Lexicographical smallest alternate Array
Given an array arr[] of distinct elements, the task is to rearrange the array such that it is lexicographically smallest and of the form arr[0] > arr[1] < arr[2] > arr[3] < …
Examples:
Input: arr[] = {3, 2, 1, 4, 5}
Output: 2 1 4 3 5
Input: arr[] = {10, 22}
Output: 22 10
Approach: In order to get the lexicographically smallest array, we can choose the minimum element as the first element but that will not satisfy the condition where the first element has to be strictly greater than the second element.
Now, the second-best choice is to choose the second minimum from the array and the only element which is smaller than it is the smallest element which will be the second element of the array.
Apply the same process for the rest of the array elements, choose the second minimum of the remaining elements and then choose the minimum for every two consecutive positions which can be obtained by first sorting the given array then swapping every two consecutive elements.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std; // Function to print the // contents of an array void printArr( int arr[], int n) { for ( int i = 0; i < n; i++) { cout << arr[i] << " " ; } } // Function to find the lexicographically // smallest alternating array void smallestArr( int arr[], int n) { // Sort the array sort(arr, arr + n); // Swap every two consecutive elements for ( int i = 0; i + 1 < n; i = i + 2) { swap(arr[i], arr[i + 1]); } // Print the re-arranged array printArr(arr, n); } // Driver code int main() { int arr[] = { 3, 2, 1, 4, 5 }; int n = sizeof (arr) / sizeof (arr[0]); smallestArr(arr, n); return 0; } |
Java
// Java implementation of the approach import java.util.Arrays; class GFG { // Function to print the // contents of an array static void printArr( int [] arr, int n) { for ( int i = 0 ; i < n; i++) System.out.print(arr[i] + " " ); } // Function to find the lexicographically // smallest alternating array static void smallestArr( int [] arr, int n) { // Sort the array Arrays.sort(arr); // Swap every two consecutive elements for ( int i = 0 ; i + 1 < n; i = i + 2 ) { int temp = arr[i]; arr[i] = arr[i + 1 ]; arr[i + 1 ] = temp; } // Print the re-arranged array printArr(arr, n); } // Driver code public static void main(String[] args) { int [] arr = { 3 , 2 , 1 , 4 , 5 }; int n = arr.length; smallestArr(arr, n); } } // This code is contributed by // sanjeev2552 |
Python3
# Python3 implementation of the approach # Function to print the # contents of an array def printArr(arr, n): for i in range (n): print (arr[i], end = " " ); # Function to find the lexicographically # smallest alternating array def smallestArr(arr, n): # Sort the array arr.sort(); # Swap every two consecutive elements for i in range ( 0 , n - 1 , 2 ): temp = arr[i]; arr[i] = arr[i + 1 ]; arr[i + 1 ] = temp; # Print the re-arranged array printArr(arr, n); # Driver code if __name__ = = '__main__' : arr = [ 3 , 2 , 1 , 4 , 5 ]; n = len (arr); smallestArr(arr, n); # This code contributed by Rajput-Ji |
C#
// C# implementation of the approach using System; class GFG { // Function to print the // contents of an array static void printArr( int [] arr, int n) { for ( int i = 0; i < n; i++) Console.Write(arr[i] + " " ); } // Function to find the lexicographically // smallest alternating array static void smallestArr( int [] arr, int n) { // Sort the array Array.Sort(arr); // Swap every two consecutive elements for ( int i = 0; i + 1 < n; i = i + 2) { int temp = arr[i]; arr[i] = arr[i + 1]; arr[i + 1] = temp; } // Print the re-arranged array printArr(arr, n); } // Driver code public static void Main(String[] args) { int [] arr = { 3, 2, 1, 4, 5 }; int n = arr.Length; smallestArr(arr, n); } } // This code is contributed by 29AjayKumar |
PHP
<?php // PHP implementation of the approach // Function to print the // contents of an array function printArr( $arr , $n ) { for ( $i = 0; $i < $n ; $i ++) { echo $arr [ $i ]; echo " " ; } } // Function to find the lexicographically // smallest alternating array function smallestArr( $arr , $n ) { // Sort the array sort( $arr ); // Swap every two consecutive elements for ( $i = 0; $i + 1 < $n ; $i = $i + 2) { $temp = $arr [ $i ]; $arr [ $i ] = $arr [ $i + 1]; $arr [ $i + 1] = $temp ; } // Print the re-arranged array printArr( $arr , $n ); } // Driver code $arr = array ( 3, 2, 1, 4, 5 ); $n = count ( $arr ); smallestArr( $arr , $n ); // This code is contributed by Naman_Garg. ?> |
Javascript
// javascript implementation of the approach // Function to print the // contents of an array function printArr(arr, n) { for ( var i = 0; i < n; i++) document.write(arr[i] + " " ); } // Function to find the lexicographically // smallest alternating array function smallestArr( arr, n) { // Sort the array arr.sort(); // Swap every two consecutive elements for ( var i = 0; i + 1 < n; i = i + 2) { var temp = arr[i]; arr[i] = arr[i + 1]; arr[i + 1] = temp; } // Print the re-arranged array printArr(arr, n); } // Driver code var arr = [ 3, 2, 1, 4, 5 ] ; var n = arr.length; smallestArr(arr, n); // This code is contributed by bunnyram19. |
2 1 4 3 5
Time Complexity: O(nlogn)
Auxiliary Space: O(1)
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