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import unittest | ||
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class TestFenwickTree(unittest.TestCase): | ||
def setUp(self): | ||
self.t = FenwickTree(3) | ||
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def test_add_and_upto(self): | ||
self.t.add(2) | ||
self.assertEqual(self.t.upto(0), 0) | ||
self.assertEqual(self.t.upto(1), 0) | ||
self.assertEqual(self.t.upto(2), 1) | ||
self.assertEqual(self.t.upto(3), 1) | ||
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def test_min_free(self): | ||
self.t.add(2) | ||
self.assertEqual(self.t.min_free(), 1) | ||
self.t.add(1) | ||
self.t.add(3) | ||
self.assertEqual(self.t.min_free(), 4) | ||
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def test_remove(self): | ||
self.t.add(2) | ||
self.t.add(1) | ||
self.assertEqual(self.t.min_free(), 3) | ||
self.t.add(3) | ||
self.t.remove(2) | ||
self.assertEqual(self.t.min_free(), 2) | ||
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class FenwickTree: | ||
"""Simple Fenwick tree. The keys are numbered from 1 to 2^k.""" | ||
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def __init__(self, N): | ||
while N != (N & -N): | ||
N += N & -N | ||
self.N = N | ||
self.cell = [0] * (N + 1) | ||
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def add(self, key, value=1): | ||
"""Add a value to the specified key in the tree.""" | ||
while key <= self.N: | ||
self.cell[key] += value | ||
key += key & -key | ||
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def remove(self, key): | ||
"""Subtract 1 from the value of the specified key in the tree.""" | ||
self.add(key, -1) | ||
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def upto(self, key): | ||
"""Sum the values of the keys that are smaller or equal to the given tree.""" | ||
s = 0 | ||
c = min(key, self.N) | ||
while c: | ||
s += self.cell[c] | ||
c -= c & -c | ||
return s | ||
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def min_free(self): | ||
"""Find the smallest key for which the value is 0. | ||
Requirement: all values are 0 or 1. | ||
:return: The minimum free key (self.N + 1 if all keys are set). | ||
""" | ||
r = 1 | ||
while self.cell[r] == r: | ||
r *= 2 | ||
if r > self.N: | ||
return self.N + 1 | ||
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b = r // 2 | ||
while b > 1: | ||
# [r - b + 1; r] has the answer | ||
b = b // 2 | ||
m = r - b | ||
if self.cell[m] < b: | ||
r = m | ||
else: | ||
assert self.cell[m] == b | ||
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return r | ||
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def main(): | ||
k, n = map(int, input().split()) | ||
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def gen(): | ||
for train in range(n): | ||
arrive, leave = [int(s) for s in input().split()] | ||
yield arrive, False, train | ||
yield leave, True, train | ||
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events = sorted(list(gen())) | ||
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# platforms are numbered from 1 to k | ||
platforms = FenwickTree(k) | ||
# trains are numbered from 0 to n-1 | ||
trains = [] | ||
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def find_platforms(): | ||
for _, leave, train in events: | ||
if leave: | ||
assert train < len(trains) | ||
platforms.remove(trains[train]) | ||
elif (platform := platforms.min_free()) <= k: | ||
assert len(trains) == train | ||
trains.append(platform) | ||
platforms.add(platform) | ||
else: | ||
return 0, train + 1 | ||
return trains | ||
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print(*find_platforms()) | ||
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if __name__ == "__main__": | ||
main() |