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temporal_revision.py
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# Copyright (c) 2019 kamyu. All rights reserved.
#
# Facebook Hacker Cup 2019 Final Round - Temporal Revision
# https://www.facebook.com/hackercup/problem/1165177510537433/
#
# Time: O((S + N) * logN + (M + K) * (log*)(N)), p.s. (log*)(N) <= 5
# Space: O(NlogN), due to skip-list of tree node ancestors
#
from collections import defaultdict
from functools import partial
# Template:
# https://github.com/kamyu104/LeetCode-Solutions/blob/master/Python/accounts-merge.py
class UnionFind(object):
def __init__(self, n):
self.set = range(n)
def get_id(self):
self.set.append(len(self.set))
return len(self.set)-1
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
self.set[min(x_root, y_root)] = max(x_root, y_root)
return True
# Template:
# https://github.com/kamyu104/FacebookHackerCup-2019/blob/master/Final%20Round/little_boat_on_the_sea.py
def find_binary_tree_infos(N, children):
def preprocess(L, P, C, curr, parent):
# ancestors of the node i
P[curr].append(parent)
i = 0
while P[curr][i] != -1:
P[curr].append(P[P[curr][i]][i] if i < len(P[P[curr][i]]) else -1)
i += 1
# the subtree of the node i is represented by traversal index L[i]..R[i]
C[0] += 1
L[curr] = C[0]
def divide(stk, L, R, P, C, curr, parent):
stk.append(partial(postprocess, R, C, curr))
for i in reversed(xrange(len(children[curr]))):
child = children[curr][i]
stk.append(partial(divide, stk, L, R, P, C, child, curr))
stk.append(partial(preprocess, L, P, C, curr, parent))
def postprocess(R, C, curr):
R[curr] = C[0]
L, R, P, C = [0]*N, [0]*N, [[] for _ in xrange(N)], [-1]
stk = []
stk.append(partial(divide, stk, L, R, P, C, N-1, -1)) # root is the last node id: N-1
while stk:
stk.pop()()
return L, R, P
def build_binary_tree(N, A, B, E, V, activity_type):
union_find = UnionFind(N)
children = defaultdict(list)
when = defaultdict(lambda x: len(E))
curr_active_cnt_from_node = defaultdict(int)
for i in xrange(N):
curr_active_cnt_from_node[i] = int(activity_type[i] == OPEN)
dp1, dp2 = defaultdict(int), defaultdict(int)
for i in reversed(xrange(len(E))): # O((M+K)*alpha(N))
if E[i] == 1:
x, y = union_find.find_set(A[V[i]]), union_find.find_set(B[V[i]])
if x == y:
continue
v = union_find.get_id()
union_find.union_set(v, x), union_find.union_set(v, y)
children[v], when[v] = [x, y], i
curr_active_cnt_from_node[v] = curr_active_cnt_from_node[x] + curr_active_cnt_from_node[y]
dp1[v] = max(dp1[x], dp1[y])
dp2[v] = max(dp2[x], dp2[y], dp1[x]+dp1[y])
else:
v, x = union_find.get_id(), union_find.find_set(V[i])
union_find.union_set(v, x)
children[v], when[v] = [x], i
curr_active_cnt_from_node[v] = curr_active_cnt_from_node[x] + (-1 if E[i] == 2 else 1) # -1 means not yet activated, +1 means activated
dp1[v] = int(E[i] == 2) + dp1[x]
dp2[v] = int(E[i] == 2) + dp2[x]
return len(union_find.set), children, when, curr_active_cnt_from_node, dp1, dp2
def query_binary_tree(E, V, end_hr, children, when, curr_active_cnt_from_node, dp1, dp2, L, R, P, X, Y):
def is_ancestor(L, R, a, b): # includes itself
return L[a] <= L[b] <= R[b] <= R[a]
v = X
for i in reversed(xrange(len(P[v]))): # O(logN)
if i < len(P[v]) and P[v][i] != -1 and when[P[v][i]] >= Y:
v = P[v][i]
stk = [v]
while P[v][0] != -1: # O(1)
v = P[v][0]
if when[v] < Y-24:
break
stk.append(v)
stk = stk[::-1]
assert(len(stk) <= 24+1)
active_cnt_to_the_end_from_hr = [0]*len(stk)
accumulated_cnt = dp1[stk[-1]]
for i in reversed(xrange(len(stk)-1)):
active_cnt_to_the_end_from_hr[i] = accumulated_cnt
h = when[stk[i]]
if E[h] == 2 and end_hr[V[h]] >= Y and is_ancestor(L, R, stk[-1], V[h]):
accumulated_cnt += 1
max_cnt, curr_cnt = 0, curr_active_cnt_from_node[stk[0]]
for i in xrange(len(stk)-1):
h = when[stk[i]]
curr_cnt += int(E[h] == 2)
if len(children[stk[i]]) == 2:
other_sibling = children[stk[i]][0] if children[stk[i]][0] != stk[i+1] else children[stk[i]][1]
max_cnt = max(max_cnt, curr_cnt + dp1[other_sibling] + active_cnt_to_the_end_from_hr[i])
return max(max_cnt, curr_cnt + dp2[stk[-1]])
def temporal_revision():
N, M, K, S = map(int, raw_input().strip().split())
A, B = [0]*M, [0]*M
E, V = [0]*K, [0]*K
for i in xrange(M):
A[i], B[i] = map(int, raw_input().strip().split())
A[i], B[i] = A[i]-1, B[i]-1
activity_type, is_collapsed, end_hr = [0]*N, [False]*M, [0]*N
for i in xrange(K):
E[i], V[i] = map(int, raw_input().strip().split())
V[i] -= 1
if E[i] == 1:
is_collapsed[V[i]] = True
elif E[i] == 2:
activity_type[V[i]] |= OPEN
else: # E[i] == 3
activity_type[V[i]] |= CLOSE
end_hr[V[i]] = i
for i in xrange(M): # make remaining conduits as branch points
if is_collapsed[i] == False:
E.append(1), V.append(i)
for i in xrange(N):
if activity_type[i] == OPEN:
end_hr[i] = len(E) # set the max time to end activity
node_count, children, when, curr_active_cnt_from_node, dp1, dp2 = build_binary_tree(N, A, B, E, V, activity_type)
L, R, P = find_binary_tree_infos(node_count, children)
result, ans = 0, 0
for _ in xrange(S):
X, Y = map(int, raw_input().strip().split())
X, Y = X^ans, Y^ans
assert(1 <= X <= N and 1 <= Y <= K)
X, Y = X-1, Y-1
ans = query_binary_tree(E, V, end_hr,
children, when, curr_active_cnt_from_node, dp1, dp2,
L, R, P, X, Y)
result += ans
return result
OPEN, CLOSE = range(1, 3)
for case in xrange(input()):
print 'Case #%d: %s' % (case+1, temporal_revision())