結果
| 問題 |
No.3348 Tree Balance
|
| コンテスト | |
| ユーザー |
 ZOI-dayo
|
| 提出日時 | 2025-11-13 01:17:19 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 2,278 ms / 5,000 ms |
| コード長 | 7,303 bytes |
| コンパイル時間 | 231 ms |
| コンパイル使用メモリ | 82,648 KB |
| 実行使用メモリ | 236,180 KB |
| 最終ジャッジ日時 | 2025-11-13 21:26:11 |
| 合計ジャッジ時間 | 23,481 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge4 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 25 |
ソースコード
import sys
sys.setrecursionlimit(200010)
# https://github.com/tatyam-prime/SortedSet/blob/main/SortedSet.py
import math
from bisect import bisect_left, bisect_right
from typing import Generic, Iterable, Iterator, TypeVar
T = TypeVar('T')
class SortedSet(Generic[T]):
BUCKET_RATIO = 16
SPLIT_RATIO = 24
def __init__(self, a: Iterable[T] = []) -> None:
"Make a new SortedSet from iterable. / O(N) if sorted and unique / O(N log N)"
a = list(a)
n = len(a)
if any(a[i] > a[i + 1] for i in range(n - 1)):
a.sort()
if any(a[i] >= a[i + 1] for i in range(n - 1)):
a, b = [], a
for x in b:
if not a or a[-1] != x:
a.append(x)
n = self.size = len(a)
num_bucket = int(math.ceil(math.sqrt(n / self.BUCKET_RATIO)))
self.a = [a[n * i // num_bucket : n * (i + 1) // num_bucket] for i in range(num_bucket)]
def __iter__(self) -> Iterator[T]:
for i in self.a:
for j in i: yield j
def __reversed__(self) -> Iterator[T]:
for i in reversed(self.a):
for j in reversed(i): yield j
def __eq__(self, other) -> bool:
return list(self) == list(other)
def __len__(self) -> int:
return self.size
def __repr__(self) -> str:
return "SortedSet" + str(self.a)
def __str__(self) -> str:
s = str(list(self))
return "{" + s[1 : len(s) - 1] + "}"
def _position(self, x: T) -> tuple[list[T], int, int]:
"return the bucket, index of the bucket and position in which x should be. self must not be empty."
for i, a in enumerate(self.a):
if x <= a[-1]: break
return (a, i, bisect_left(a, x))
def __contains__(self, x: T) -> bool:
if self.size == 0: return False
a, _, i = self._position(x)
return i != len(a) and a[i] == x
def add(self, x: T) -> bool:
"Add an element and return True if added. / O(√N)"
if self.size == 0:
self.a = [[x]]
self.size = 1
return True
a, b, i = self._position(x)
if i != len(a) and a[i] == x: return False
a.insert(i, x)
self.size += 1
if len(a) > len(self.a) * self.SPLIT_RATIO:
mid = len(a) >> 1
self.a[b:b+1] = [a[:mid], a[mid:]]
return True
def _pop(self, a: list[T], b: int, i: int) -> T:
ans = a.pop(i)
self.size -= 1
if not a: del self.a[b]
return ans
def discard(self, x: T) -> bool:
"Remove an element and return True if removed. / O(√N)"
if self.size == 0: return False
a, b, i = self._position(x)
if i == len(a) or a[i] != x: return False
self._pop(a, b, i)
return True
def lt(self, x: T) -> T | None:
"Find the largest element < x, or None if it doesn't exist."
for a in reversed(self.a):
if a[0] < x:
return a[bisect_left(a, x) - 1]
def le(self, x: T) -> T | None:
"Find the largest element <= x, or None if it doesn't exist."
for a in reversed(self.a):
if a[0] <= x:
return a[bisect_right(a, x) - 1]
def gt(self, x: T) -> T | None:
"Find the smallest element > x, or None if it doesn't exist."
for a in self.a:
if a[-1] > x:
return a[bisect_right(a, x)]
def ge(self, x: T) -> T | None:
"Find the smallest element >= x, or None if it doesn't exist."
for a in self.a:
if a[-1] >= x:
return a[bisect_left(a, x)]
def __getitem__(self, i: int) -> T:
"Return the i-th element."
if i < 0:
for a in reversed(self.a):
i += len(a)
if i >= 0: return a[i]
else:
for a in self.a:
if i < len(a): return a[i]
i -= len(a)
raise IndexError
def pop(self, i: int = -1) -> T:
"Pop and return the i-th element."
if i < 0:
for b, a in enumerate(reversed(self.a)):
i += len(a)
if i >= 0: return self._pop(a, ~b, i)
else:
for b, a in enumerate(self.a):
if i < len(a): return self._pop(a, b, i)
i -= len(a)
raise IndexError
def index(self, x: T) -> int:
"Count the number of elements < x."
ans = 0
for a in self.a:
if a[-1] >= x:
return ans + bisect_left(a, x)
ans += len(a)
return ans
def index_right(self, x: T) -> int:
"Count the number of elements <= x."
ans = 0
for a in self.a:
if a[-1] > x:
return ans + bisect_right(a, x)
ans += len(a)
return ans
def main():
I = sys.stdin.readline
O = sys.stdout.write
n = int(I())
w = list(map(int, I().split()))
graph = [[] for _ in range(n)]
for _ in range(n - 1):
a, b = map(int, I().split())
a -= 1
b -= 1
graph[a].append(b)
graph[b].append(a)
sum_ = list(w)
stack = [(0, -1, 0)]
while stack:
v, p, state = stack.pop()
if state == 0:
stack.append((v, p, 1))
for u in graph[v]:
if u == p:
continue
stack.append((u, v, 0))
else:
# 帰りがけ
for u in graph[v]:
if u == p:
continue
sum_[v] += sum_[u]
total = sum_[0]
ans = 1 << 60
def update(s1, s2):
nonlocal ans
s3 = total - s1 - s2
mn = min(s1, s2, s3)
mx = max(s1, s2, s3)
ans = min(ans, mx - mn)
stack = [(0, -1, 0)]
res_map = {}
while stack:
v, p, state = stack.pop()
if state == 0:
stack.append((v, p, 1))
for u in graph[v]:
if u == p:
continue
stack.append((u, v, 0))
else:
sums = SortedSet()
current = sum_[v]
remain = total - current
for u in graph[v]:
if u == p:
continue
res = res_map[u]
X1 = current // 2
itr_lower = res.le(X1)
if itr_lower is not None:
update(remain, itr_lower)
itr_pred = res.gt(X1)
if itr_pred is not None:
update(remain, itr_pred)
if len(sums) < len(res):
sums, res = res, sums
for e in res:
X2 = (total - e) // 2
itr_lower_2 = sums.le(X2)
if itr_lower_2 is not None:
update(e, itr_lower_2)
itr_pred_2 = sums.gt(X2)
if itr_pred_2 is not None:
update(e, itr_pred_2)
for e in res:
sums.add(e)
sums.add(current)
res_map[v] = sums
O(f"{ans}\n")
if __name__ == "__main__":
main()