# 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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