Open In App

# 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 the simple approach is sorting all numbers in ascending order. But if there is some 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[0]);``    ``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

 ``

## Javascript

 ``

Output:

`1212569`

Time Complexity: O(nlogn)
Auxiliary Space: O(1)

Approach 2: Implementing a custom quicksort algorithm

Another way to solve the problem is to implement a custom quicksort algorithm that uses the same comparison function as in approach 1. The quicksort algorithm recursively partitions the array into two subarrays based on the comparison function, and then combines the sorted subarrays to form the final result.

## C++

 `#include ``#include ``#include ` `using` `namespace` `std;` `bool` `compare(string a, string b) {``    ``return` `(a+b) < (b+a);``}` `int` `partition(vector& arr, ``int` `low, ``int` `high) {``    ``string pivot = arr[high];``    ``int` `i = low - 1;``    ``for` `(``int` `j = low; j <= high - 1; j++) {``        ``if` `(compare(arr[j], pivot)) {``            ``i++;``            ``swap(arr[i], arr[j]);``        ``}``    ``}``    ``swap(arr[i+1], arr[high]);``    ``return` `i+1;``}` `void` `quicksort(vector& arr, ``int` `low, ``int` `high) {``    ``if` `(low < high) {``        ``int` `pi = partition(arr, low, high);``        ``quicksort(arr, low, pi - 1);``        ``quicksort(arr, pi + 1, high);``    ``}``}` `string smallestNumber(vector<``int``>& nums) {``    ``vector numStrs;``    ``for` `(``int` `num : nums) {``        ``numStrs.push_back(to_string(num));``    ``}``    ``quicksort(numStrs, 0, numStrs.size()-1);``    ``string result = ``""``;``    ``for` `(string numStr : numStrs) {``        ``result += numStr;``    ``}``    ``return` `result;``}` `int` `main() {``    ``vector<``int``> nums = { 5, 6, 2, 9, 21, 1 };``    ``cout << smallestNumber(nums) << endl; ``// Output: 3033459``    ``return` `0;``}`

Output

```1212569
```

Time Complexity: O(nlogn)
Auxiliary Space: O(n)