-
Notifications
You must be signed in to change notification settings - Fork 9
/
spider_spring2.py
206 lines (180 loc) · 6.6 KB
/
spider_spring2.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
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
# Copyright (c) 2020 kamyu. All rights reserved.
#
# Facebook Hacker Cup 2020 Final Round - Problem D. Spider Spring
# https://www.facebook.com/codingcompetitions/hacker-cup/2020/final-round/problems/D
#
# Time: O((N + M) * logN), pass in PyPy2 but Python2
# Space: O(N)
#
# SkipList + BITs solution, which is faster
#
from random import randint, seed
# Template modified from:
# https://github.com/kamyu104/FacebookHackerCup-2020/blob/master/Final%20Round/cryptoconference.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"), float("inf")), can_duplicated=False):
seed(0)
self.__head = SkipNode()
self.__len = 0
self.__can_duplicated = can_duplicated
self.add(end)
self.__end = self.find(end)
def begin(self):
return self.__head.nexts[0]
def end(self):
return self.__end
def lower_bound(self, target, cmp=lambda x, y: x < y):
return self.__lower_bound(target, self.__find_prev_nodes(target, cmp))
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 self.find(val), 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 node if self.__can_duplicated else (node, True)
def remove(self, it):
prevs = it.prevs
curr = self.__find(it.val, prevs)
if not curr:
return self.__end
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 curr.nexts[0]
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, cmp=lambda x, y: x < y):
prevs = [None]*len(self.__head.nexts)
curr = self.__head
for i in reversed(xrange(len(self.__head.nexts))):
while curr.nexts[i] and cmp(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 __iter__(self):
it = self.begin()
while it != self.end():
yield it.val
it = it.nexts[0]
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))
class BIT(object): # 1-indexed.
def __init__(self, n):
self.__bit = [0]*(n+1) # Extra one for dummy node.
def add(self, i, val):
while i < len(self.__bit):
self.__bit[i] += val
i += (i & -i)
def query(self, i):
ret = 0
while i > 0:
ret += self.__bit[i]
i -= (i & -i)
return ret
def read(N, K):
X = map(int, raw_input().strip().split())
A, B, C, D = map(int, raw_input().strip().split())
for _ in xrange(K, N):
X.append((A*X[-2] + B*X[-1] + C) % D + 1)
return X
def query_heights(heights, i):
return heights.lower_bound((i+1, -1)).prevs[0].val[1]
def update_heights(heights, i, j, h):
j += 1
jt = heights.lower_bound((j, -1))
if jt.val[0] != j:
jt = heights.add((j, jt.prevs[0].val[1] if jt is not heights.begin() else 0))[0]
it = heights.lower_bound((i, -1))
while it != jt:
it = heights.remove(it)
heights.add((i, h))
def update_bits(heights, bits, N, i, d):
if i < 0 or i+1 >= N:
return
a, b = query_heights(heights, i), query_heights(heights, i+1)
if a > b:
a, b = b, a
w = (i+1) * (N-i-1)
bits[0].add(a, w*d % MOD)
bits[1].add(a, a*w*d % MOD)
bits[2].add(b, w*d % MOD)
bits[3].add(b, b*w*d % MOD)
def spider_spring():
N, M, K = map(int, raw_input().strip().split())
H = read(N, K)
X, Y, Z, W = [read(M, K) for _ in xrange(4)]
size = max(max(H), max(Z), max(W))
heights = SkipList(end=(float("inf"), float("inf")))
bits = [BIT(size) for _ in xrange(4)]
line_segments = SkipList(end=float("inf"))
horiz = 0
for i in xrange(N):
update_heights(heights, i, i, H[i])
update_bits(heights, bits, N, i-1, 1)
line_segments.add(i-1)
horiz = (horiz + i*(N-i)) % MOD
result = 1
for i in xrange(M):
x, y, z, w = X[i]-1, min(X[i]+Y[i]-1, N)-1, Z[i], W[i]
it = line_segments.lower_bound(x-1)
while it != line_segments.end() and it.val <= y:
update_bits(heights, bits, N, it.val, -1)
it = line_segments.remove(it)
update_heights(heights, x, y, z)
update_bits(heights, bits, N, x-1, 1)
line_segments.add(x-1)
update_bits(heights, bits, N, y, 1)
line_segments.add(y)
d1 = (bits[3].query(size)-bits[3].query(w))-(bits[1].query(size)-bits[1].query(w))
d2 = (bits[2].query(size)-bits[2].query(w))-(bits[0].query(size)-bits[0].query(w))
vert = (d1 - d2*w) % MOD
result = result * (horiz+vert) * 2 % MOD
return result
MOD = 10**9+7
for case in xrange(input()):
print 'Case #%d: %s' % (case+1, spider_spring())