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final_exam.py
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final_exam.py
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# Copyright (c) 2021 kamyu. All rights reserved.
#
# Google Kick Start 2021 Round D - Problem C. Final Exam
# https://codingcompetitions.withgoogle.com/kickstart/round/00000000004361e3/000000000082bffc
#
# Time: O(NlogN + M * log(N + M)), pass in PyPy2 but Python2
# Space: O(N + M)
#
from random import randint, seed
# Template:
# https://github.com/kamyu104/FacebookHackerCup-2020/blob/master/Round%202/log_drivin_hirin.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(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))
def remove_x_from_interval(sl, it, x):
l, r = it.val
sl.remove(it)
if l <= x-1:
sl.add((l, x-1))
if x+1 <= r:
sl.add((x+1, r))
def final_exam():
N, M = map(int, raw_input().strip().split())
sl = SkipList() # alternative of sortedcontainers.SortedList
for l, r in (map(int, raw_input().strip().split()) for _ in xrange(N)):
sl.add((l, r))
result = []
for x in map(int, raw_input().strip().split()):
it = sl.lower_bound((x+1,))
if it != sl.begin() and it.prevs[0].val[0] <= x <= it.prevs[0].val[1]:
it = it.prevs[0]
result.append(x)
elif it == sl.end() or (it != sl.begin() and x-it.prevs[0].val[1] <= it.val[0]-x):
it = it.prevs[0]
result.append(it.val[1])
else:
result.append(it.val[0])
remove_x_from_interval(sl, it, result[-1])
return " ".join(map(str, result))
for case in xrange(input()):
print 'Case #%d: %s' % (case+1, final_exam())