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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 ` `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

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Javascript

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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 ``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 ` `// 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

 `= 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

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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.

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