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chainblock2.py
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# Copyright (c) 2021 kamyu. All rights reserved.
#
# Facebook Hacker Cup 2021 Round 2 - Problem B. Chainblock
# https://www.facebook.com/codingcompetitions/hacker-cup/2021/round-2/problems/B
#
# Time: O(N)
# Space: O(N)
#
from functools import partial
class UnionFind(object): # Time: O(n * alpha(n)), Space: O(n)
def __init__(self, n):
self.set = range(n)
self.rank = [0]*n
self.ancestor = range(n) # modified
def find_set(self, x):
stk = []
while self.set[x] != x: # path compression
stk.append(x)
x = self.set[x]
while stk:
self.set[stk.pop()] = x
return x
def union_set(self, x, y):
x_root, y_root = map(self.find_set, (x, y))
if x_root == y_root:
return False
if self.rank[x_root] < self.rank[y_root]: # union by rank
self.set[x_root] = y_root
elif self.rank[x_root] > self.rank[y_root]:
self.set[y_root] = x_root
else:
self.set[y_root] = x_root
self.rank[x_root] += 1
return True
def find_ancestor_of_set(self, x): # modified
return self.ancestor[self.find_set(x)]
def update_ancestor_of_set(self, x): # modified
self.ancestor[self.find_set(x)] = x
# Template:
# https://github.com/kamyu104/GoogleCodeJam-2020/blob/master/Round%202/emacs++2_concise.py
class TreeInfos(object): # Time: O(N), Space: O(N), N is the number of nodes
def __init__(self, children):
def preprocess(curr, parent):
# visited order of the nodes
if curr:
O.append(curr) # modified
# depth of the node i
D[curr] = 1 if parent == -1 else D[parent]+1
# parent of the node i
P[curr] = parent # modified
def divide(curr, parent):
for i in reversed(xrange(len(children[curr]))):
child = children[curr][i]
if child == parent:
continue
stk.append(partial(divide, child, curr))
stk.append(partial(preprocess, curr, parent))
N = len(children)
D, P, O = [0]*N, [-1]*N, []
stk = []
stk.append(partial(divide, 0, -1))
while stk:
stk.pop()()
self.D, self.P, self.O = D, P, O
# Reference:
# https://en.wikipedia.org/wiki/Tarjan%27s_off-line_lowest_common_ancestors_algorithm
def iter_tarjan_offline_lca(adj, pairs, cb): # Time: O(N)
def divide(parent, i):
stk.append(partial(conquer, i))
for child in reversed(adj[i]):
if child == parent:
continue
stk.append(partial(merge, i, child))
stk.append(partial(divide, i, child))
def merge(parent, i):
uf.union_set(parent, i)
uf.update_ancestor_of_set(parent)
def conquer(i):
lookup[i] = True
for j in pairs[i]:
if not lookup[j]:
continue
cb(i, uf.find_ancestor_of_set(j))
N = len(adj)
uf = UnionFind(N)
stk, lookup = [], [False]*N
stk.append(partial(divide, -1, 0))
while stk:
stk.pop()()
def chainblock():
N = input()
adj = [[] for _ in xrange(N)]
for _ in xrange(N-1):
A, B = map(int, raw_input().strip().split())
adj[A-1].append(B-1)
adj[B-1].append(A-1)
F = map(lambda x: int(x)-1, raw_input().strip().split())
tree_infos = TreeInfos(adj)
groups = [[] for _ in xrange(N)]
for i, f in enumerate(F):
groups[f].append(i)
min_depth = [float("inf")]*N
pairs = [[] for _ in xrange(N)]
for f, idxs in enumerate(groups):
if not idxs:
continue
min_depth[f] = tree_infos.D[idxs[0]]
for i in xrange(len(idxs)-1):
pairs[idxs[i]].append(idxs[i+1])
pairs[idxs[i+1]].append(idxs[i])
def cb(i, lca):
min_depth[F[i]] = min(min_depth[F[i]], tree_infos.D[lca])
iter_tarjan_offline_lca(adj, pairs, cb)
A = [float("inf")]*N
for f, idxs in enumerate(groups):
for i in idxs:
A[i] = min_depth[f]
result = 0
for i in reversed(tree_infos.O):
if A[i] == tree_infos.D[i]:
result += 1
else:
A[tree_infos.P[i]] = min(A[tree_infos.P[i]], A[i])
return result
for case in xrange(input()):
print 'Case #%d: %s' % (case+1, chainblock())