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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Java














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// 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 



















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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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C#














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// 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 



















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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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