# Length of Shortest sub-array containing ‘k’ distinct elements of another Array | Sliding Window Problem

I came across this variant of the **Sliding Window Problem** during the coding round of a software engineering interview. I couldn’t find any references to it on the internet, hence this article. 😀

**Problem Statement:**Given two arrays of integers (

**array**and

*A***array**) and a

*B***number**(

**), find the length of the shortest sub-array of array**

*K***which contains exactly**

*A*

*K**distinct elements of array*

**.**

*B*The problem statement might be a bit difficult to grasp at a single glance (*and the original question used fancy words like stream of network data…*), but the below details should make it clearer

**Input Format:**

The first line contains **3** space separated integers ** N** and

**and**

*M***, in this particular order. The next line contains**

*K***integers i.e. the elements of the array**

*N***, and the next line contains**

*A***integers denoting the elements of the array**

*M***.**

*B***Input Constraints:**

1 ≤** K** ≤

**≤**

*M***≤ 2 x 10⁵**

*N*1 ≤

**[**

*A**i*],

**[**

*B**i*] ≤ 10⁹

**Sample Input: **

`5 3 2`

1 1 1 2 1

1 2 3

**Sample Output:**`2`

**Explanation:**In this case

**, so the required sub-array of**

*K*= 2**array**should contain 2 distinct elements of

*A***array**. The shortest sub-array fulfilling our requirements would be sub array [4…5] i.e.

*B***{2, 1}**

**Solution:**

On analyzing the problem statement, it’s evident that this is another instance of the sliding window problem, with the window in this case representing the sub-array of **array A**.

*To read more about sliding window problems, you can refer to this medium article by **outco.io*

Let’s have a look at the solution and then go through it’s major points

- We’ve created a
`set`

and added all elements of`arrayB`

in the set. We’ll use this set to determine if the number being considered is part of`arrayB`

or not - The
`map`

will store numbers from`arrayA`

, along with the indices at which the numbers occur. Every time we encounter a number again, we’ll put the number and the new index into the`map`

. Hence the`map`

will always store the index of the right-most occurrence of the number (that we’ve encountered so far) - We’ll only insert a number in the
`map`

if it is also part of the`set`

. Hence the size of the`map`

will give us the number of distinct elements in the sub-array, which are also part of`arrayB`

- The variable
`minLen`

is initialized with the value`Integer.MAX_VALUE`

and holds our interim result - The variables
`start`

and`end`

represent the starting index and ending index of the window - With every iteration of the
`for`

loop (*line 10*), we increment (*slide*) the end of the window, increasing the length of the sub-array by 1 - If the size of the map is less than
`k`

, we’ll continue to the next iteration of the loop - If the size of the map is greater than
`k`

, we’ll keep sliding the start of the window to remove elements which do not impact the size of the`map`

. We ensure this by using the following conditions — either the number at the start of the window is not part of the`set`

or it’s not the first occurrence of that number in our window (*line 17*) - Then we’ll remove the number at the
`start`

of the window and increment the`start`

by 1. This will make the size of the`map`

equal to`k`

(Since at every step since we only slide the`end`

of the window by 1, the size of the`map`

will never exceed`k`

by more than 1) - Line 20 will repeat the same operation as line 17, sliding the start of the window to the right, without affecting the size of the
`map`

- We’ll update the interim result variable
`minLen`

by comparing it with the current length of the window - At the end of the for loop, we’ll return the result if it holds a valid value. Else we’ll return
`-1`

to indicate that no sub-array could be found which satisfies our requirements

Below is a runnable version of the same method, complete with input and output statements