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Arrange given numbers to form the smallest number
• Difficulty Level : Hard
• Last Updated : 03 Jul, 2019

Given an array arr[] of integer elements, the task is to arrange them in such a way that these numbers form the smallest possible number.
For example, if the given array is {5, 6, 2, 9, 21, 1} then the arrangement will be 1212569.

Examples:

Input: arr[] = {5, 6, 2, 9, 21, 1}
Output: 1212569

Input: arr[] = {1, 2, 1, 12, 33, 211, 50}
Output: 111221123350

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: If all the given numbers are of at most one digit then simple approach is sorting all numbers in ascending order. But if there are sum number which have more than a single digit then this approach will not work.
Therefore, we have to sort the array by comparing any two elements in the following way:
If the elements are A and B, then compare (A + B) with (B + A) where + represents concatenation.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``#include ``using` `namespace` `std;`` ` `// Utility function to print``// the contents of an array``void` `printArr(``int` `arr[], ``int` `n)``{``    ``for` `(``int` `i = 0; i < n; i++)``        ``cout << arr[i];``}`` ` `// A comparison function that return true``// if 'AB' is smaller than 'BA' when``// we concatenate two numbers 'A' and 'B'``// For example, it will return true if``// we pass 12 and 24 as arguments.``// This function will be used by sort() function``bool` `compare(``int` `num1, ``int` `num2)``{``    ``// to_string function is predefined function``    ``// to convert a number in string`` ` `    ``// Convert first number to string format``    ``string A = to_string(num1);`` ` `    ``// Convert second number to string format``    ``string B = to_string(num2);`` ` `    ``// Check if 'AB' is smaller or 'BA'``    ``// and return bool value since``    ``// comparison operator '<=' returns``    ``// true or false``    ``return` `(A + B) <= (B + A);``}`` ` `// Function to print the arrangement``// with the smallest value``void` `printSmallest(``int` `N, ``int` `arr[])``{``    ``// If we pass the name of the comparison``    ``// function it will sort the array``    ``// according to the compare function``    ``sort(arr, arr + N, compare);`` ` `    ``// Print the sorted array``    ``printArr(arr, N);``}`` ` `// Driver code``int` `main()``{``    ``int` `arr[] = { 5, 6, 2, 9, 21, 1 };``    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);``    ``printSmallest(N, arr);`` ` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach ``class` `GFG``{`` ` `    ``// Utility function to print``    ``// the contents of an array``    ``public` `static` `void` `printArr(``int``[] arr, ``int` `n) ``    ``{``        ``for` `(``int` `i = ``0``; i < n; i++)``            ``System.out.print(arr[i]);``    ``}`` ` `    ``// A comparison function that return negative``    ``// if 'AB' is smaller than 'BA' when``    ``// we concatenate two numbers 'A' and 'B'``    ``// For example, it will return negative value if``    ``// we pass 12 and 24 as arguments.``    ``// This function will be used during sort``    ``public` `static` `int` `compare(``int` `num1, ``int` `num2)``    ``{`` ` `        ``// toString function is predefined function``        ``// to convert a number in string`` ` `        ``// Convert first number to string format``        ``String A = Integer.toString(num1);`` ` `        ``// Convert second number to string format``        ``String B = Integer.toString(num2);``         ` `        ``// Check if 'AB' is smaller or 'BA'``        ``// and return integer value``        ``return` `(A+B).compareTo(B+A);``    ``}`` ` `    ``// Function to print the arrangement``    ``// with the smallest value``    ``public` `static` `void` `printSmallest(``int` `N, ``int``[] arr) ``    ``{`` ` `        ``// Sort using compare function which``        ``// is defined above``        ``for` `(``int` `i = ``0``; i < N; i++)``        ``{``            ``for` `(``int` `j = i + ``1``; j < N; j++)``            ``{``                ``if` `(compare(arr[i], arr[j]) > ``0``)``                ``{``                    ``int` `temp = arr[i];``                    ``arr[i] = arr[j];``                    ``arr[j] = temp;``                ``}``            ``}``        ``}`` ` `        ``// Print the sorted array``        ``printArr(arr, N);``    ``}`` ` `    ``// Driver code``    ``public` `static` `void` `main(String[] args) ``    ``{``        ``int``[] arr = { ``5``, ``6``, ``2``, ``9``, ``21``, ``1` `};``        ``int` `N = arr.length;``        ``printSmallest(N, arr);``    ``}``}`` ` `// This code is contributed by``// sanjeev2552`

## Python3

 `# Python3 implementation of the approach`` ` `# Utility function to print``# the contents of an array``def` `printArr(arr, n):`` ` `    ``for` `i ``in` `range``(``0``, n):``        ``print``(arr[i], end ``=` `"")`` ` `# A comparison function that return true``# if 'AB' is smaller than 'BA' when``# we concatenate two numbers 'A' and 'B'``# For example, it will return true if``# we pass 12 and 24 as arguments.``# This function will be used by sort() function``def` `compare(num1, num2):`` ` `    ``# Convert first number to string format``    ``A ``=` `str``(num1)`` ` `    ``# Convert second number to string format``    ``B ``=` `str``(num2)`` ` `    ``# Check if 'AB' is smaller or 'BA'``    ``# and return bool value since``    ``# comparison operator '<=' returns``    ``# true or false``    ``return` `int``(A ``+` `B) <``=` `int``(B ``+` `A)``     ` `def` `sort(arr):``     ` `    ``for` `i ``in` `range``(``len``(arr)):``        ``for` `j ``in` `range``(i ``+` `1``, ``len``(arr)):``             ` `            ``if` `compare(arr[i], arr[j]) ``=``=` `False``:``                ``arr[i], arr[j] ``=` `arr[j], arr[i]`` ` `# Function to print the arrangement``# with the smallest value``def` `printSmallest(N, arr):`` ` `    ``# If we pass the name of the comparison``    ``# function it will sort the array``    ``# according to the compare function``    ``sort(arr)`` ` `    ``# Print the sorted array``    ``printArr(arr, N)`` ` `# Driver code``if` `__name__ ``=``=` `"__main__"``:`` ` `    ``arr ``=` `[``5``, ``6``, ``2``, ``9``, ``21``, ``1``]``    ``N ``=` `len``(arr)``    ``printSmallest(N, arr)`` ` `# This code is contributed by Rituraj Jain`

## C#

 `// C# implementation for above approach``using` `System;`` ` `class` `GFG``{`` ` `    ``// Utility function to print``    ``// the contents of an array``    ``public` `static` `void` `printArr(``int``[] arr, ``int` `n) ``    ``{``        ``for` `(``int` `i = 0; i < n; i++)``            ``Console.Write(arr[i]);``    ``}`` ` `    ``// A comparison function that return negative``    ``// if 'AB' is smaller than 'BA' when``    ``// we concatenate two numbers 'A' and 'B'``    ``// For example, it will return negative value if``    ``// we pass 12 and 24 as arguments.``    ``// This function will be used during sort``    ``public` `static` `int` `compare(``int` `num1, ``int` `num2)``    ``{`` ` `        ``// toString function is predefined function``        ``// to convert a number in string`` ` `        ``// Convert first number to string format``        ``String A = num1.ToString();`` ` `        ``// Convert second number to string format``        ``String B = num2.ToString();``         ` `        ``// Check if 'AB' is smaller or 'BA'``        ``// and return integer value``        ``return` `(A+B).CompareTo(B+A);``    ``}`` ` `    ``// Function to print the arrangement``    ``// with the smallest value``    ``public` `static` `void` `printSmallest(``int` `N, ``int``[] arr) ``    ``{`` ` `        ``// Sort using compare function which``        ``// is defined above``        ``for` `(``int` `i = 0; i < N; i++)``        ``{``            ``for` `(``int` `j = i + 1; j < N; j++)``            ``{``                ``if` `(compare(arr[i], arr[j]) > 0)``                ``{``                    ``int` `temp = arr[i];``                    ``arr[i] = arr[j];``                    ``arr[j] = temp;``                ``}``            ``}``        ``}`` ` `        ``// Print the sorted array``        ``printArr(arr, N);``    ``}`` ` `    ``// Driver code``    ``public` `static` `void` `Main(String[] args) ``    ``{``        ``int``[] arr = { 5, 6, 2, 9, 21, 1 };``        ``int` `N = arr.Length;``        ``printSmallest(N, arr);``    ``}``}`` ` `// This code is contributed by Rajput-Ji`

## PHP

 ``
Output:
```1212569
```

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