Given an array arr of N (even) integer elements. The task is to check if it is possible to reorder the elements of the array such that:
arr[2*i + 1] = 2 * A[2 * i] for i = 0 ... N-1.
Print True if it is possible, otherwise print False.
Examples:
Input: arr[] = {4, -2, 2, -4}
Output: True
{-2, -4, 2, 4} is a valid arrangement, -2 * 2 = -4 and 2 * 2 = 4Input: arr[] = {1, 2, 4, 16, 8, 4}
Output: False
Approach: The idea is that, if k is current minimum element in the array then it must pair with 2 * k as there does not exist any other element k / 2 to pair it with.
We check elements in ascending order. When we check an element k and it isn’t used, it must pair with 2 * k. We will attempt to arrange k followed by 2 * k however if we can’t, then the answer is False. In the end, if all the operations are successful, then print True.
We will store a count of each element to keep track of what we have not yet considered.
Below is the implementation of above approach:
C++
// C++ implementation of the approach#include<bits/stdc++.h>using namespace std; // Function to return true if the elements // can be arranged in the desired orderstring canReorder(int A[],int n){ map<int,int> m; for(int i=0;i<n;i++) m[A[i]]++; sort(A,A+n); int count = 0; for(int i=0;i<n;i++) { if (m[A[i]] == 0) continue; // If 2 * x is not found to pair if (m[2 * A[i]]){ count+=2; // Remove an occurrence of x // and an occurrence of 2 * x m[A[i]] -= 1; m[2 * A[i]] -= 1; } } if(count ==n) return "true"; else return "false";} // Driver Codeint main(){int A[] = {4, -2, 2, -4};int n= sizeof(A)/sizeof(int); // Function call to print required answercout<<(canReorder(A,n)); return 0;}//contributed by Arnab Kundu |
Java
// Java implementation of the approach import java.util.HashMap;import java.util.Map;import java.util.Arrays; class GfG{ // Function to return true if the elements // can be arranged in the desired order static String canReorder(int A[],int n) { HashMap<Integer,Integer> m = new HashMap<>(); for(int i = 0; i < n; i++) { if (m.containsKey(A[i])) m.put(A[i], m.get(A[i]) + 1); else m.put(A[i], 1); } Arrays.sort(A); int count = 0; for(int i = 0; i < n; i++) { if (m.get(A[i]) == 0) continue; // If 2 * x is not found to pair if (m.containsKey(2 * A[i])) { count += 2; // Remove an occurrence of x // and an occurrence of 2 * x m.put(A[i], m.get(A[i]) - 1); m.put(2 * A[i], m.get(2 * A[i]) - 1); } } if(count == n) return "true"; else return "false"; } // Driver code public static void main(String []args) { int A[] = {4, -2, 2, -4}; int n = A.length; // Function call to print required answer System.out.println(canReorder(A,n)); }} // This code is contributed by Rituraj Jain |
Python
# Python implementation of the approachimport collections # Function to return true if the elements # can be arranged in the desired orderdef canReorder(A): count = collections.Counter(A) for x in sorted(A, key = abs): if count[x] == 0: continue # If 2 * x is not found to pair if count[2 * x] == 0: return False # Remove an occurrence of x # and an occurrence of 2 * x count[x] -= 1 count[2 * x] -= 1 return True # Driver CodeA = [4, -2, 2, -4] # Function call to print required answerprint(canReorder(A)) |
C#
// C# implementation of the approachusing System;using System.Collections.Generic; class GFG{ // Function to return true if the elements // can be arranged in the desired order static String canReorder(int []A,int n) { Dictionary<int, int> m = new Dictionary<int, int>(); for(int i = 0; i < n; i++) { if (m.ContainsKey(A[i])) m[A[i]]= m[A[i]] + 1; else m.Add(A[i], 1); } Array.Sort(A); int count = 0; for(int i = 0; i < n; i++) { if (m[A[i]] == 0) continue; // If 2 * x is not found to pair if (m.ContainsKey(2 * A[i])) { count += 2; // Remove an occurrence of x // and an occurrence of 2 * x m[A[i]]= m[A[i]] - 1; if (m.ContainsKey(2 * A[i])) m[2 * A[i]]= m[2 * A[i]] - 1; else m.Add(2 * A[i], m[2 * A[i]] - 1); } } if(count == n) return "True"; else return "False"; } // Driver codepublic static void Main(String []args){ int []A = {4, -2, 2, -4}; int n = A.Length; // Function call to print required answer Console.WriteLine(canReorder(A,n));}} // This code is contributed by Rajput-Ji |
True
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