Given an array of n distinct elements and a number x, arrange array elements according to the absolute difference with x, i. e., element having minimum difference comes first and so on, using constant extra space.
Note : If two or more elements are at equal distance arrange them in same sequence as in the given array.
Examples:
Input : arr[] = {10, 5, 3, 9, 2}
x = 7
Output : arr[] = {5, 9, 10, 3, 2}
Explanation :
7 - 10 = 3(abs)
7 - 5 = 2
7 - 3 = 4
7 - 9 = 2(abs)
7 - 2 = 5
So according to the difference with X,
elements are arranged as 5, 9, 10, 3, 2.
Input : arr[] = {1, 2, 3, 4, 5}
x = 6
Output : arr[] = {5, 4, 3, 2, 1}
The above problem has already been explained in a previous post here. It takes O(n log n) time and O(n) extra space. The below solution though has a relatively bad time complexity i.e O(n^2) but it does the work without using any additional space or memory.
The solution is a based on Insertion Sort . For every i (1<= i < n) we compare the absolute value of the difference of arr[i] with the given number x (Let this be ‘diff’ ). We then compare this difference with the difference of abs(arr[j]-x) where 0<= j < i (Let this if abdiff). If diff is greater than abdiff, we shift the values in the array to accommodate arr[i] in it’s correct position.
C++
// C++ program to sort an array based on absolute// difference with a given value x.#include <bits/stdc++.h>using namespace std;void arrange(int arr[], int n, int x){ // Below lines are similar to insertion sort for (int i = 1; i < n; i++) { int diff = abs(arr[i] - x); // Insert arr[i] at correct place int j = i - 1; if (abs(arr[j] - x) > diff) { int temp = arr[i]; while (abs(arr[j] - x) > diff && j >= 0) { arr[j + 1] = arr[j]; j--; } arr[j + 1] = temp; } }}// Function to print the arrayvoid print(int arr[], int n){ for (int i = 0; i < n; i++) cout << arr[i] << " ";}// Main Functionint main(){ int arr[] = { 10, 5, 3, 9, 2 }; int n = sizeof(arr) / sizeof(arr[0]); int x = 7; arrange(arr, n, x); print(arr, n); return 0;} |
Java
// Java program to sort an array based on absolute// difference with a given value x.class GFG {static void arrange(int arr[], int n, int x){ // Below lines are similar to insertion sort for (int i = 1; i < n; i++) { int diff = Math.abs(arr[i] - x); // Insert arr[i] at correct place int j = i - 1; if (Math.abs(arr[j] - x) > diff) { int temp = arr[i]; while (j >= 0 && Math.abs(arr[j] - x) > diff) { arr[j + 1] = arr[j]; j--; } arr[j + 1] = temp; } }}// Function to print the arraystatic void print(int arr[], int n){ for (int i = 0; i < n; i++) System.out.print(arr[i] + " ");}// Driver codepublic static void main(String[] args) { int arr[] = { 10, 5, 3, 9, 2 }; int n = arr.length; int x = 7; arrange(arr, n, x); print(arr, n); }}// This code is contributed by PrinciRaj1992 |
Python 3
# Python 3 program to sort an array # based on absolute difference with# a given value x.def arrange(arr, n, x): # Below lines are similar to # insertion sort for i in range(1, n) : diff = abs(arr[i] - x) # Insert arr[i] at correct place j = i - 1 if (abs(arr[j] - x) > diff) : temp = arr[i] while (abs(arr[j] - x) > diff and j >= 0) : arr[j + 1] = arr[j] j -= 1 arr[j + 1] = temp# Function to print the arraydef print_1(arr, n): for i in range(n): print(arr[i], end = " ")# Driver Codeif __name__ == "__main__": arr = [ 10, 5, 3, 9, 2 ] n = len(arr) x = 7 arrange(arr, n, x) print_1(arr, n)# This code is contributed by ita_c |
C#
// C# program to sort an array based on absolute// difference with a given value x.using System;class GFG { static void arrange(int []arr, int n, int x) { // Below lines are similar to insertion sort for (int i = 1; i < n; i++) { int diff = Math.Abs(arr[i] - x); // Insert arr[i] at correct place int j = i - 1; if (Math.Abs(arr[j] - x) > diff) { int temp = arr[i]; while (j >= 0 && Math.Abs(arr[j] - x) > diff) { arr[j + 1] = arr[j]; j--; } arr[j + 1] = temp; } } } // Function to print the array static void print(int []arr, int n) { for (int i = 0; i < n; i++) Console.Write(arr[i] + " "); } // Driver code public static void Main() { int []arr = { 10, 5, 3, 9, 2 }; int n = arr.Length; int x = 7; arrange(arr, n, x); print(arr, n); }}// This code is contributed by 29AjayKumar |
PHP
<?php// PHP program to sort an array based on // absolute difference with a given value x.function arrange($arr, $n, $x){ // Below lines are similar to // insertion sort for ($i = 1; $i < $n; $i++) { $diff = abs($arr[$i] - $x); // Insert arr[i] at correct place $j = $i - 1; if (abs($arr[$j] - $x) > $diff) { $temp = $arr[$i]; while (abs($arr[$j] - $x) > $diff && $j >= 0) { $arr[$j + 1] = $arr[$j]; $j--; } $arr[$j + 1] = $temp; } } return $arr;}// Function to print the arrayfunction print_arr($arr, $n){ for ($i = 0; $i < $n; $i++) echo $arr[$i] . " ";}// Driver Code$arr = array(10, 5, 3, 9, 2);$n = sizeof($arr);$x = 7;$arr1 = arrange($arr, $n, $x);print_arr($arr1, $n);// This code is contributed // by Akanksha Rai?> |
Javascript
<script>// Javascript program to sort // an array based on absolute// difference with a given value x. function arrange(arr,n,x) { // Below lines are similar // to insertion sort for (let i = 1; i < n; i++) { let diff = Math.abs(arr[i] - x); // Insert arr[i] at correct place let j = i - 1; if (Math.abs(arr[j] - x) > diff) { let temp = arr[i]; while (j >= 0 && Math.abs(arr[j] - x) > diff) { arr[j + 1] = arr[j]; j--; } arr[j + 1] = temp; } } } // Function to print the array function print(arr,n) { for (let i = 0; i < n; i++) document.write(arr[i] + " "); } // Driver code let arr=[10, 5, 3, 9, 2 ]; let n = arr.length; let x = 7; arrange(arr, n, x); print(arr, n); // This code is contributed // by avanitrachhadiya2155 </script> |
Output:
5 9 10 3 2
Time Complexity: O(n^2) where n is the size of the array.
Auxiliary Space: O(1)
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