Find the longest sub-array having exactly k odd numbers

Given an array of size n. The problem is to find the longest sub-array having exactly k odd numbers.

Examples: 

Input : arr[] = {2, 3, 4, 11, 4, 12, 7}, k = 1
Output : 4
The sub-array is {4, 11, 4, 12}.

Input : arr[] = {3, 4, 6, 1, 9, 8, 2, 10}, k = 2
Output : 7
The sub-array is {4, 6, 1, 9, 8, 2, 10}.

Naive Approach: Consider all the sub-arrays and count the number of odd numbers in them. Return the length of the one having exactly ‘k’ odd numbers and has the maximum length. Time Complexity is of O(n^2).

Efficient Approach: The idea is to use sliding window.  Create a variable count, which stores the number of odd integers in the current window. If the value of count exceeds K at any point, decrease the window size from the start, otherwise include the element in the current window. Similarly, iterate for the complete array and maintain the maximum value of length of all the windows having exactly k odd numbers in a variable max. 

longSubarrWithKOddNum(arr, n, k)
    Initialize max = 0, count = 0, start = 0

    for i = 0 to n-1
        if arr[i] % 2 != 0, then
        count++
    while (count > k && start <= i)    
        if arr[start++] % 2 != 0, then
            count--
    if count == k, then
        if max < (i - start + 1), then
            max = i - start + 1    
    return max

Implementation:

C++

// C++ implementation to find the longest
// sub-array having exactly k odd numbers
#include <bits/stdc++.h>
using namespace std;

// function to find the longest sub-array
// having exactly k odd numbers
int longSubarrWithKOddNum(int arr[], int n,
                                     int k)
{
    int max = 0, count = 0, start = 0;

    // traverse the given array
    for (int i = 0; i < n; i++) {
        // if number is odd increment count
        if (arr[i] % 2 != 0)
            count++;

        // remove elements from sub-array from
        // 'start' index when count > k
        while (count > k && start <= i)
            if (arr[start++] % 2 != 0)
                count--;

        // if count == k, then compare max with
        // current sub-array length
        if (count == k)
            if (max < (i - start + 1))
                max = i - start + 1;
    }

    // required length
    return max;
}

// Driver program to test above
int main()
{
    int arr[] = {3, 4, 6, 1, 9, 8, 2, 10};
    int n = sizeof(arr) / sizeof(arr[0]);
    int k = 2;

    cout << "Length = "
         << longSubarrWithKOddNum(arr, n, k);

    return 0;
}

Java

// Java implementation to find the longest
// sub-array having exactly k odd numbers
import java.io.*;

class GFG {

    // function to find the longest sub-array
    // having exactly k odd numbers
    static int longSubarrWithKOddNum(int arr[], int n,
                                        int k)
    {
        int max = 0, count = 0, start = 0;

        // traverse the given array
        for (int i = 0; i < n; i++)
        {
            // if number is odd increment count
            if (arr[i] % 2 != 0)
                count++;

            // remove elements from sub-array from
            // 'start' index when count > k
            while (count > k && start <= i)
                if (arr[start++] % 2 != 0)
                    count--;

            // if count == k, then compare max
            // with current sub-array length
            if (count == k)
                if (max < (i - start + 1))
                    max = i - start + 1;
        }

        // required length
        return max;
    }

    // Driver program
    public static void main(String args[])
    {
        int arr[] = {3, 4, 6, 1, 9, 8, 2, 10};
        int n = arr.length;
        int k = 2;

        System.out.println("Length = "
                          + longSubarrWithKOddNum(arr, n, k));
    }
}


// This code is contributed
// by Nikita Tiwari.

Python3

# Python3 implementation to find the longest
# sub-array having exactly k odd numbers

# Function to find the longest sub-array
# having exactly k odd numbers
def longSubarrWithKOddNum(arr, n, k) :

    mx, count, start = 0, 0, 0

    # Traverse the given array
    for i in range(0, n) :

        # if number is odd increment count
        if (arr[i] % 2 != 0) :
            count = count + 1

        # remove elements from sub-array from
        # 'start' index when count > k
        while (count > k and start <= i) :

            if (arr[start] % 2 != 0) :
                count = count - 1

            start = start + 1

        # if count == k, then compare max
        # with current sub-array length
        if (count == k) :
            if (mx < (i - start + 1)) :
                mx = i - start + 1

    # required length
    return mx


# Driver Code
arr = [3, 4, 6, 1, 9, 8, 2, 10]
n = len(arr)
k = 2

print("Length = ", longSubarrWithKOddNum(arr, n, k))

# This code is contributed by Nikita Tiwari.

C#

// C# implementation to find the longest
// sub-array having exactly k odd numbers
using System;

class GFG {

    // function to find the longest sub-array
    // having exactly k odd numbers
    static int longSubarrWithKOddNum(int []arr, int n,
                                                int k)
    {
        int max = 0, count = 0, start = 0;

        // traverse the given array
        for (int i = 0; i < n; i++)
        {
            // if number is odd increment count
            if (arr[i] % 2 != 0)
                count++;

            // remove elements from sub-array from
            // 'start' index when count > k
            while (count > k && start <= i)
                if (arr[start++] % 2 != 0)
                    count--;

            // if count == k, then compare max
            // with current sub-array length
            if (count == k)
                if (max < (i - start + 1))
                    max = i - start + 1;
        }

        // required length
        return max;
    }

    // Driver program
    public static void Main()
    {
        int []arr = {3, 4, 6, 1, 9, 8, 2, 10};
        int n = arr.Length;
        int k = 2;

        Console.WriteLine("Length = "
                        + longSubarrWithKOddNum(arr, n, k));
    }
}


// This code is contributed
// by vt_m.

PHP

<?php
// PHP implementation to find the longest
// sub-array having exactly k odd numbers

// function to find the longest sub-array
// having exactly k odd numbers
function longSubarrWithKOddNum($arr, $n,
                                    $k)
{
    $max = 0; $count = 0; $start = 0;

    // traverse the given array
    for ($i = 0; $i < $n; $i++)
    {

        // if number is odd increment count
        if ($arr[$i] % 2 != 0)
            $count++;

        // remove elements from sub-array from
        // 'start' index when count > k
        while ($count > $k && $start <= $i)
            if ($arr[$start++] % 2 != 0)
                $count--;

        // if count == k, then compare max with
        // current sub-array length
        if ($count == $k)
            if ($max < ($i - $start + 1))
                $max = $i - $start + 1;
    }

    // required length
    return $max;
}

// Driver Code
{
    $arr = array(3, 4, 6, 1, 9, 8, 2, 10);
    $n = sizeof($arr) / sizeof($arr[0]);
    $k = 2;

    echo "Length = ", longSubarrWithKOddNum($arr, $n, $k);
    return 0;
}

// This code is contributed by nitin mittal.
?>

Javascript

<script>

// Javascript implementation to find the longest
// sub-array having exactly k odd numbers

// function to find the longest sub-array
// having exactly k odd numbers
function longSubarrWithKOddNum(arr, n, k)
{
    var max = 0, count = 0, start = 0;

    // traverse the given array
    for (var i = 0; i < n; i++) {
        // if number is odd increment count
        if (arr[i] % 2 != 0)
            count++;

        // remove elements from sub-array from
        // 'start' index when count > k
        while (count > k && start <= i)
            if (arr[start++] % 2 != 0)
                count--;

        // if count == k, then compare max with
        // current sub-array length
        if (count == k)
            if (max < (i - start + 1))
                max = i - start + 1;
    }

    // required length
    return max;
}

// Driver program to test above
var arr = [3, 4, 6, 1, 9, 8, 2, 10];
var n = arr.length;
var k = 2;

document.write( "Length = "
     +  longSubarrWithKOddNum(arr, n, k));


</script>

Output

Length = 7

Time Complexity: O(n).