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}.

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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.

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

C++

 // C++ implementation to find the longest // sub-array having exactly k odd numbers #include 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);     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

 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);     \$k = 2;            echo "Length = ", longSubarrWithKOddNum(\$arr, \$n, \$k);     return 0;      }     // This code is contributed by nitin mittal. ?>

Output :

Length = 7

Time Complexity: O(n).

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