Find the largest Number that can be formed with the given Digits

Given an array of integers arr[] represents digits of a number. The task is to write a program to generate the largest number possible using these digits.

Note: The digits in the array are between 0 and 9. That is, 0 < arr[i] < 9.

Examples: 

Input: arr[] = {4, 7, 9, 2, 3}
Output: Largest number: 97432 

Input: arr[] = {8, 6, 0, 4, 6, 4, 2, 7}
Output: Largest number: 87664420 

Naive Approach:

The naive approach is to sort the given array of digits in descending order and then form the number using the digits in the array keeping the order of digits in the number the same as that of the sorted array.
Time Complexity: O(N logN), where N is the number of digits.

Below is the implementation of the above idea: 

C++

// C++ program to generate largest possible
// number with given digits
#include <bits/stdc++.h>

using namespace std;

// Function to generate largest possible
// number with given digits
int findMaxNum(int arr[], int n)
{
    // sort the given array in
    // descending order
    sort(arr, arr + n, greater<int>());

    int num = arr[0];

    // generate the number
    for (int i = 1; i < n; i++) {
        num = num * 10 + arr[i];
    }

    return num;
}

// Driver code
int main()
{
    int arr[] = { 1, 2, 3, 4, 5, 0 };

    int n = sizeof(arr) / sizeof(arr[0]);

    cout << findMaxNum(arr, n);

    return 0;
}

Java

// Java program to generate largest
// possible number with given digits
import java.util.*;
import java.util.Arrays;

class GFG {
    // Function to generate largest
    // possible number with given digits
    static int findMaxNum(int arr[], int n)
    {
        // sort the given array in
        // ascending order and then
        // traverse into descending
        Arrays.sort(arr);

        int num = arr[n - 1];

        // generate the number
        for (int i = n - 2; i >= 0; i--) {
            num = num * 10 + arr[i];
        }

        return num;
    }

    // Driver code
    public static void main(String[] args)
    {
        int arr[] = { 1, 2, 3, 4, 5, 0 };

        int n = arr.length;

        System.out.println(findMaxNum(arr, n));
    }
}

// This code is contributed by mits

Python3

# Python3 program to generate largest possible
# number with given digits

# Function to generate largest possible
# number with given digits


def findMaxNum(arr, n):

    # sort the given array in
    # descending order
    arr.sort(reverse=True)

    # initialize num with starting
    # element of an arr
    num = arr[0]

    # generate the number
    for i in range(1, n):
        num = num * 10 + arr[i]

    return num


# Driver code
if __name__ == "__main__":
    arr = [1, 2, 3, 4, 5, 0]
    n = len(arr)
    print(findMaxNum(arr, n))

C#

// C#  program to generate largest
// possible number with given digits
using System;

public class GFG {
    // Function to generate largest
    // possible number with given digits
    static int findMaxNum(int[] arr, int n)
    {
        // sort the given array in
        // ascending order and then
        // traverse into descending
        Array.Sort(arr);

        int num = arr[0];

        // generate the number
        for (int i = n - 1; i >= 0; i--) {
            num = num * 10 + arr[i];
        }

        return num;
    }

    // Driver code
    static public void Main()
    {
        int[] arr = { 1, 2, 3, 4, 5, 0 };
        int n = arr.Length;
        Console.WriteLine(findMaxNum(arr, n));
    }
}

// This code is contributed by Sachin..

PHP

<?php
// PHP program to generate
// largest possible number
// with given digits

// Function to generate
// largest possible number
// with given digits
function findMaxNum(&$arr, $n)
{
    // sort the given array
    // in descending order
    rsort($arr);

    $num = $arr[0];

    // generate the number
    for($i = 1; $i < $n; $i++)
    {
        $num = $num * 10 + $arr[$i];
    }

    return $num;
}

// Driver code
$arr = array(1, 2, 3, 4, 5, 0);
$n = sizeof($arr);
echo findMaxNum($arr,$n);

// This code is contributed
// by ChitraNayal
?>

Javascript

<script>

// Javascript program to generate largest possible
// number with given digits

// Function to generate largest possible
// number with given digits
function findMaxNum(arr, n)
{
    // sort the given array in
    // descending order
    arr.sort(function(a,b){return b-a;});

    var num = arr[0];

    // generate the number
    for(var i=1; i<n; i++)
    {
        num = num*10 + arr[i];
    }

    return num;
}

// Driver code
var arr = [1, 2, 3, 4, 5, 0];

var n = arr.length;

document.write(findMaxNum(arr,n));

</script>

Output

543210

Time complexity: O(nlogn)
Auxiliary space: O(1)

Efficient Approach: An efficient approach is to observe that we have to form the number using only digits from 0-9. Hence we can create a hash of size 10 to store the number of occurrences of the digits in the given array into the hash table. Where the key in the hash table will be digits from 0 to 9 and their values will be the count of their occurrences in the array.

Finally, print the digits the number of times they occur in descending order starting from the digit 9.

Below is the implementation of the above approach: 

C++

// C++ program to generate largest possible number with
// given digits
#include <bits/stdc++.h>
using namespace std;

// Function to generate largest possible number with given
// digits
void findMaxNum(int arr[], int n)
{
    // Declare a hash array of size 10 and initialize all
    // the elements to zero
    int hash[10] = { 0 };

    // store the number of occurrences of the digits in the
    // given array into the hash table
    for (int i = 0; i < n; i++)
        hash[arr[i]]++;

    // Traverse the hash in descending order to print the
    // required number
    for (int i = 9; i >= 0; i--)
        // Print the number of times a digits occurs
        for (int j = 0; j < hash[i]; j++)
            cout << i;
}

// Driver code
int main()
{
    int arr[] = { 1, 2, 3, 4, 5, 0 };
    int n = sizeof(arr) / sizeof(arr[0]);
    findMaxNum(arr, n);
    return 0;
}

// This code is contributed by Sania Kumari Gupta

C

// C program to generate largest possible number with
// given digits
#include <stdio.h>

// Function to generate largest possible number with given
// digits
void findMaxNum(int arr[], int n)
{
    // Declare a hash array of size 10 and initialize all
    // the elements to zero
    int hash[10] = { 0 };

    // store the number of occurrences of the digits in the
    // given array into the hash table
    for (int i = 0; i < n; i++)
        hash[arr[i]]++;

    // Traverse the hash in descending order to print the
    // required number
    for (int i = 9; i >= 0; i--)
        // Print the number of times a digits occurs
        for (int j = 0; j < hash[i]; j++)
            printf("%d", i);
}

// Driver code
int main()
{
    int arr[] = { 1, 2, 3, 4, 5, 0 };
    int n = sizeof(arr) / sizeof(arr[0]);
    findMaxNum(arr, n);
    return 0;
}

// This code is contributed by Sania Kumari Gupta

Java

// Java program to generate  largest possible number with
// given digits
class GFG {
    // Function to generate  largest possible number  with
    // given digits
    static void findMaxNum(int arr[], int n)
    {
        // Declare a hash array of  size 10 and initialize
        // all the elements to zero
        int[] hash = new int[10];
        // store the number of occurrences  of the digits in
        // the given array into the hash table
        for (int i = 0; i < n; i++)
            hash[arr[i]]++;

        // Traverse the hash in descending order to print
        // the required number
        for (int i = 9; i >= 0; i--)
            // Print the number of times a digits occurs
            for (int j = 0; j < hash[i]; j++)
                System.out.print(i);
    }

    // Driver code
    public static void main(String[] args)
    {
        int arr[] = { 1, 2, 3, 4, 5, 0 };
        int n = arr.length;
        findMaxNum(arr, n);
    }
}

// This code is contributed by Sania Kumari Gupta

Python 3

# Python 3 program to generate
# largest possible number
# with given digits

# Function to generate
# largest possible number
# with given digits
def findMaxNum(arr, n):

    # Declare a hash array of
    # size 10 and initialize
    # all the elements to zero
    hash = [0] * 10

    # store the number of occurrences
    # of the digits in the given array
    # into the hash table
    for i in range(n):
        hash[arr[i]] += 1

    # Traverse the hash in
    # descending order to
    # print the required number
    for i in range(9, -1, -1):

        # Print the number of
        # times a digits occurs
        for j in range(hash[i]):
            print(i, end = "")

# Driver code
if __name__ == "__main__":
    arr = [1, 2, 3, 4, 5, 0]
    n =len(arr)
    findMaxNum(arr,n)

# This code is contributed
# by ChitraNayal

C#

// C# program to generate
// largest possible number
// with given digits
using System;

class GFG
{

// Function to generate
// largest possible number
// with given digits
static void findMaxNum(int[] arr,
                       int n)
{
// Declare a hash array of
// size 10 and initialize
// all the elements to zero
int[] hash = new int[10];

// store the number of
// occurrences of the
// digits in the given
// array into the hash table
for(int i = 0; i < n; i++)
{
    hash[arr[i]]++;
}

// Traverse the hash in
// descending order to
// print the required number
for(int i = 9; i >= 0; i--)
{
    // Print the number of
    // times a digits occurs
    for(int j = 0; j < hash[i]; j++)
        Console.Write(i);
}
}

// Driver code
public static void Main()
{
    int[] arr = {1, 2, 3, 4, 5, 0};

    int n = arr.Length;

    findMaxNum(arr,n);
}
}

// This code is contributed
// by ChitraNayal

PHP

<?php
// PHP program to generate
// largest possible number
// with given digits

// Function to generate
// largest possible number
// with given digits
function findMaxNum($arr, $n)
{
    // Declare a hash array of
    // size 10 and initialize
    // all the elements to zero
    $hash = array_fill(0, 10, 0);

    // store the number of occurrences
    // of the digits in the given array
    // into the hash table
    for($i = 0; $i < $n; $i++)
        $hash[$arr[$i]] += 1;

    // Traverse the hash in
    // descending order to
    // print the required number
    for($i = 9; $i >= 0; $i--)

        // Print the number of
        // times a digits occurs
        for($j = 0; $j < $hash[$i]; $j++)
            echo $i;
}

// Driver code
$arr = array(1, 2, 3, 4, 5, 0);
$n = sizeof($arr);
findMaxNum($arr,$n);

// This code is contributed
// by mits
?>

Javascript

<script>

// Javascript program to generate largest possible
// number with given digits

// Function to generate largest possible
// number with given digits
function findMaxNum( arr, n)
{
    // Declare a hash array of size 10
    // and initialize all the elements to zero
    var hash = Array(10).fill(0);

    // store the number of occurrences of the digits
    // in the given array into the hash table
    for(var i=0; i<n; i++)
    {
        hash[arr[i]]++;
    }

    // Traverse the hash in descending order
    // to print the required number
    for(var i=9; i>=0; i--)
    {
        // Print the number of times a digits occurs
        for(var j=0; j<hash[i]; j++)
            document.write(i);
    }
}

// Driver code
var arr = [1, 2, 3, 4, 5, 0];

var n = arr.length;

findMaxNum(arr,n);

</script>

Output

543210

Complexity Analysis:

• Time Complexity: O(N), where N is the number of digits. 
• Auxiliary Space: O(1), size of hash is only 10 which is a constant.