Subarrays, Subsequences, and Subsets in Array

  • Last Updated : 15 Sep, 2022

What is a Subarray?

A subarray is a contiguous part of array, i.e., Subarray is an array that is inside another array.

In general, for an array of size n, there are n*(n+1)/2 non-empty subarrays.

For example, Consider the array [1, 2, 3, 4], There are 10 non-empty sub-arrays. The subarrays are:

(1), (2), (3), (4), 
(1,2), (2,3), (3,4), 
(1,2,3), (2,3,4), and 
(1,2,3,4)

What is a Subsequence?

A subsequence is a sequence that can be derived from another sequence by removing zero or more elements, without changing the order of the remaining elements.

More generally, we can say that for a sequence of size n, we can have (2n – 1) non-empty sub-sequences in total.

For the same above example, there are 15 sub-sequences. They are:

(1), (2), (3), (4), 
(1,2), (1,3),(1,4), (2,3), (2,4), (3,4), 
(1,2,3), (1,2,4), (1,3,4), (2,3,4), 
(1,2,3,4). 

What is a Subset?

If a Set has all its elements belonging to other sets, this set will be known as a subset of the other set.

A Subset is denoted as ““. If set A is a subset of set B, it is represented as A ⊆ B.

For example, Let Set_A = {m, n, o, p, q}, Set_ B = {k, l, m, n, o, p, q, r}

Then, A ⊆ B.

 

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Problems on Subarray:

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Problems on Subset:

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