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valet_parking_chapter_2-2.py
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valet_parking_chapter_2-2.py
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# Copyright (c) 2021 kamyu. All rights reserved.
#
# Facebook Hacker Cup 2021 Round 2 - Problem C. Valet Parking - Chapter 2
# https://www.facebook.com/codingcompetitions/hacker-cup/2021/round-2/problems/C2
#
# Time: O((R * C + S) * logR), pass in PyPy2 but Python2
# Space: O(R * C)
#
from random import randint, seed
# Template:
# https://github.com/kamyu104/GoogleKickStart-2021/blob/master/Round%20D/final_exam.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)
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(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, prevs):
if prevs:
candidate = prevs[0].nexts[0]
if candidate:
return candidate
return None
def __find(self, val, prevs):
candidate = self.__lower_bound(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))
# Template:
# https://github.com/kamyu104/GoogleCodeJam-2020/blob/master/Virtual%20World%20Finals/pack_the_slopes.py
class SegmentTree(object): # 0-based index
def __init__(self, N,
build_fn=lambda x, y: [y]*(2*x),
query_fn=lambda x, y: y if x is None else min(x, y),
update_fn=lambda x, y: y if x is None else x+y,
default_val=float("inf")):
self.N = N
self.H = (N-1).bit_length()
self.query_fn = query_fn
self.update_fn = update_fn
self.tree = build_fn(N, default_val)
self.lazy = [None]*N
for i in reversed(xrange(1, N)):
self.tree[i] = query_fn(self.tree[2*i], self.tree[2*i+1])
def __apply(self, x, val):
self.tree[x] = self.update_fn(self.tree[x], val)
if x < self.N:
self.lazy[x] = self.update_fn(self.lazy[x], val)
def update(self, L, R, h): # Time: O(logN), Space: O(N)
def pull(x):
while x > 1:
x //= 2
self.tree[x] = self.query_fn(self.tree[x*2], self.tree[x*2+1])
if self.lazy[x] is not None:
self.tree[x] = self.update_fn(self.tree[x], self.lazy[x])
if L > R:
return
L += self.N
R += self.N
L0, R0 = L, R
while L <= R:
if L & 1: # is right child
self.__apply(L, h)
L += 1
if R & 1 == 0: # is left child
self.__apply(R, h)
R -= 1
L //= 2
R //= 2
pull(L0)
pull(R0)
def query(self, L, R): # Time: O(logN), Space: O(N)
def push(x):
n = 2**self.H
while n != 1:
y = x // n
if self.lazy[y] is not None:
self.__apply(y*2, self.lazy[y])
self.__apply(y*2 + 1, self.lazy[y])
self.lazy[y] = None
n //= 2
result = None
if L > R:
return result
L += self.N
R += self.N
push(L)
push(R)
while L <= R:
if L & 1: # is right child
result = self.query_fn(result, self.tree[L])
L += 1
if R & 1 == 0: # is left child
result = self.query_fn(result, self.tree[R])
R -= 1
L //= 2
R //= 2
return result
def __str__(self):
showList = []
for i in xrange(self.N):
showList.append(self.query(i, i))
return ",".join(map(str, showList))
# Template:
# https://github.com/kamyu104/GoogleKickStart-2021/blob/main/Round%20F/festival2.py
def update_skip_lists(K, c, r, sl):
if c == 1:
sl[0].add(-r)
if len(sl[0]) <= K:
sl[1] = sl[0].end().prevs[0]
elif r >= -sl[1].val:
sl[1] = sl[1].prevs[0]
else:
sl[0].remove(sl[0].find(-r))
if len(sl[0]) < K:
sl[1] = sl[0].end().prevs[0]
elif r >= -sl[1].val:
sl[1] = sl[1].nexts[0]
def update(R, K, r, sls, st, diff):
s1, s2 = sls
A = -s1[1].val if R-K+1 <= len(s1[0]) else -1
B = s2[1].val if K <= len(s2[0]) else R+2
update_skip_lists(R-K+1, diff, r, s1)
update_skip_lists(K, diff, -r, s2)
if r >= A:
new_A = -s1[1].val if R-K+1 <= len(s1[0]) else -1
st.update(A+1, new_A-1, diff) if diff == 1 else st.update(new_A+1, A-1, diff)
A = new_A
if r <= B:
new_B = s2[1].val if K <= len(s2[0]) else R+2
st.update(new_B+1, B-1, diff) if diff == 1 else st.update(B+1, new_B-1, diff)
B = new_B
if not (r < A or r > B):
st.update(r, r, diff)
def valet_parking_chapter_2():
R, C, K, S = map(int, raw_input().strip().split())
G = [list(raw_input().strip()) for _ in xrange(R)]
sls = [[[SkipList(), None] for _ in xrange(2)] for _ in xrange(C)]
st = SegmentTree(R+2, build_fn=lambda x, y: [abs((i-x)-K) if i >= x else y for i in xrange(2*x)])
for j in xrange(C):
for i in xrange(R):
if G[i][j] == 'X':
update(R, K, i+1, sls[j], st, 1)
result = 0
for _ in xrange(S):
i, j = map(lambda x: int(x)-1, raw_input().strip().split())
G[i][j] = 'X' if G[i][j] == '.' else '.'
update(R, K, i+1, sls[j], st, 1 if G[i][j] == 'X' else -1)
result += st.query(0, R+1)
return result
for case in xrange(input()):
print 'Case #%d: %s' % (case+1, valet_parking_chapter_2())