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Added make_root in DSU #342

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merged 3 commits into from
Mar 13, 2021
Merged

Added make_root in DSU #342

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e0b1c99
add make_root method
Smit-create Mar 10, 2021
28a4d0b
new test
Smit-create Mar 11, 2021
0f8e381
maintain tree
Smit-create Mar 12, 2021
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18 changes: 18 additions & 0 deletions pydatastructs/miscellaneous_data_structures/disjoint_set.py
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Original file line number Diff line number Diff line change
Expand Up @@ -16,6 +16,9 @@ class DisjointSetForest(object):
>>> dst.union(1, 2)
>>> dst.find_root(2).key
1
>>> dst.make_root(2)
>>> dst.find_root(2).key
2

References
==========
Expand Down Expand Up @@ -74,3 +77,18 @@ def union(self, key1, key2):

y_root.parent = x_root
x_root.size += y_root.size

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

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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

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

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

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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

"""
Finds the set to which the key belongs
and makes it as the root of the set.
"""
if self.tree.get(key, None) is None:
raise KeyError("Invalid key, %s"%(key))

current_root = self.find_root(key)
if current_root.key != key:
key_set = self.tree[key]
current_root.parent = key_set
key_set.size = current_root.size
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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.

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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

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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.

key_set.parent = key_set
8 changes: 8 additions & 0 deletions pydatastructs/miscellaneous_data_structures/tests/test_disjoint_set.py
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Original file line number Diff line number Diff line change
Expand Up @@ -21,3 +21,11 @@ def test_DisjointSetForest():
assert raises(KeyError, lambda: dst.find_root(9))
dst.union(3, 1)
assert dst.find_root(3).key == 1
assert dst.find_root(5).key == 1
dst.make_root(6)
assert dst.find_root(3).key == 6
assert dst.find_root(5).key == 6
dst.make_root(5)
assert dst.find_root(1).key == 5
assert dst.find_root(5).key == 5
assert raises(KeyError, lambda: dst.make_root(9))