In normal DS when we change or update a particular value the entire DS gets changed. Consider an array arr = [1, 2, 3, 4, 4], now if we want to update arr[2] to 6 it will become [1, 2, 6, 4, 4]. This final array now lost its pervious state. But in case of Persistent DS it will preserve it's previous states as well.

Persistent Datastructure preserves all versions of itself

• Every update to the data structure creates a new version
• Update(version, <value>): returns a new version

• Query any versions of the DS
• Update only the latest version of DS

Let's say we have a series of versions as follows (in the form of Linked List):

v1 -> v2 -> v3

Now if we want to make some changes we can only do that to the v3, so after this update we will have

v1 -> v2 -> v3 -> v4

Hence, all the versions will always be linearly ordered (due to the additional constraint)

• Query any versions of the DS (typical of any persistence)
• Update any version of the DS

Let's say initially you only one version v1, and then you make an update you get

v1 -> v2

Now you apply another update but again to v1 (this was not possible in partial persistence) here it will branch off as show below

        v1
       /  \ 
     v2    v3

Again if we update v3 we will get:-

        v1
       /  \ 
     v2    v3
            \
            v4 

Hence, in full persistence the versions will form a tree.

A DS that supports full persistence will always support partial persistence.