Count of pairs containing even or consecutive elements from given Array
Last Updated :
31 May, 2022
Given an array arr[] of even size, the task is to find the count of pairs after partitioning arr[] into pairs, such that:
- each element of arr[] belongs to exactly one pair
- both of them are even or
- absolute difference between them is 1, i.e, |X - Y| = 1.
Examples:
Input: arr[] = {11, 12, 16, 14}
Output: {11, 12}, {16, 14}
Explanation: arr[] can be partitioned into pairs in the following way.
Pair 1 - {11, 12}, as |11-12| = 1.
Pair 2 - {16, 14}, both 16 and 14 are even.
Therefore, {11, 12} and {16, 14} are the two pairs.
Input: A = {4, 7}
Output: No
Approach: This problem is observation-based. Firstly, if even numbers count and odd numbers count does not have the same parity then the answer does not exist. That means if the count of even and odd both are either even or both are either odd. Now the left case when even numbers and odd numbers are equal in frequency, then 2 cases are there:
- Occurrence of even and odd numbers are even, then answer exists always.
- Occurrence even and odd numbers are odd, then check if there are 2 numbers in the array such that their absolute difference is 1, and then even and odd numbers occurrence becomes, even so, answer exist.
Follow the steps below to solve the given problem.
- Create a variable even_count = 0 as count of even numbers and odd_count = 0, as count of odd numbers.
- Iterate the array from index = 0 to n-1, check if arr[index]%2 == 0, increment even_count else increment odd_count.
- Check if even_count = odd_count
- if condition false output No as the array pairs cannot exist.
- Else check if there exist 2 elements in the array such that their absolute difference is 1. To check such a pair exists, create an array temp and store the count of each number of the array, then iterate the array and check if the consecutive element count is greater than 1 or not.
- If exists output Yes.
- For printing the required pairs, print even numbers in pairs, then odd numbers in pairs, and the left 2 elements as the last pair.
Below is the implementation of the above approach:
C++
// C++ program for above approach
#include <bits/stdc++.h>
using namespace std;
// Function to find similar pairs in arr[]
void CheckSimilarPair(int arr[], int n)
{
// Variable to count
// Odd and even numbers
int odd_count = 0;
int even_count = 0;
// Count even and odd occurrences
for (int index = 0; index < n; index++) {
if (arr[index] % 2 == 0)
even_count++;
else
odd_count++;
}
// Checking same parity of count of even
// and odd numbers
if ((even_count % 2 == 0
&& odd_count % 2 == 1)
|| (even_count % 2 == 1
&& odd_count % 2 == 0)) {
cout << "-1\n";
}
else {
// Check if there exist 2 numbers
// with absolute difference is 1
// Vector to store frequency
// of elements of the array
vector<int> temp(1001, 0);
// Maximum element upto which
// temp should be checked
int max_element = 0;
// Iterate the array and store their counts
for (int index = 0; index < n; index++) {
temp[arr[index]]++;
max_element
= max(max_element, arr[index]);
}
int element1 = -1;
int element2 = -1;
bool pair_exist = false;
// Iterate the temp array
// upto max_element and check
// if 2 element exist
// having 1 abs' difference
for (int index = 1; index <= max_element; index++) {
if (temp[index - 1] >= 1
&& temp[index] >= 1) {
element1 = index - 1;
element2 = index;
pair_exist = true;
break;
}
}
// If pair exist
if (pair_exist) {
// Vector storing pairs
vector<int> res;
// Even pairs
for (int index = 0; index < n; index++) {
if (arr[index] % 2 == 0
&& arr[index] != element1
&& arr[index] != element2) {
res.push_back(arr[index]);
}
}
// Odd pairs
for (int index = 0; index < n; index++) {
if (arr[index] % 2 == 1
&& arr[index] != element1
&& arr[index] != element2) {
res.push_back(arr[index]);
}
}
// Printing all pairs
for (int index = 0; index < res.size() - 1; index += 2) {
cout << "{" << res[index] << ", "
<< res[index + 1] << "}"
<< " ";
}
cout << "{" << element1 << ", "
<< element2 << "}";
}
else {
cout << "\nNo";
}
}
}
// Driver code
int main()
{
int arr[4] = { 11, 12, 16, 14 };
int N = 4;
CheckSimilarPair(arr, N);
return 0;
}
// Java program for above approach
import java.util.*;
class GFG{
// Function to find similar pairs in arr[]
static void CheckSimilarPair(int arr[], int n)
{
// Variable to count
// Odd and even numbers
int odd_count = 0;
int even_count = 0;
// Count even and odd occurrences
for (int index = 0; index < n; index++) {
if (arr[index] % 2 == 0)
even_count++;
else
odd_count++;
}
// Checking same parity of count of even
// and odd numbers
if ((even_count % 2 == 0
&& odd_count % 2 == 1)
|| (even_count % 2 == 1
&& odd_count % 2 == 0)) {
System.out.print("-1\n");
}
else {
// Check if there exist 2 numbers
// with absolute difference is 1
// Vector to store frequency
// of elements of the array
int []temp = new int[1001];
// Maximum element upto which
// temp should be checked
int max_element = 0;
// Iterate the array and store their counts
for (int index = 0; index < n; index++) {
temp[arr[index]]++;
max_element
= Math.max(max_element, arr[index]);
}
int element1 = -1;
int element2 = -1;
boolean pair_exist = false;
// Iterate the temp array
// upto max_element and check
// if 2 element exist
// having 1 abs' difference
for (int index = 1; index <= max_element; index++) {
if (temp[index - 1] >= 1
&& temp[index] >= 1) {
element1 = index - 1;
element2 = index;
pair_exist = true;
break;
}
}
// If pair exist
if (pair_exist)
{
// Vector storing pairs
Vector<Integer> res = new Vector<Integer>();
// Even pairs
for (int index = 0; index < n; index++) {
if (arr[index] % 2 == 0
&& arr[index] != element1
&& arr[index] != element2) {
res.add(arr[index]);
}
}
// Odd pairs
for (int index = 0; index < n; index++) {
if (arr[index] % 2 == 1
&& arr[index] != element1
&& arr[index] != element2) {
res.add(arr[index]);
}
}
// Printing all pairs
for (int index = 0; index < res.size() - 1; index += 2) {
System.out.print("{" + res.get(index)+ ", "
+ res.get(index+1)+ "}"
+ " ");
}
System.out.print("{" + element1+ ", "
+ element2+ "}");
}
else {
System.out.print("\nNo");
}
}
}
// Driver code
public static void main(String[] args)
{
int arr[] = { 11, 12, 16, 14 };
int N = 4;
CheckSimilarPair(arr, N);
}
}
// This code is contributed by 29AjayKumar
# Python program for above approach
# Function to find similar pairs in arr[]
def CheckSimilarPair(arr, n):
# Variable to count
# Odd and even numbers
odd_count = 0
even_count = 0
# Count even and odd occurrences
for index in range(n):
if (arr[index] % 2 == 0):
even_count += 1
else:
odd_count += 1
# Checking same parity of count of even
# and odd numbers
if ((even_count % 2 == 0 and odd_count % 2 == 1) or (even_count % 2 == 1 and odd_count % 2 == 0)):
print("-1")
else:
# Check if there exist 2 numbers
# with absolute difference is 1
# Vector to store frequency
# of elements of the array
temp = [0] * 1001
# Maximum element upto which
# temp should be checked
max_element = 0
# Iterate the array and store their counts
for index in range(n):
temp[arr[index]] += 1
max_element = max(max_element, arr[index])
element1 = -1
element2 = -1
pair_exist = False
# Iterate the temp array
# upto max_element and check
# if 2 element exist
# having 1 abs' difference
for index in range(max_element + 1):
if (temp[index - 1] >= 1 and temp[index] >= 1):
element1 = index - 1
element2 = index
pair_exist = True
break
# If pair exist
if (pair_exist):
# Vector storing pairs
res = []
# Even pairs
for index in range(n):
if (arr[index] % 2 == 0 and arr[index] != element1 and arr[index] != element2):
res.append(arr[index])
# Odd pairs
for index in range(n):
if (arr[index] % 2 == 1 and arr[index] != element1 and arr[index] != element2):
res.append(arr[index])
# Printing all pairs
for index in range(0, len(res) - 1, 2):
print("{", end=" ")
print(f"{res[index]} , {res[index + 1]}", end=" ")
print("}", end=" ")
print("{", end=" ")
print(f"{element1} ,{element2}", end=" ")
print("}")
else:
print('<br>' + "No")
# Driver code
arr = [11, 12, 16, 14]
N = 4
CheckSimilarPair(arr, N)
# This code is contributed by gfgking
// C# program for the above approach
using System;
using System.Collections;
class GFG{
// Function to find similar pairs in arr[]
static void CheckSimilarPair(int []arr, int n)
{
// Variable to count
// Odd and even numbers
int odd_count = 0;
int even_count = 0;
// Count even and odd occurrences
for (int index = 0; index < n; index++) {
if (arr[index] % 2 == 0)
even_count++;
else
odd_count++;
}
// Checking same parity of count of even
// and odd numbers
if ((even_count % 2 == 0
&& odd_count % 2 == 1)
|| (even_count % 2 == 1
&& odd_count % 2 == 0)) {
Console.Write("-1\n");
}
else {
// Check if there exist 2 numbers
// with absolute difference is 1
// Vector to store frequency
// of elements of the array
int []temp = new int[1001];
// Maximum element upto which
// temp should be checked
int max_element = 0;
// Iterate the array and store their counts
for (int index = 0; index < n; index++) {
temp[arr[index]]++;
max_element
= Math.Max(max_element, arr[index]);
}
int element1 = -1;
int element2 = -1;
bool pair_exist = false;
// Iterate the temp array
// upto max_element and check
// if 2 element exist
// having 1 abs' difference
for (int index = 1; index <= max_element; index++) {
if (temp[index - 1] >= 1
&& temp[index] >= 1) {
element1 = index - 1;
element2 = index;
pair_exist = true;
break;
}
}
// If pair exist
if (pair_exist)
{
// Vector storing pairs
ArrayList res = new ArrayList();
// Even pairs
for (int index = 0; index < n; index++) {
if (arr[index] % 2 == 0
&& arr[index] != element1
&& arr[index] != element2) {
res.Add(arr[index]);
}
}
// Odd pairs
for (int index = 0; index < n; index++) {
if (arr[index] % 2 == 1
&& arr[index] != element1
&& arr[index] != element2) {
res.Add(arr[index]);
}
}
// Printing all pairs
for (int index = 0; index < res.Count - 1; index += 2) {
Console.Write("{" + res[index]+ ", "
+ res[index+1]+ "}"
+ " ");
}
Console.Write("{" + element1+ ", "
+ element2+ "}");
}
else {
Console.Write("\nNo");
}
}
}
// Driver Code
public static void Main()
{
int []arr = { 11, 12, 16, 14 };
int N = 4;
CheckSimilarPair(arr, N);
}
}
// This code is contributed by Samim Hossain Mondal.
<script>
// JavaScript program for above approach
// Function to find similar pairs in arr[]
function CheckSimilarPair(arr, n)
{
// Variable to count
// Odd and even numbers
let odd_count = 0;
let even_count = 0;
// Count even and odd occurrences
for(let index = 0; index < n; index++)
{
if (arr[index] % 2 == 0)
even_count++;
else
odd_count++;
}
// Checking same parity of count of even
// and odd numbers
if ((even_count % 2 == 0 && odd_count % 2 == 1) ||
(even_count % 2 == 1 && odd_count % 2 == 0))
{
cout << "-1\n";
}
else
{
// Check if there exist 2 numbers
// with absolute difference is 1
// Vector to store frequency
// of elements of the array
let temp = new Array(1001).fill(0)
// Maximum element upto which
// temp should be checked
let max_element = 0;
// Iterate the array and store their counts
for(let index = 0; index < n; index++)
{
temp[arr[index]]++;
max_element = Math.max(max_element,
arr[index]);
}
let element1 = -1;
let element2 = -1;
let pair_exist = false;
// Iterate the temp array
// upto max_element and check
// if 2 element exist
// having 1 abs' difference
for(let index = 1; index <= max_element; index++)
{
if (temp[index - 1] >= 1 && temp[index] >= 1)
{
element1 = index - 1;
element2 = index;
pair_exist = true;
break;
}
}
// If pair exist
if (pair_exist)
{
// Vector storing pairs
let res = [];
// Even pairs
for(let index = 0; index < n; index++)
{
if (arr[index] % 2 == 0 &&
arr[index] != element1 &&
arr[index] != element2)
{
res.push(arr[index]);
}
}
// Odd pairs
for(let index = 0; index < n; index++)
{
if (arr[index] % 2 == 1 &&
arr[index] != element1 &&
arr[index] != element2)
{
res.push(arr[index]);
}
}
// Printing all pairs
for(let index = 0;
index < res.length - 1;
index += 2)
{
document.write("{" + res[index] + ", " +
res[index + 1] + "}" +
" ");
}
document.write("{" + element1 + ", " +
element2 + "}");
}
else
{
document.write('<br>' + "No");
}
}
}
// Driver code
let arr = [ 11, 12, 16, 14 ];
let N = 4;
CheckSimilarPair(arr, N);
// This code is contributed by Potta Lokesh
</script>
Time Complexity: O(N)
Auxiliary Space: O(N)
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