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

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 <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; 
} 

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 

PHP

<?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 
  
?> 

Output:

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

C++

Python3

PHP

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