Check if an array is Wave Array (original) (raw)

Last Updated : 02 May, 2025

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++ `

// CPP code to check if the array is wave array #include using namespace std;

// Function to check if array is wave array // arr : input array // n : size of array bool isWaveArray(int arr[], int n) {

bool result = false;

/* Check the wave form
* If arr[1] is greater than left and right
* Same pattern will be followed by whole 
* elements, else reverse pattern
* will be followed by array elements
*/
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;
        }
    }

    // Check for last element
    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;
        }
    }

    // Check for last element
    if (result == true && n % 2 == 0) {
        if (arr[n - 1] >= arr[n - 2]) {
            result = false;
        }
    }
}

return result;

}

// Driver Code int main() {

// Array
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

// Java code to check if the array is wave array

public class GFG {

// Function to check if array is wave array 
// arr : input array 
// n : size of array 
static boolean isWaveArray(int arr[], int n) 
{ 
  
    boolean result = true; 
  
    /* Check the wave form 
    * If arr[1] is greater than left and right 
    * Same pattern will be followed by whole  
    * elements, else reverse pattern 
    * will be followed by array elements 
    */
    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; 
            } 
        } 
  
        // Check for last element 
        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; 
            } 
        } 
  
        // Check for last element 
        if (result == true && n % 2 == 0) { 
            if (arr[n - 1] >= arr[n - 2]) { 
                result = false; 
            } 
        } 
    } 
  
    return result; 
} 

// Driver code
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"); 
        }       
}
// This Code is contributed by ANKITRAI1

}

Python 3

Python 3 code to check if

the array is wave array

Function to check if

array is wave array

arr : input array

n : size of array

def isWaveArray(arr , n):

result = True

# Check the wave form
# If arr[1] is greater than 
# left and right. Same pattern 
# will be followed by whole 
# elements, else reverse pattern
# will be followed by array elements

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

    # Check for last element
    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

    # Check for last element
    if (result == True and n % 2 == 0) :
        if (arr[n - 1] >= arr[n - 2]) :
            result = False

return result

Driver Code

if name == "main":

# Array
arr = [ 1, 3, 2, 4 ]

n = len(arr)

if (isWaveArray(arr, n)):
    print("YES")
else:
    print("NO")

This code is contributed

by ChitraNayal

C#

// C# code to check if the // array is wave array using System;

class GFG {

// Function to check if array // is wave array // arr : input array // n : size of array static bool isWaveArray(int []arr, int n) {

bool result = true; 

/* Check the wave form 
* If arr[1] is greater than left 
* and right. Same pattern will be 
* followed by whole elements, else 
* reverse pattern will be followed 
  by array elements */
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; 
        } 
    } 

    // Check for last element 
    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; 
        } 
    } 

    // Check for last element 
    if (result == true && n % 2 == 0)
    { 
        if (arr[n - 1] >= arr[n - 2]) 
        { 
            result = false; 
        } 
    } 
} 

return result;

}

// Driver code 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"); 
}

} }

// This code is contributed // by inder_verma

JavaScript

PHP

arr,arr, arr,n) { $result = true; /* Check the wave form * If arr[1] is greater than left and right * Same pattern will be followed by whole * elements, else reverse pattern * will be followed by array elements */ if ($arr[1] > $arr[0] && arr[1]>arr[1] > arr[1]>arr[2]) { for ( i=1;i = 1; i=1;i < ($n - 1); $i += 2) { if ($arr[$i] > arr[arr[arr[i - 1] && arr[arr[arr[i] > arr[arr[arr[i + 1]) { $result = true; } else { $result = false; break; } } // Check for last element if ($result == true && $n % 2 == 0) { if ($arr[$n - 1] <= arr[arr[arr[n - 2]) { $result = false; } } } else if ($arr[1] < $arr[0] && arr[1]<arr[1] < arr[1]<arr[2]) { for ($i = 1; i<i < i<n - 1; $i += 2) { if ($arr[$i] < arr[arr[arr[i - 1] && arr[arr[arr[i] < arr[arr[arr[i + 1]) { $result = true; } else { $result = false; break; } } // Check for last element if ($result == true && $n % 2 == 0) { if ($arr[$n - 1] >= arr[arr[arr[n - 2]) { $result = false; } } } return $result; } // Driver Code // Array $arr = array (1, 3, 2, 4 ); n=sizeof(n = sizeof(n=sizeof(arr); if (isWaveArray($arr, $n)) { echo "YES"; } else { echo "NO"; } // This code is contributed by jit_t ?>

**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 the array sort(arr, arr + n);

// swap adjacent elements to form wave
for (int i = 0; i < n - 1; i += 2) {
    swap(arr[i], arr[i + 1]);
}

// check if wave property is satisfied
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 { // Function to check if the given array is a wave array static boolean isWave(int[] arr, int n) { // Sort the array in ascending order Arrays.sort(arr);

    // Swap adjacent elements to form a wave
    for (int i = 0; i < n - 1; i += 2) {
        swap(arr, i, i + 1);
    }

    // Check if the wave property is satisfied
    for (int i = 0; i < n - 1; i++) {
        // For even indices, check if the current element is greater than the next element
        // For odd indices, check if the current element is smaller than the next element
        if ((i % 2 == 0 && arr[i] > arr[i + 1]) || (i % 2 == 1 && arr[i] < arr[i + 1])) {
            return true; // If the wave property is satisfied, return true
        }
    }

    return false; // If the wave property is not satisfied for any pair, return false
}

// Helper function to swap two elements in an array
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): # Sort the array in ascending order arr.sort()

# Swap adjacent elements to form a wave
for i in range(0, len(arr) - 1, 2):
    arr[i], arr[i + 1] = arr[i + 1], arr[i]

# Check if the wave property is satisfied
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

Driver code

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 { // Function to check if the array is a wave array public static bool IsWave(int[] arr, int n) { // Sort the array Array.Sort(arr);

    // Swap adjacent elements to form a wave
    for (int i = 0; i < n - 1; i += 2)
    {
        int temp = arr[i];
        arr[i] = arr[i + 1];
        arr[i + 1] = temp;
    }

    // Check if the wave property is satisfied
    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) { // Sort the array arr.sort((a, b) => a - b);

// Swap adjacent elements to form a wave
for (let i = 0; i < arr.length - 1; i += 2) {
    [arr[i], arr[i + 1]] = [arr[i + 1], arr[i]];
}

// Check if the wave property is satisfied
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;

}

//Driver code 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).