Consider the following alternative implimentation of the disjoint-sets data structure. class Partition: definit_(P,n): #sometimes called makeset (j) P.parent [j for j in range(n)] P.weight [1] * n - def find (P, key): if P.parent [key] != key: key P. find (P.parent [key]) M return key def union (P,x,y): rx = P.find(x) ry = P.find(y) if rx == ry: return if P.weight [rx] > P.weight[ry]: P.parent [ry] - rx P.weight [rx] += P.weight[ry] else: P.parent[rx] - ry P.weight [ry] + P.weight[rx]
Consider the following alternative implimentation of the disjoint-sets data structure. class Partition: definit_(P,n): #sometimes called makeset (j) P.parent [j for j in range(n)] P.weight [1] * n - def find (P, key): if P.parent [key] != key: key P. find (P.parent [key]) M return key def union (P,x,y): rx = P.find(x) ry = P.find(y) if rx == ry: return if P.weight [rx] > P.weight[ry]: P.parent [ry] - rx P.weight [rx] += P.weight[ry] else: P.parent[rx] - ry P.weight [ry] + P.weight[rx]
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![Consider the following alternative implimentation of the disjoint-sets data structure.
class Partition:
definit_(P,n):
# sometimes called makeset(j)
P.parent = [j for j in range(n)]
P.weight = [1] * n
def find(P, key):
if P.parent [key] != key:
key = P.find(P.parent [key])
return key
def union(P,x,y) ::
rx = P.find(x)
ry = P.find(y)
if rx == ry:
return
if P.weight[rx] > P.weight[ry]:
P.parent [ry] = rx
P.weight [rx] += P.weight[ry]
else:
P.parent [rx] ry
=
P.weight [ry] += P.weight[rx]
Prove that after any sequence of union operations, P.find(x) takes O(lg n) time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2895c32f-ae30-4ee7-b668-b0d596d7ce2b%2Face0a997-d3e7-46b5-9bf4-2535dfc06ac6%2Fx5hh9ic_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following alternative implimentation of the disjoint-sets data structure.
class Partition:
definit_(P,n):
# sometimes called makeset(j)
P.parent = [j for j in range(n)]
P.weight = [1] * n
def find(P, key):
if P.parent [key] != key:
key = P.find(P.parent [key])
return key
def union(P,x,y) ::
rx = P.find(x)
ry = P.find(y)
if rx == ry:
return
if P.weight[rx] > P.weight[ry]:
P.parent [ry] = rx
P.weight [rx] += P.weight[ry]
else:
P.parent [rx] ry
=
P.weight [ry] += P.weight[rx]
Prove that after any sequence of union operations, P.find(x) takes O(lg n) time.
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