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Count of subarrays of size K with elements having even frequencies

  • Difficulty Level : Hard
  • Last Updated : 12 May, 2021

Given an array arr[] and an integer K, the task is to count subarrays of size K in which every element appears an even number of times in the subarray.
 

Examples:

Input: arr[] = {1, 4, 2, 10, 2, 10, 0, 20}, K = 4 
Output:
Explanation: Only subarray {2, 10, 2, 10} satisfies the required condition.

Input: arr[] = {1, 4, 2, 10, 2, 3, 1, 0, 20}, K = 3 
Output:
 

 



Naive Approach: 
The idea is to generate all subarrays of size K and check each of them whether all its elements are present even a number of times or not.

 
Time complexity: O(N*K)
Efficient Approach: 
 

The idea is to use Window Sliding and the XOR concept here.

  1. If the given K is odd, then return 0 as it is guaranteed that at least one number appears an odd number of times if K is odd.
  2. Check if K is greater than the length of arr[] then return 0.
  3. Initialize the following variables:
    • count: Store the count of subarrays of size K with all elements.
    • start: Remove left most element which is no longer part of k size subarray.
    • currXor: Store Xor of the current subarray.
  4. Calculate the Xor of the first K size subarray and check if currXor becomes 0, then increment the count and update currXor by eliminating Xor with arr[start] and increment start by 1.
  5. Traverse arr[] from K to the length of arr[]:
    • Update currXor by doing Xor with arr[i].
    • Increment count if currXor becomes 0 otherwise ignore.
    • Update currXor by eliminating Xor with arr[start].
    • Increment start by 1.
  6. Return count.

Below is the implementation of the above approach:
 

C++




// C++ program to count subarrays
// of size K with all elements
// having even frequencies
#include<bits/stdc++.h>
using namespace std;
 
// Function to return count of
// required subarrays
int countSubarray(int arr[], int K,
                             int N)
{
     
    // If K is odd
    if (K % 2 != 0)
         
        // Not possible to have
        // any such subarrays
        return 0;
 
    if (N < K)
        return 0;
 
    // Stores the starting index
    // of every subarrays
    int start = 0;
 
    int i = 0;
     
    // Stores the count of
    // required subarrays
    int count = 0;
     
    // Stores Xor of the
    // current subarray.
    int currXor = arr[i++];
 
    // Xor of first subarray
    // of size K
    while (i < K)
    {
        currXor ^= arr[i];
        i++;
    }
 
    // If all elements appear
    // even number of times,
    // increase the count of
    // such subarrays
    if (currXor == 0)
        count++;
 
    // Remove the starting element
    // from the current subarray
    currXor ^= arr[start++];
 
    // Traverse the array
    // for the remaining
    // subarrays
    while (i < N)
    {
         
        // Update Xor by adding the
        // last element of the
        // current subarray
        currXor ^= arr[i];
         
        // Increment i
        i++;
 
        // If currXor becomes 0,
        // then increment count
        if (currXor == 0)
            count++;
 
        // Update currXor by removing
        // the starting element of the
        // current subarray
        currXor ^= arr[start++];
    }
 
    // Return count
    return count;
}
 
// Driver Code
int main()
{
    int arr[] = { 2, 4, 4, 2, 2, 4 };
    int K = 4;
    int N = sizeof(arr) / sizeof(arr[0]);
     
    cout << (countSubarray(arr, K, N));
}
 
// This code is contributed by chitranayal

Java




// Java program to count subarrays
// of size K with all elements
// having even frequencies
 
import java.util.*;
 
class GFG {
 
    // Function to return count of
    // required subarrays
    static int countSubarray(int[] arr,
                             int K, int N)
    {
        // If K is odd
        if (K % 2 != 0)
            // Not possible to have
            // any such subarrays
            return 0;
 
        if (N < K)
            return 0;
 
        // Stores the starting index
        // of every subarrays
        int start = 0;
 
        int i = 0;
        // Stores the count of
        // required subarrays
        int count = 0;
        // Stores Xor of the
        // current subarray.
        int currXor = arr[i++];
 
        // Xor of first subarray
        // of size K
        while (i < K) {
            currXor ^= arr[i];
            i++;
        }
 
        // If all elements appear
        // even number of times,
        // increase the count of
        // such subarrays
        if (currXor == 0)
            count++;
 
        // Remove the starting element
        // from the current subarray
        currXor ^= arr[start++];
 
        // Traverse the array
        // for the remaining
        // subarrays
        while (i < N) {
            // Update Xor by adding the
            // last element of the
            // current subarray
            currXor ^= arr[i];
            // Increment i
            i++;
 
            // If currXor becomes 0,
            // then increment count
            if (currXor == 0)
                count++;
 
            // Update currXor by removing
            // the starting element of the
            // current subarray
            currXor ^= arr[start++];
        }
 
        // Return count
        return count;
    }
 
    // Driver Code
    public static void main(String[] args)
    {
        int[] arr = { 2, 4, 4, 2, 2, 4 };
        int K = 4;
        int N = arr.length;
        System.out.println(
            countSubarray(arr, K, N));
    }
}

Python3




# Python3 program to count subarrays
# of size K with all elements
# having even frequencies
 
# Function to return count of
# required subarrays
def countSubarray(arr, K, N):
     
    # If K is odd
    if (K % 2 != 0):
         
        # Not possible to have
        # any such subarrays
        return 0
 
    if (N < K):
        return 0
 
    # Stores the starting index
    # of every subarrays
    start = 0
    i = 0
     
    # Stores the count of
    # required subarrays
    count = 0
     
    # Stores Xor of the
    # current subarray.
    currXor = arr[i]
    i += 1
 
    # Xor of first subarray
    # of size K
    while (i < K):
        currXor ^= arr[i]
        i += 1
 
    # If all elements appear
    # even number of times,
    # increase the count of
    # such subarrays
    if (currXor == 0):
        count += 1
 
    # Remove the starting element
    # from the current subarray
    currXor ^= arr[start]
    start += 1
 
    # Traverse the array
    # for the remaining
    # subarrays
    while (i < N):
         
        # Update Xor by adding the
        # last element of the
        # current subarray
        currXor ^= arr[i]
         
        # Increment i
        i += 1
 
        # If currXor becomes 0,
        # then increment count
        if (currXor == 0):
            count += 1
 
        # Update currXor by removing
        # the starting element of the
        # current subarray
        currXor ^= arr[start]
        start += 1
 
    # Return count
    return count
     
# Driver Code
if __name__ == '__main__':
     
    arr = [ 2, 4, 4, 2, 2, 4 ]
    K = 4
    N = len(arr)
     
    print(countSubarray(arr, K, N))
 
# This code is contributed by mohit kumar 29   

C#




// C# program to count subarrays
// of size K with all elements
// having even frequencies
using System;
class GFG{
 
// Function to return count of
// required subarrays
static int countSubarray(int[] arr,
                         int K, int N)
{
    // If K is odd
    if (K % 2 != 0)
     
        // Not possible to have
        // any such subarrays
        return 0;
 
    if (N < K)
        return 0;
 
    // Stores the starting index
    // of every subarrays
    int start = 0;
 
    int i = 0;
     
    // Stores the count of
    // required subarrays
    int count = 0;
     
    // Stores Xor of the
    // current subarray.
    int currXor = arr[i++];
 
    // Xor of first subarray
    // of size K
    while (i < K)
    {
        currXor ^= arr[i];
        i++;
    }
 
    // If all elements appear
    // even number of times,
    // increase the count of
    // such subarrays
    if (currXor == 0)
        count++;
 
    // Remove the starting element
    // from the current subarray
    currXor ^= arr[start++];
 
    // Traverse the array
    // for the remaining
    // subarrays
    while (i < N)
    {
        // Update Xor by adding the
        // last element of the
        // current subarray
        currXor ^= arr[i];
         
        // Increment i
        i++;
 
        // If currXor becomes 0,
        // then increment count
        if (currXor == 0)
            count++;
 
        // Update currXor by removing
        // the starting element of the
        // current subarray
        currXor ^= arr[start++];
    }
 
    // Return count
    return count;
}
 
// Driver Code
public static void Main()
{
    int[] arr = { 2, 4, 4, 2, 2, 4 };
    int K = 4;
    int N = arr.Length;
    Console.Write(countSubarray(arr, K, N));
}
}
 
// This code is contributed by Akanksha_Rai

Javascript




<script>
 
// Javascript program to count subarrays
// of size K with all elements
// having even frequencies
 
// Function to return count of
// required subarrays
function countSubarray(arr, K, N)
{
     
    // If K is odd
    if (K % 2 != 0)
         
        // Not possible to have
        // any such subarrays
        return 0;
 
    if (N < K)
        return 0;
 
    // Stores the starting index
    // of every subarrays
    var start = 0;
 
    var i = 0;
     
    // Stores the count of
    // required subarrays
    var count = 0;
     
    // Stores Xor of the
    // current subarray.
    var currXor = arr[i];
    i++;
 
    // Xor of first subarray
    // of size K
    while (i < K)
    {
        currXor ^= arr[i];
        i++;
    }
 
    // If all elements appear
    // even number of times,
    // increase the count of
    // such subarrays
    if (currXor == 0)
        count++;
 
    // Remove the starting element
    // from the current subarray
    currXor ^= arr[start];
    start++;
 
    // Traverse the array
    // for the remaining
    // subarrays
    while (i < N)
    {
         
        // Update Xor by adding the
        // last element of the
        // current subarray
        currXor ^= arr[i];
         
        // Increment i
        i++;
 
        // If currXor becomes 0,
        // then increment count
        if (currXor == 0)
            count++;
 
        // Update currXor by removing
        // the starting element of the
        // current subarray
        currXor ^= arr[start];
        start++;
    }
 
    // Return count
    return count;
}
 
// Driver Code
    var arr = [2, 4, 4, 2, 2, 4];
    var K = 4;
    var N = arr.length;
     
    document.write(countSubarray(arr, K, N));
 
</script>
Output: 
3

 

Time Complexity: O(N) 
Space Complexity: O(1)

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