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personal_space.py
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personal_space.py
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# Copyright (c) 2019 kamyu. All rights reserved.
#
# Facebook Hacker Cup 2018 Final Round - Personal Space
# https://www.facebook.com/hackercup/problem/659927157741948/
#
# Time: O(NlogN), there is no built-in rbtree in python, so we can use skip list alternatively,
# which implementation is much simpler than rbtree
# and has the same complexity on average
# Space: O(N)
#
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=False):
seed(0)
self.__head = SkipNode()
self.__len = 0
self.__can_duplicated = can_duplicated
self.add(end)
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 add_rect(rects, x1, y1, x2, y2):
if x2 < 0 or y1 > MAX_X_Y:
return
i = len(rects)+1
rects.append(((y1, 1), (x1, i)))
rects.append(((y2, -1), (x2, i)))
def add_rects(x_ordered_set, rects, x):
it = x_ordered_set.lower_bound(x)
for i in xrange(3):
it = it.prevs[0]
X = []
for i in xrange(7):
X.append(it.val)
it = it.nexts[0]
for i in xrange(4):
add_rect(rects, X[i], X[i+1], X[i+2], X[i+3])
def query(x_max_dp_ordered_set, x):
return x_max_dp_ordered_set.lower_bound((x+1, 0)).prevs[0].val[1]
def update(x_max_dp_ordered_set, x, v):
it = x_max_dp_ordered_set.lower_bound((x+1, 0)).prevs[0]
if v <= it.val[1]:
return
if it.val[0] < x:
it = it.nexts[0]
while it and it.val[1] <= v:
curr = it
it = it.nexts[0]
x_max_dp_ordered_set.remove(curr.val)
x_max_dp_ordered_set.add((x, v))
def personal_space():
N = input()
intervals = []
for i in xrange(N):
X, A, B = map(int, raw_input().strip().split())
intervals.append((((A, X), 1)))
intervals.append((((B+1, X), -1)))
# bottom-up line sweep to generate all possible fish placement "rectangles"
intervals.sort()
x_ordered_set = SkipList()
for i in xrange(3):
x_ordered_set.add(-1-i)
x_ordered_set.add(MAX_X_Y+1+i)
rects = []
i = 0
while i < len(intervals):
j = i
while j+1 < len(intervals) and intervals[j+1][0][0] == intervals[i][0][0]:
j += 1
for k in xrange(i, j+1):
if intervals[k][1] > 0:
x_ordered_set.add(intervals[k][0][1])
else:
x_ordered_set.remove(intervals[k][0][1])
for k in xrange(i, j+1):
add_rects(x_ordered_set, rects, intervals[k][0][1])
i = j
i += 1
# bottom-up line sweep DP on rectangles
rects.sort()
x_max_dp_ordered_set = SkipList((float("inf"), float("inf")))
x_max_dp_ordered_set.add((float("-inf"), 0))
result = 0
dp = [0]*len(rects)
for i in xrange(len(rects)):
x, j = rects[i][1][0], rects[i][1][1]
if rects[i][0][1] > 0:
dp[j] = query(x_max_dp_ordered_set, x)+1
result = max(result, dp[j])
else:
update(x_max_dp_ordered_set, x, dp[j])
return result
MAX_X_Y = 10**9
for case in xrange(input()):
print 'Case #%d: %s' % (case+1, personal_space())