number
    if (possibility(m, l, s) == false)
    {
        Console.Write("Palindrome cannot be formed");
        return;
    }

    // string array that stores the largest
    // permuted palindromic number
    char []largest = new char[l];

    // Pointer of front
    int front = 0;

    // Greedily start from 9 to 0 and place the
    // greater number in front and odd in the
    // middle
    for(int i = 9; i >= 0; i--)
    {

        // If the occurrence of number is odd
        if ((m[i] & 1) != 0)
        {

            // Place one odd occurring number
            // in the middle
            largest[l / 2] = (char)(i + '0');

            // Decrease the count
            m[i]--;

            // Place the rest of numbers greedily
            while (m[i] > 0)
            {
                largest[front] = (char)(i + '0');
                largest[l - front - 1] = (char)(i + '0');
                m[i] -= 2;
                front++;
            }
        }
        else
        {

            // If all numbers occur even times,
            // then place greedily
            while (m[i] > 0)
            {

                // Place greedily at front
                largest[front] = (char)(i + '0');
                largest[l - front - 1] = (char)(i + '0');

                // 2 numbers are placed, so
                // decrease the count
                m[i] -= 2;

                // Increase placing position
                front++;
            }
        }
    }

    // Print the largest string thus formed
    for(int i = 0; i < l; i++)
    {
        Console.Write(largest[i]);
    }
}

// Driver Code
public static void Main(string[] args)
{
    string s = "313551";

    largestPalindrome(s);
}
}

// This code is contributed by rutvik_56

Javascript

<script>
// Javascript program to print the largest palindromic
// number by permuting digits of a number

// function to check if a number can be
// permuted to form a palindrome number
function possibility(m,length, s)
{
    // counts the occurrence of number which is odd
    var countodd = 0;
    for (var i = 0; i < length; i++) {

        // if occurrence is odd
        if (m.get(s.charCodeAt(i) - 48) & 1)
            countodd++;

        // if number exceeds 1
        if (countodd > 1)
            return false;
    }

    return true;
}

// function to print the largest palindromic number
// by permuting digits of a number
function largestPalindrome(s)
{

    // string length
    var l = s.length;

    // map that marks the occurrence of a number
    var m = new Map();
    for (var i = 0; i < l; i++){
        if (m.has(s.charCodeAt(i) - 48))
            m.set(s.charCodeAt(i) - 48, m.get(s.charCodeAt(i) - 48)+1);
        else
            m.set(s.charCodeAt(i) - 48, 1);

       }

    // check the possibility of a palindromic number
    if (possibility(m, l, s) == false) {
        document.write("Palindrome cannot be formed");
        return;
    }

    // string array that stores the largest
    // permuted palindromic number
    var largest = new Array(l);

    // pointer of front
    var front = 0;

    // greedily start from 9 to 0 and place the
    // greater number in front and odd in the
    // middle
    for (var i = 9; i >= 0; i--) {

        // if the occurrence of number is odd
        if (m.get(i) & 1) {

            // place one odd occurring number
            // in the middle
            largest[(Math.floor(l / 2))] = String.fromCharCode(i + 48);

            // decrease the count
            m.set(i, m.get(i)-1);

            // place the rest of numbers greedily
            while (m.get(i) > 0) {
                largest[front] = String.fromCharCode(i + 48);
                largest[l - front - 1] = String.fromCharCode(i + 48);
                m.set(i, m.get(i)-2);
                front++;
            }
        }
        else {

            // if all numbers occur even times,
            // then place greedily
            while (m.get(i) > 0){

                // place greedily at front
                largest[front] = String.fromCharCode(i + 48);
                largest[l - front - 1] = String.fromCharCode(i + 48);

                // 2 numbers are placed, so decrease the count
                m.set(i, m.get(i)-2);

                // increase placing position
                front++;
            }
        }
    }

    // print the largest string thus formed
    for (var i = 0; i < l; i++)
        document.write(largest[i]);
}
// driver code
var s = "313551";
largestPalindrome(s);
// This code contributed by shubhamsingh10
</script>

Output

531135

Time Complexity: O(N), as we are using loop to traverse N times.
Auxiliary Space: O(N), as we are using extra space for map m and largest array.