# 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++ 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 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 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# 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 `

 ` `

Output:
```1212569
```

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