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: 1212569Input: 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++
// 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
// 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
# 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#
// 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
<?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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