Added make_root in DSU

[Smit-create]

References to other Issues or PRs or Relevant literature

Brief description of what is fixed or changed

Added a method to modify the parent of set to which key belongs

>>> dst = DisjointSetForest()
>>> dst.make_set(1)
>>> dst.make_set(2)
>>> dst.union(1, 2)
>>> dst.find_root(2).key
1
>>> dst.make_root(2)
>>> dst.find_root(2).key
2

[codecov]

Codecov Report

Merging #342 (0f8e381) into master (a21d00e) will increase coverage by 0.006%.
The diff coverage is 100.000%.

@@              Coverage Diff              @@
##            master      #342       +/-   ##
=============================================
+ Coverage   98.550%   98.556%   +0.006%     
=============================================
  Files           25        25               
  Lines         3243      3257       +14     
=============================================
+ Hits          3196      3210       +14     
  Misses          47        47               

Impacted Files	Coverage Δ
...ucts/miscellaneous_data_structures/disjoint_set.py	100.000% <100.000%> (ø)

[Smit-create]

@czgdp1807 I was thinking if we could change the implementation of the current DSU from maps to arrays(take n(size of array) as an argument while creating the instance) as it is costing an additional factor O(logN) in time complexity

[czgdp1807]

In Python dict is a hashing based data structure It's counterpart in C++ is unordered_map. map in C++ is based on red-black tree and is not hashing based hence, it costs O(lg N) overhead.

[czgdp1807]

The feature looks good. Could you share an example (book/lecture notes examples will work) where this is used/required?

[Smit-create]

Presently, I don't remember the exact the example but, we can consider this example https://cp-algorithms.com/data_structures/disjoint_set_union.html#toc-tgt-10 wherein we generally make root which Is largest element in set

[czgdp1807]

I see. That's great. Could you solve one such problem using DSU API in pydatastructs and show the code here?

[Smit-create]

I will trying finding the exact problem I solved using this method and show that

[Smit-create]

Well, this is the problem where I used the above method: https://codeforces.com/contest/1133/problem/F2, and the submission of mine can be found at: https://codeforces.com/contest/1133/submission/109674863

[Smit-create]

@czgdp1807 Looks good to go?

[czgdp1807]

I think the size of current_root should change. Just take the following example,

>>> from pydatastructs import *
>>> dst = DisjointSetForest()
>>> dst.make_set(1)
>>> dst.make_set(2)
>>> dst.make_set(3)
>>> dst.tree[1].size
1
>>> dst.tree[2].size
1
>>> dst.tree[3].size
1
>>> dst.union(2, 3)
>>> dst.tree[1].size
1
>>> dst.tree[2].size
2
>>> dst.tree[3].size
1
>>> dst.make_root(3)
>>> dst.tree[1].size
1
>>> dst.tree[2].size # should have been 1 because now 2 is pointing to 3
2
>>> dst.tree[3].size
2

I think this inconsistency can cause problems when root is shifted a lot of times to different elements of set. We should keep things correct wherever possible.

[Smit-create]

I think this inconsistency can cause problems when root is shifted a lot of times to different elements of set. We should keep things correct wherever possible.

This can be recitifed using re-rooting technique: https://wiki.algo.is/Rerooting%20technique. Actually while changing the root I didn't tried to maintain tree/subtree structure and just focused on the size of total elements belonging to that set. However using above technique we can re-root by maintaing tree/subtree structure too

[czgdp1807]

I think we should have it. We may need to track the nodes whose size will change due to change of root. It may or not be that tricky. Try to do it by just using the parent pointers.

[czgdp1807]

LGTM. Merging. Thanks.