Check if an array is Wave Array
Given an array of N positive integers. The task is to check if the array is sorted in wave form.
Examples:
Input: arr[] = {1, 2, 3, 4, 5}
Output: NO
Input: arr[] = {1, 5, 3, 7, 2, 8, 6}
Output: YES
Approach:
- First check the element at index 1, i.e, arr[1] and observe the pattern.
- If arr[1] is greater than its left and right element, then this pattern will be followed by other elements.
- Else If arr[1] is smaller than its left and right element, then this pattern will be followed by other elements.
- Check for the same pattern found from above steps. If at any point, this rule violates, return false, else return true.
Below is the implementation of above approach:
C++
#include <iostream>
using namespace std;
bool isWaveArray( int arr[], int n)
{
bool result = false ;
if (arr[1] > arr[0] && arr[1] > arr[2]) {
for ( int i = 1; i < n - 1; i += 2) {
if (arr[i] > arr[i - 1] && arr[i] > arr[i + 1]) {
result = true ;
}
else {
result = false ;
break ;
}
}
if (result == true && n % 2 == 0) {
if (arr[n - 1] <= arr[n - 2]) {
result = false ;
}
}
}
else if (arr[1] < arr[0] && arr[1] < arr[2]) {
for ( int i = 1; i < n - 1; i += 2) {
if (arr[i] < arr[i - 1] && arr[i] < arr[i + 1]) {
result = true ;
}
else {
result = false ;
break ;
}
}
if (result == true && n % 2 == 0) {
if (arr[n - 1] >= arr[n - 2]) {
result = false ;
}
}
}
return result;
}
int main()
{
int arr[] = { 1, 3, 2, 4 };
int n = sizeof (arr) / sizeof ( int );
if (isWaveArray(arr, n)) {
cout << "YES" << endl;
}
else {
cout << "NO" << endl;
}
return 0;
}
|
Java
public class GFG {
static boolean isWaveArray( int arr[], int n)
{
boolean result = true ;
if (arr[ 1 ] > arr[ 0 ] && arr[ 1 ] > arr[ 2 ]) {
for ( int i = 1 ; i < n - 1 ; i += 2 ) {
if (arr[i] > arr[i - 1 ] && arr[i] > arr[i + 1 ]) {
result = true ;
}
else {
result = false ;
break ;
}
}
if (result == true && n % 2 == 0 ) {
if (arr[n - 1 ] <= arr[n - 2 ]) {
result = false ;
}
}
}
else if (arr[ 1 ] < arr[ 0 ] && arr[ 1 ] < arr[ 2 ]) {
for ( int i = 1 ; i < n - 1 ; i += 2 ) {
if (arr[i] < arr[i - 1 ] && arr[i] < arr[i + 1 ]) {
result = true ;
}
else {
result = false ;
break ;
}
}
if (result == true && n % 2 == 0 ) {
if (arr[n - 1 ] >= arr[n - 2 ]) {
result = false ;
}
}
}
return result;
}
public static void main(String args[])
{
int arr[] = { 1 , 3 , 2 , 4 };
int n = arr.length;
if (isWaveArray(arr, n)) {
System.out.println( "YES" );
}
else {
System.out.println( "NO" );
}
}
}
|
Python 3
def isWaveArray(arr , n):
result = True
if (arr[ 1 ] > arr[ 0 ] and arr[ 1 ] > arr[ 2 ]):
for i in range ( 1 , n - 1 , 2 ):
if (arr[i] > arr[i - 1 ] and
arr[i] > arr[i + 1 ]):
result = True
else :
result = False
break
if (result = = True and n % 2 = = 0 ):
if (arr[n - 1 ] < = arr[n - 2 ]) :
result = False
elif (arr[ 1 ] < arr[ 0 ] and
arr[ 1 ] < arr[ 2 ]) :
for i in range ( 1 , n - 1 , 2 ) :
if (arr[i] < arr[i - 1 ] and
arr[i] < arr[i + 1 ]):
result = True
else :
result = False
break
if (result = = True and n % 2 = = 0 ) :
if (arr[n - 1 ] > = arr[n - 2 ]) :
result = False
return result
if __name__ = = "__main__" :
arr = [ 1 , 3 , 2 , 4 ]
n = len (arr)
if (isWaveArray(arr, n)):
print ( "YES" )
else :
print ( "NO" )
|
C#
using System;
class GFG
{
static bool isWaveArray( int []arr, int n)
{
bool result = true ;
if (arr[1] > arr[0] && arr[1] > arr[2])
{
for ( int i = 1; i < n - 1; i += 2)
{
if (arr[i] > arr[i - 1] &&
arr[i] > arr[i + 1])
{
result = true ;
}
else
{
result = false ;
break ;
}
}
if (result == true && n % 2 == 0)
{
if (arr[n - 1] <= arr[n - 2])
{
result = false ;
}
}
}
else if (arr[1] < arr[0] &&
arr[1] < arr[2])
{
for ( int i = 1; i < n - 1; i += 2)
{
if (arr[i] < arr[i - 1] &&
arr[i] < arr[i + 1])
{
result = true ;
}
else
{
result = false ;
break ;
}
}
if (result == true && n % 2 == 0)
{
if (arr[n - 1] >= arr[n - 2])
{
result = false ;
}
}
}
return result;
}
public static void Main()
{
int []arr = { 1, 3, 2, 4 };
int n = arr.Length;
if (isWaveArray(arr, n))
{
Console.WriteLine( "YES" );
}
else
{
Console.WriteLine( "NO" );
}
}
}
|
Javascript
<script>
function isWaveArray(arr, n)
{
let result = true ;
if (arr[1] > arr[0] && arr[1] > arr[2]) {
for (let i = 1; i < n - 1; i += 2) {
if (arr[i] > arr[i - 1] && arr[i] > arr[i + 1]) {
result = true ;
}
else {
result = false ;
break ;
}
}
if (result == true && n % 2 == 0) {
if (arr[n - 1] <= arr[n - 2]) {
result = false ;
}
}
}
else if (arr[1] < arr[0] && arr[1] < arr[2]) {
for (let i = 1; i < n - 1; i += 2) {
if (arr[i] < arr[i - 1] && arr[i] < arr[i + 1]) {
result = true ;
}
else {
result = false ;
break ;
}
}
if (result == true && n % 2 == 0) {
if (arr[n - 1] >= arr[n - 2]) {
result = false ;
}
}
}
return result;
}
let arr = [ 1, 3, 2, 4 ];
let n = arr.length;
if (isWaveArray(arr, n)) {
document.write( "YES" );
}
else {
document.write( "NO" );
}
</script>
|
PHP
<?php
function isWaveArray( $arr , $n )
{
$result = true;
if ( $arr [1] > $arr [0] &&
$arr [1] > $arr [2])
{
for ( $i = 1; $i < ( $n - 1); $i += 2)
{
if ( $arr [ $i ] > $arr [ $i - 1] &&
$arr [ $i ] > $arr [ $i + 1])
{
$result = true;
}
else
{
$result = false;
break ;
}
}
if ( $result == true && $n % 2 == 0)
{
if ( $arr [ $n - 1] <= $arr [ $n - 2])
{
$result = false;
}
}
}
else if ( $arr [1] < $arr [0] &&
$arr [1] < $arr [2])
{
for ( $i = 1; $i < $n - 1; $i += 2)
{
if ( $arr [ $i ] < $arr [ $i - 1] &&
$arr [ $i ] < $arr [ $i + 1])
{
$result = true;
}
else
{
$result = false;
break ;
}
}
if ( $result == true && $n % 2 == 0)
{
if ( $arr [ $n - 1] >= $arr [ $n - 2])
{
$result = false;
}
}
}
return $result ;
}
$arr = array (1, 3, 2, 4 );
$n = sizeof( $arr );
if (isWaveArray( $arr , $n ))
{
echo "YES" ;
}
else
{
echo "NO" ;
}
?>
|
Time Complexity: O(n)
Auxiliary Space: O(1)
Approach :- 2 One approach to check if an array is a wave array is to first sort the array in ascending order. Then, we can swap adjacent elements to form a wave-like pattern. If at least one element does not satisfy the wave property, the array is not a wave array.
Here is the implementation of this approach:
Traverse the array from the second element to the second last element.
Check if the current element is greater than or equal to both its adjacent elements or smaller than or equal to both its adjacent elements.
If it satisfies the above condition, move to the next element, else return false.
If the entire array has been traversed without any element failing the condition, return true.
C++
#include <bits/stdc++.h>
using namespace std;
bool isWave( int arr[], int n) {
sort(arr, arr + n);
for ( int i = 0; i < n - 1; i += 2) {
swap(arr[i], arr[i + 1]);
}
for ( int i = 0; i < n - 1; i++) {
if ((i % 2 == 0 && arr[i] > arr[i + 1]) ||
(i % 2 == 1 && arr[i] < arr[i + 1])) {
return true ;
}
}
return false ;
}
int main() {
int arr[] = { 1, 3, 2, 4 };
int n = sizeof (arr) / sizeof (arr[0]);
if (isWave(arr, n)) {
cout << "The array is a wave array" ;
} else {
cout << "The array is not a wave array" ;
}
return 0;
}
|
Java
import java.util.Arrays;
public class GFG {
static boolean isWave( int [] arr, int n) {
Arrays.sort(arr);
for ( int i = 0 ; i < n - 1 ; i += 2 ) {
swap(arr, i, i + 1 );
}
for ( int i = 0 ; i < n - 1 ; i++) {
if ((i % 2 == 0 && arr[i] > arr[i + 1 ]) || (i % 2 == 1 && arr[i] < arr[i + 1 ])) {
return true ;
}
}
return false ;
}
static void swap( int [] arr, int i, int j) {
int temp = arr[i];
arr[i] = arr[j];
arr[j] = temp;
}
public static void main(String[] args) {
int [] arr = { 1 , 3 , 2 , 4 };
int n = arr.length;
if (isWave(arr, n)) {
System.out.println( "The array is a wave array" );
} else {
System.out.println( "The array is not a wave array" );
}
}
}
|
Python3
def is_wave(arr):
arr.sort()
for i in range ( 0 , len (arr) - 1 , 2 ):
arr[i], arr[i + 1 ] = arr[i + 1 ], arr[i]
for i in range ( len (arr) - 1 ):
if (i % 2 = = 0 and arr[i] > arr[i + 1 ]) or (i % 2 = = 1 and arr[i] < arr[i + 1 ]):
return True
return False
if __name__ = = "__main__" :
arr = [ 1 , 3 , 2 , 4 ]
if is_wave(arr):
print ( "The array is a wave array" )
else :
print ( "The array is not a wave array" )
|
C#
using System;
public class GFG
{
public static bool IsWave( int [] arr, int n)
{
Array.Sort(arr);
for ( int i = 0; i < n - 1; i += 2)
{
int temp = arr[i];
arr[i] = arr[i + 1];
arr[i + 1] = temp;
}
for ( int i = 0; i < n - 1; i++)
{
if ((i % 2 == 0 && arr[i] > arr[i + 1]) ||
(i % 2 == 1 && arr[i] < arr[i + 1]))
{
return true ;
}
}
return false ;
}
public static void Main( string [] args)
{
int [] arr = { 1, 3, 2, 4 };
int n = arr.Length;
if (IsWave(arr, n))
{
Console.WriteLine( "The array is a wave array" );
}
else
{
Console.WriteLine( "The array is not a wave array" );
}
}
}
|
Javascript
function isWave(arr) {
arr.sort((a, b) => a - b);
for (let i = 0; i < arr.length - 1; i += 2) {
[arr[i], arr[i + 1]] = [arr[i + 1], arr[i]];
}
for (let i = 0; i < arr.length - 1; i++) {
if ((i % 2 === 0 && arr[i] > arr[i + 1]) || (i % 2 === 1 && arr[i] < arr[i + 1])) {
return true ;
}
}
return false ;
}
const arr = [1, 3, 2, 4];
if (isWave(arr)) {
console.log( "The array is a wave array" );
} else {
console.log( "The array is not a wave array" );
}
|
Output
The array is a wave array
Time Complexity:
The algorithm involves a linear scan of the entire array, which takes O(nlogn) time, where n is the size of the array.
Auxiliary Space:
The algorithm uses only constant extra space to store the indices and variables, which does not depend on the size of the array. Hence, the space complexity is O(1).
Last Updated :
14 Oct, 2023
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