# Friend Circle Queries

##### Short Problem Definition:

##### Link

##### Complexity:

time complexity is O(n(logq+logn))

space complexity is O(N)

##### Execution:

This is a typical Union-find problem statement. The particular UF implementation I use does not track groups and their sizes. The best way to determine the current largest group is to assume that the group that was just merged is the largest one.

##### Solution:

#!/bin/python import math import os import random import re import sys from collections import defaultdict """UnionFind.py Union-find data structure. Based on Josiah Carlson's code, <a class="vglnk" href="http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/215912" rel="nofollow"><span>http</span><span>://</span><span>aspn</span><span>.</span><span>activestate</span><span>.</span><span>com</span><span>/</span><span>ASPN</span><span>/</span><span>Cookbook</span><span>/</span><span>Python</span><span>/</span><span>Recipe</span><span>/</span><span>215912</span></a> with significant additional changes by D. Eppstein. """ class UnionFind: """Union-find data structure. Each unionFind instance X maintains a family of disjoint sets of hashable objects, supporting the following two methods: - X[item] returns a name for the set containing the given item. Each set is named by an arbitrarily-chosen one of its members; as long as the set remains unchanged it will keep the same name. If the item is not yet part of a set in X, a new singleton set is created for it. - X.union(item1, item2, ...) merges the sets containing each item into a single larger set. If any item is not yet part of a set in X, it is added to X as one of the members of the merged set. """ def __init__(self): """Create a new empty union-find structure.""" self.weights = {} self.parents = {} def __getitem__(self, object): """Find and return the name of the set containing the object.""" # check for previously unknown object if object not in self.parents: self.parents[object] = object self.weights[object] = 1 return object # find path of objects leading to the root path = [object] root = self.parents[object] while root != path[-1]: path.append(root) root = self.parents[root] # compress the path and return for ancestor in path: self.parents[ancestor] = root return root def __iter__(self): """Iterate through all items ever found or unioned by this structure.""" return iter(self.parents) def union(self, *objects): """Find the sets containing the objects and merge them all.""" roots = [self[x] for x in objects] heaviest = max([(self.weights[r],r) for r in roots])[1] for r in roots: if r != heaviest: self.weights[heaviest] += self.weights[r] self.parents[r] = heaviest # Complete the maxCircle function below. def maxCircle(queries): uf = UnionFind() largest_element = 0 result = [] for query in queries: uf.union(query[0], query[1]) current_grouping = uf.weights[uf[query[0]]] largest_element = max(largest_element, current_grouping) result.append(largest_element) return result if __name__ == '__main__': fptr = open(os.environ['OUTPUT_PATH'], 'w') q = int(raw_input()) queries = [] for _ in xrange(q): queries.append(map(int, raw_input().rstrip().split())) ans = maxCircle(queries) fptr.write('\n'.join(map(str, ans))) fptr.write('\n') fptr.close()

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