Arrange given numbers to form the smallest number

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



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++

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// C++ implementation of the approach
#include <algorithm>
#include <iostream>
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[0]);
    printSmallest(N, arr);
  
    return 0;
}

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Python3

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# 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

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PHP

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<?php
// Php implementation of the approach 
  
// Utility function to print 
// the contents of an array 
function printArr($arr, $n
    for ($i = 0; $i < $n; $i++) 
        echo $arr[$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 
function compare($num1, $num2
    // to_string function is predefined function 
    // to convert a number in string 
  
    // Convert first number to string format 
    $A = (string)$num1
  
    // Convert second number to string format 
    $B = (string)$num2
  
    // Check if 'AB' is smaller or 'BA' 
    // and return bool value since 
    // comparison operator '<=' returns 
    // true or false 
    if((int)($A . $B) <= (int)($B . $A))
    {
        return true;
    }
    else
        return false;
  
  
function sort_arr($arr)
{
      
    for ($i = 0; $i < count($arr) ; $i++)
    {
        for ($j = $i + 1;$j < count($arr) ; $j++)
        {
            if (compare($arr[$i], $arr[$j]) == false)
            {
                $temp = $arr[$i] ;
                $arr[$i] = $arr[$j] ;
                $arr[$j] = $temp ;
            }
        }
    }
        return $arr ;
    }
  
// Function to print the arrangement 
// with the smallest value 
function printSmallest($N, $arr
    // If we pass the name of the comparison 
    // function it will sort the array 
    // according to the compare function 
    $arr = sort_arr($arr); 
  
    // Print the sorted array 
    printArr($arr, $N); 
  
    // Driver code 
    $arr = array(5, 6, 2, 9, 21, 1 ); 
    $N = count($arr); 
    printSmallest($N, $arr); 
  
    // This code is contributed by Ryuga
  
?>

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Output:

1212569


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Improved By : rituraj_jain, AnkitRai01