-
Notifications
You must be signed in to change notification settings - Fork 9
/
circular_circles.py
176 lines (151 loc) · 6.07 KB
/
circular_circles.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
# Copyright (c) 2020 kamyu. All rights reserved.
#
# Facebook Hacker Cup 2020 Round 2 - Problem C. Circular Circles
# https://www.facebook.com/codingcompetitions/hacker-cup/2020/round-2/problems/C
#
# Time: O((N * M + E) * log(N * M)) = O((N * M + E) * (logN + logM)), pass in PyPy2 but Python2
# Space: O(N * M)
#
from itertools import izip
from random import randint, seed
# Template:
# https://github.com/kamyu104/LeetCode-Solutions/blob/master/Python/design-skiplist.py
class SkipNode(object):
def __init__(self, level=0, val=None):
self.val = val
self.nexts = [None]*level
self.prevs = [None]*level
class SkipList(object):
P_NUMERATOR, P_DENOMINATOR = 1, 2 # P = 1/4 in redis implementation
MAX_LEVEL = 32 # enough for 2^32 elements
def __init__(self, end=float("-inf"), can_duplicated=True):
seed(0)
self.__head = SkipNode()
self.__len = 0
self.__can_duplicated = can_duplicated
self.add(end)
def begin(self):
return self.__head.nexts[0]
def lower_bound(self, target):
return self.__lower_bound(target, self.__find_prev_nodes(target))
def find(self, target):
return self.__find(target, self.__find_prev_nodes(target))
def add(self, val):
if not self.__can_duplicated and self.find(val):
return False
node = SkipNode(self.__random_level(), val)
if len(self.__head.nexts) < len(node.nexts):
self.__head.nexts.extend([None]*(len(node.nexts)-len(self.__head.nexts)))
prevs = self.__find_prev_nodes(val)
for i in xrange(len(node.nexts)):
node.nexts[i] = prevs[i].nexts[i]
if prevs[i].nexts[i]:
prevs[i].nexts[i].prevs[i] = node
prevs[i].nexts[i] = node
node.prevs[i] = prevs[i]
self.__len += 1
return True
def remove(self, val):
prevs = self.__find_prev_nodes(val)
curr = self.__find(val, prevs)
if not curr:
return False
self.__len -= 1
for i in reversed(xrange(len(curr.nexts))):
prevs[i].nexts[i] = curr.nexts[i]
if curr.nexts[i]:
curr.nexts[i].prevs[i] = prevs[i]
if not self.__head.nexts[i]:
self.__head.nexts.pop()
return True
def __lower_bound(self, val, prevs):
if prevs:
candidate = prevs[0].nexts[0]
if candidate:
return candidate
return None
def __find(self, val, prevs):
candidate = self.__lower_bound(val, prevs)
if candidate and candidate.val == val:
return candidate
return None
def __find_prev_nodes(self, val):
prevs = [None]*len(self.__head.nexts)
curr = self.__head
for i in reversed(xrange(len(self.__head.nexts))):
while curr.nexts[i] and curr.nexts[i].val > val:
curr = curr.nexts[i]
prevs[i] = curr
return prevs
def __random_level(self):
level = 1
while randint(1, SkipList.P_DENOMINATOR) <= SkipList.P_NUMERATOR and \
level < SkipList.MAX_LEVEL:
level += 1
return level
def __len__(self):
return self.__len-1 # excluding end node
def __str__(self):
result = []
for i in reversed(xrange(len(self.__head.nexts))):
result.append([])
curr = self.__head.nexts[i]
while curr:
result[-1].append(str(curr.val))
curr = curr.nexts[i]
return "\n".join(map(lambda x: "->".join(x), result))
def read(K, N, M):
X = map(int, raw_input().strip().split())
A, B, C = map(int, raw_input().strip().split())
for _ in xrange(K, N):
X.append((A*X[-2] + B*X[-1] + C) % M)
return X
def max_weight(circle_weights, i):
return circle_weights[i].begin().val
def max_delta_weight(circle_weights, half_circle_weights, i):
return half_circle_weights[i][0].begin().val+half_circle_weights[i][1].begin().val-circle_weights[i].begin().val
def group(X, Y, i, j):
return 0 if X[i] <= j < Y[i] else 1
def update(s, v1, v2):
s.remove(v1)
s.add(v2)
def update_circle_edge(X, Y, circle_weights, half_circle_weights, circle_delta_weights, i, j, w1, w2):
r1, d1 = max_weight(circle_weights, i), max_delta_weight(circle_weights, half_circle_weights, i)
update(circle_weights[i], w1, w2), update(half_circle_weights[i][group(X, Y, i, j)], w1, w2)
r2, d2 = max_weight(circle_weights, i), max_delta_weight(circle_weights, half_circle_weights, i)
update(circle_delta_weights, d1, d2)
return r2-r1
def circular_circles():
N, M, E, K = map(int, raw_input().strip().split())
X = read(K, N, M)
Y = read(K, N, M)
I = read(K, E, N*M + N)
W = read(K, E, 10**9)
weights = [1]*(M*N + N)
circle_weights = [SkipList() for _ in xrange(N)]
half_circle_weights = [[SkipList() for _ in xrange(2)] for _ in xrange(N)]
circle_delta_weights, inter_circle_weights = SkipList(), SkipList()
for i in xrange(N):
if X[i] > Y[i]:
X[i], Y[i] = Y[i], X[i]
for j in xrange(len(half_circle_weights[i])):
half_circle_weights[i][j].add(0)
for j in xrange(M):
circle_weights[i].add(1)
half_circle_weights[i][group(X, Y, i, j)].add(1)
circle_delta_weights.add(max_delta_weight(circle_weights, half_circle_weights, i))
inter_circle_weights.add(1)
result, total, max_circle_weight_sum = 1, N*M+N, N
for j, w2 in izip(I, W):
w1, weights[j] = weights[j], w2
total += w2-w1
if j < N*M:
max_circle_weight_sum += update_circle_edge(X, Y, circle_weights, half_circle_weights, circle_delta_weights, j//M, j%M, w1, w2)
else:
update(inter_circle_weights, w1, w2)
curr = (total-max_circle_weight_sum-max(circle_delta_weights.begin().val, inter_circle_weights.begin().val)) % MOD
result = result*curr % MOD
return result
MOD = 10**9+7
for case in xrange(input()):
print 'Case #%d: %s' % (case+1, circular_circles())