Permutation of Array such that products of all adjacent elements are even
Last Updated :
07 Mar, 2022
Given an array arr[] consisting of N positive integers, the task is to find any permutation of given array such that the product of adjacent elements is even. Print any such permutation or -1 if not possible.
Example:
Input: arr[] = {6,7,9,8,10,11}
Output: 8 9 10 7 6 11
Explanation:
Product of adjacent elements =>
8 x 9 = 72 (even)
9 x 10 = 90 (even)
10 x 7 = 70 (even)
7 x 6 = 42 (even)
6 x 11 = 66 (even)
Input: arr[] = {3,2,5,7,1,4,9}
Output: -1
Explanation: There is no possible arrangements of elements such that product of adjacent elements is equal.
Naive Approach: The simplest approach to solve this problem is to try every possible arrangement of the elements and check the condition to be true.
Time Complexity: O(N*N!) where N is the number of elements in the array. O(N!) is the time taken to create all permutations of the given array and O(N) is the time required to check if the current permutation is the required one or not.
Auxiliary Space: O(N) to store the permutation each time.
Efficient Approach: The solution can be found using simple observations. If there are multiple odd and even elements in the array then an optimal arrangement of any adjacent elements can be either of the below cases for the product to be even:
{Odd, Even}
{Even, Odd}
{Even, Even}
Please note that {Odd, Odd} arrangement of any adjacent element will give an Odd product. Hence, this arrangement is not possible.
The above arrangements is only possible if
number_of_odd_elements <= number_of_even_elements + 1 in the array.
Follow the steps below to solve the problem.
- Take two vectors even and odd to store the even and odd elements of the array separately.
- If the size of odd vector is greater than size of even vector + 1, (as explained above) then solution is not possible. Therefore, print -1.
- Else first print one element from the odd vector and then one element from even vector until both vectors are empty.
Below is the implementation of the above approach.
C++
// C++ program to Permutation of Array
// such that product of all
// adjacent elements is even
#include <bits/stdc++.h>
using namespace std;
// Function to print
// the required permutation
void printPermutation(int arr[], int n)
{
vector<int> odd, even;
// push odd elements in 'odd'
// and even elements in 'even'
for (int i = 0; i < n; i++) {
if (arr[i] % 2 == 0)
even.push_back(arr[i]);
else
odd.push_back(arr[i]);
}
int size_odd = odd.size();
int size_even = even.size();
// Check if it possible to
// arrange the elements
if (size_odd > size_even + 1)
cout << -1 << endl;
// else print the permutation
else {
int i = 0;
int j = 0;
while (i < size_odd && j < size_even) {
cout << odd[i] << " ";
++i;
cout << even[j] << " ";
++j;
}
// Print remaining odds are even.
// and even elements
while (i < size_odd) {
cout << odd[i] << " ";
++i;
}
while (j < size_even) {
cout << even[j] << " ";
}
}
}
// Driver code
int main()
{
int arr[] = { 6, 7, 9, 8, 10, 11 };
int N = sizeof(arr) / sizeof(arr[0]);
printPermutation(arr, N);
return 0;
}
// Java program to permutation of array
// such that product of all adjacent
// elements is even
import java.io.*;
import java.util.*;
class GFG{
// Function to print
// the required permutation
static void printPermutation(int arr[], int n)
{
ArrayList<Integer> odd = new ArrayList<Integer>();
ArrayList<Integer> even = new ArrayList<Integer>();
// push odd elements in 'odd'
// and even elements in 'even'
for(int i = 0; i < n; i++)
{
if (arr[i] % 2 == 0)
even.add(arr[i]);
else
odd.add(arr[i]);
}
int size_odd = odd.size();
int size_even = even.size();
// Check if it possible to
// arrange the elements
if (size_odd > size_even + 1)
System.out.println("-1");
// Else print the permutation
else
{
int i = 0;
int j = 0;
while (i < size_odd && j < size_even)
{
System.out.print(odd.get(i) + " ");
++i;
System.out.print(even.get(j) + " ");
++j;
}
// Print remaining odds are even.
// and even elements
while (i < size_odd)
{
System.out.print(odd.get(i) + " ");
++i;
}
while (j < size_even)
{
System.out.print(even.get(j) + " ");
}
}
}
// Driver Code
public static void main (String[] args)
{
int arr[] = { 6, 7, 9, 8, 10, 11 };
int N = arr.length;
printPermutation(arr, N);
}
}
// This code is contributed by offbeat
# Python3 program to Permutation of Array
# such that product of all
# adjacent elements is even
# Function to print
# the required permutation
def printPermutation(arr, n):
odd, even = [], []
# push odd elements in 'odd'
# and even elements in 'even'
for i in range(n):
if(arr[i] % 2 == 0):
even.append(arr[i])
else:
odd.append(arr[i])
size_odd = len(odd)
size_even = len(even)
# Check if it possible to
# arrange the elements
if(size_odd > size_even + 1):
print(-1)
# else print the permutation
else:
i, j = 0, 0
while(i < size_odd and j < size_even):
print(odd[i], end = " ")
i += 1
print(even[j], end = " ")
j += 1
# Print remaining odds are even.
# and even elements
while(i < size_odd):
print(odd[i], end = " ")
i += 1
while(j < size_even):
print(even[j], end = " ")
j += 1
# Driver Code
arr = [ 6, 7, 9, 8, 10, 11 ]
N = len(arr)
# Function call
printPermutation(arr, N)
# This code is contributed by Shivam Singh
// C# program to permutation of array
// such that product of all adjacent
// elements is even
using System;
using System.Collections.Generic;
class GFG{
// Function to print
// the required permutation
static void printPermutation(int []arr, int n)
{
List<int> odd = new List<int>();
List<int> even = new List<int>();
// push odd elements in 'odd'
// and even elements in 'even'
for(int i = 0; i < n; i++)
{
if (arr[i] % 2 == 0)
even.Add(arr[i]);
else
odd.Add(arr[i]);
}
int size_odd = odd.Count;
int size_even = even.Count;
// Check if it possible to
// arrange the elements
if (size_odd > size_even + 1)
Console.WriteLine("-1");
// Else print the permutation
else
{
int i = 0;
int j = 0;
while (i < size_odd && j < size_even)
{
Console.Write(odd[i] + " ");
++i;
Console.Write(even[j] + " ");
++j;
}
// Print remaining odds are even.
// and even elements
while (i < size_odd)
{
Console.Write(odd[i] + " ");
++i;
}
while (j < size_even)
{
Console.Write(even[j] + " ");
}
}
}
// Driver Code
public static void Main(String[] args)
{
int []arr = { 6, 7, 9, 8, 10, 11 };
int N = arr.Length;
printPermutation(arr, N);
}
}
// This code is contributed by PrinciRaj1992
<script>
// JavaScript program to permutation of array
// such that product of all adjacent
// elements is even
// Function to print
// the required permutation
function printPermutation(arr, n)
{
let odd = [];
let even = [];
// push odd elements in 'odd'
// and even elements in 'even'
for(let i = 0; i < n; i++)
{
if (arr[i] % 2 == 0)
even.push(arr[i]);
else
odd.push(arr[i]);
}
let size_odd = odd.length;
let size_even = even.length;
// Check if it possible to
// arrange the elements
if (size_odd > size_even + 1)
document.write("-1");
// Else print the permutation
else
{
let i = 0;
let j = 0;
while (i < size_odd && j < size_even)
{
document.write(odd[i] + " ");
++i;
document.write(even[j] + " ");
++j;
}
// Print remaining odds are even.
// and even elements
while (i < size_odd)
{
document.write(odd[i] + " ");
++i;
}
while (j < size_even)
{
document.write(even[j] + " ");
}
}
}
// Driver Code
let arr = [ 6, 7, 9, 8, 10, 11 ];
let N = arr.length;
printPermutation(arr, N);
</script>
Time Complexity: O(N) where N the number of elements. O(N) time is required to traverse the given array and form the odd & even vectors and O(N) is required to print the permutation.
Auxiliary Space: O(N) because the given array elements are distributed among the two vectors.
Similar Reads
Basics & Prerequisites
Data Structures
Array Data StructureIn this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous
3 min read
String in Data StructureA string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut
2 min read
Hashing in Data StructureHashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The
2 min read
Linked List Data StructureA linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Here’s the comparison of Linked List vs Arrays Linked List:
2 min read
Stack Data StructureA Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first
2 min read
Queue Data StructureA Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of "First in, First out" (FIFO), where the first element added to the queue is the first one to be removed. It is used as a buffer in computer systems
2 min read
Tree Data StructureTree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes. Types of TreeBinary Tree : Every node has at most two childrenTernary Tree : Every node has at most
4 min read
Graph Data StructureGraph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities. If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms. Basics of
3 min read
Trie Data StructureThe Trie data structure is a tree-like structure used for storing a dynamic set of strings. It allows for efficient retrieval and storage of keys, making it highly effective in handling large datasets. Trie supports operations such as insertion, search, deletion of keys, and prefix searches. In this
15+ min read
Algorithms
Searching AlgorithmsSearching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input
2 min read
Sorting AlgorithmsA Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ
3 min read
Introduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution
14 min read
Greedy AlgorithmsGreedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. At every step of the algorithm, we make a choice that looks the best at the moment. To make the choice, we sometimes sort the array so that we can always get
3 min read
Graph AlgorithmsGraph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social net
3 min read
Dynamic Programming or DPDynamic Programming is an algorithmic technique with the following properties.It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of
3 min read
Bitwise AlgorithmsBitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. These algorithms utilize bitwise operators like AND, OR, XOR, NOT, Left Shift, and Right Shift.BasicsIntroduction to Bitwise Algorit
4 min read
Advanced
Segment TreeSegment Tree is a data structure that allows efficient querying and updating of intervals or segments of an array. It is particularly useful for problems involving range queries, such as finding the sum, minimum, maximum, or any other operation over a specific range of elements in an array. The tree
3 min read
Pattern SearchingPattern searching algorithms are essential tools in computer science and data processing. These algorithms are designed to efficiently find a particular pattern within a larger set of data. Patten SearchingImportant Pattern Searching Algorithms:Naive String Matching : A Simple Algorithm that works i
2 min read
GeometryGeometry is a branch of mathematics that studies the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. From basic lines and angles to complex structures, it helps us understand the world around us.Geometry for Students and BeginnersThis section covers key br
2 min read
Interview Preparation
Practice Problem