Difference between subarray, subset & subsequence

I'm a bit confused between subarray, subsequence & subset

if I have {1,2,3,4}

then

subsequence can be {1,2,4} OR {2,4} etc. So basically I can omit some elements but keep the order.

subarray would be( say subarray of size 3)

{1,2,3}
{2,3,4} 

Then what would be the subset?

I'm bit confused between these 3.

Solution 1:

In my opinion, if the given pattern is array, the so called subarray means contiguous subsequence.

For example, if given {1, 2, 3, 4}, subarray can be

{1, 2, 3}
{2, 3, 4}
etc.

While the given pattern is a sequence, subsequence contain elements whose subscripts are increasing in the original sequence.

For example, also {1, 2, 3, 4}, subsequence can be

{1, 3}
{1，4}
etc.

While the given pattern is a set, subset contain any possible combinations of original set.

For example, {1, 2, 3, 4}, subset can be

{1}
{2}
{3}
{4}
{1, 2}
{1, 3}
{1, 4}
{2, 3}
etc.

Solution 2:

Consider an array:

 {1,2,3,4}

Subarray: contiguous sequence in an array i.e.

{1,2},{1,2,3}

Subsequence: Need not to be contiguous, but maintains order i.e.

{1,2,4}

Subset: Same as subsequence except it has empty set i.e.

 {1,3},{}

Given an array/sequence of size n, possible

Subarray = n*(n+1)/2
Subseqeunce = (2^n) -1 (non-empty subsequences)
Subset = 2^n

Solution 3:

Consider these two properties in collection (array, sequence, set, etc) of elements: Order and Continuity.

Order is when you cannot switch the indices or locations of two or more elements (a collection with a single element has an irrelevant order).

Continuity is that an element must have their neighbors remain with them or be null.

A subarray has Order and Continuity.

A subsequence has Order but not Continuity.

A subset does not Order nor Continuity.

A collection with Continuity but not Order does not exist (to my knowledge)

Solution 4:

In the context of an array, SubSequence - need not be contigious but needs to maintain the order. But SubArray is contigious and inherently maintains the order.

if you have {1,2,3,4} --- {1,3,4} is a valid SubSequence but its not a subarray.

And subset is no order and no contigious.. So you {1,3,2} is a valid sub set but not a subsequence or subarray.

{1,2} is a valid subarray, subset and subsequence.

All Subarrays are subsequences and all subsequence are subset.

But sometimes subset and subarrays and sub sequences are used interchangably and the word contigious is prefixed to make it more clear.