結果
| 問題 | No.235 めぐるはめぐる (5) |
| ユーザー |
 terasa
|
| 提出日時 | 2023-01-14 15:42:51 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 8,553 bytes |
| コンパイル時間 | 411 ms |
| コンパイル使用メモリ | 86,672 KB |
| 実行使用メモリ | 275,132 KB |
| 最終ジャッジ日時 | 2023-08-26 21:42:22 |
| 合計ジャッジ時間 | 30,257 ms |
|
ジャッジサーバーID （参考情報） |
judge11 / judge14 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | WA | - |
| testcase_01 | WA | - |
| testcase_02 | WA | - |
ソースコード
from typing import List, Tuple, Callable, TypeVar, Optional
import sys
import itertools
import heapq
import bisect
import math
from collections import deque, defaultdict
from functools import lru_cache, cmp_to_key
input = sys.stdin.readline
if __file__ != 'prog.py':
sys.setrecursionlimit(10 ** 6)
def readints(): return map(int, input().split())
def readlist(): return list(readints())
def readstr(): return input()[:-1]
def readlist1(): return list(map(lambda x: int(x) - 1, input().split()))
S = TypeVar('S')
F = TypeVar('F')
class LazySegTree:
# reference: https://github.com/shakayami/ACL-for-python
# reference: https://maspypy.com/segment-tree-%E3%81%AE%E3%81%8A%E5%8B%89%E5%BC%B72
# reference: https://betrue12.hateblo.jp/entry/2020/09/22/194541
def __init__(self, N: int, op: Callable[[S, S], S], e: S,
mapping: Callable[[F, S], S],
composition: Callable[[F, F], F], id_: F):
""" 遅延セグメント木
Args:
N (int): 配列の長さ
op (Callable[[S, S], S]): 区間取得に用いる演算
e (S): 全てのaに対して op(a, e) = a が成り立つ単位元
mapping (Callable[[F, S], S]): dataに作用させる関数
composition (Callable[[F, F], F]): lazyに作用させる関数 f(g(x))
id_ (F): 全てのaに対して mapping(id_, a) = a が成り立つ恒等写像
Note:
任意の x, y ∈ S, f, g ∈ F に対して、
- f(op(x, y)) = op(f(x), f(y))
- f(g(x)) = (g ∘ f)(x)
であることが必要
例) RMQ and RAQ
- min(x, y) + a = min(x + a, y + a)
- ((x + b) + a) = x + (a + b)
"""
self.N = N
self.op = op
self.e = e
self.mapping = mapping
self.composition = composition
self.id = id_
self.K = (self.N - 1).bit_length()
self.size = 1 << (self.K)
self.data = [e] * (self.size << 1)
self.lazy = [id_] * (self.size)
def build(self, A: List[S]) -> None:
for i in range(self.N):
self.data[self.size + i] = A[i]
for i in range(self.size - 1, 0, -1):
self.data[i] = self.op(self.data[i << 1], self.data[i << 1 | 1])
def _eval_at(self, i: int, f: F) -> None:
self.data[i] = self.mapping(f, self.data[i])
if i < self.size:
self.lazy[i] = self.composition(f, self.lazy[i])
def _propagate_at(self, i: int) -> None:
self._eval_at(i << 1, self.lazy[i])
self._eval_at(i << 1 | 1, self.lazy[i])
self.lazy[i] = self.id
def _propagate_above(self, i: int) -> None:
H = i.bit_length() - 1
for h in range(H, 0, -1):
self._propagate_at(i >> h)
def _recalc_at(self, i: int) -> None:
self.data[i] = self.op(self.data[i << 1], self.data[i << 1 | 1])
def _recalc_above(self, i: int) -> None:
while i > 1:
i >>= 1
self._recalc_at(i)
def set(self, i: int, x: S) -> None:
i += self.size
self._propagate_above(i)
self.data[i] = x
self._recalc_above(i)
def get(self, i) -> S:
i += self.size
self._propagate_above(i)
return self.data[i]
def prod(self, l: int, r: int) -> S:
assert 0 <= l and l <= r and r <= self.N
if l == r:
return self.e
l += self.size
r += self.size
self._propagate_above(l // (l & -l))
self._propagate_above(r // (r & -r) - 1)
vl = self.e
vr = self.e
while l < r:
if l & 1:
vl = self.op(vl, self.data[l])
l += 1
if r & 1:
r -= 1
vr = self.op(self.data[r], vr)
l >>= 1
r >>= 1
return self.op(vl, vr)
def all_prod(self) -> S:
return self.data[1]
def apply(self, l: int, r: int, f: F) -> None:
assert 0 <= l and l <= r and r <= self.N
if l == r:
return
l += self.size
r += self.size
l0 = l // (l & -l)
r0 = r // (r & -r) - 1
self._propagate_above(l0)
self._propagate_above(r0)
while l < r:
if l & 1:
self._eval_at(l, f)
l += 1
if r & 1:
r -= 1
self._eval_at(r, f)
l >>= 1
r >>= 1
self._recalc_above(l0)
self._recalc_above(r0)
class HLD:
# reference: https://codeforces.com/blog/entry/53170
def __init__(self, N, E, root: int = 0):
self.N = N
self.E = E
self.root = root
self.D = [0] * self.N
self.par = [-1] * self.N
self.sz = [0] * self.N
self.top = [0] * self.N
self.ord = [None] * self.N
self._dfs_sz()
self._dfs_hld()
def path_query_range(self, u: int, v: int, is_edge_query: bool = False) -> List[Tuple[int, int]]:
"""return list of [l, r) ranges that cover u-v path"""
ret = []
while True:
if self.ord[u] > self.ord[v]:
u, v = v, u
if self.top[u] == self.top[v]:
ret.append((self.ord[u] + is_edge_query, self.ord[v] + 1))
return ret
ret.append((self.ord[self.top[v]], self.ord[v] + 1))
v = self.par[self.top[v]]
def subtree_query_range(self, v: int, is_edge_query: bool = False) -> Tuple[int, int]:
"""return [l, r) range that cover vertices of subtree v"""
return (self.ord[v] + is_edge_query, self.ord[v] + self.sz[v])
def get_index(self, v: int) -> int:
return self.ord[v]
def lca(self, u, v):
while True:
if self.ord[u] > self.ord[v]:
u, v = v, u
if self.top[u] == self.top[v]:
return u
v = self.par[self.top[v]]
def _dfs_sz(self):
stack = [(self.root, -1)]
while stack:
v, p = stack.pop()
if v < 0:
v = ~v
self.sz[v] = 1
for i, dst in enumerate(self.E[v]):
if dst == p:
continue
self.sz[v] += self.sz[dst]
# v -> E[v][0] will be heavy path
if self.sz[self.E[v][0]] < self.sz[dst]:
self.E[v][0], self.E[v][i] = self.E[v][i], self.E[v][0]
else:
if ~p:
self.D[v] = self.D[p] + 1
self.par[v] = p
# avoid first element of E[v] is parent of vertex v if v has some children
if len(self.E[v]) >= 2 and self.E[v][0] == p:
self.E[v][0], self.E[v][1] = self.E[v][1], self.E[v][0]
stack.append((~v, p))
for dst in self.E[v]:
if dst == p:
continue
stack.append((dst, v))
def _dfs_hld(self):
stack = [(self.root, -1)]
cnt = 0
while stack:
v, p = stack.pop()
self.ord[v] = cnt
cnt += 1
heavy_path_idx = len(self.E[v]) - 1
for i, dst in enumerate(self.E[v][::-1]):
if dst == p:
continue
# top[dst] is top[v] if v -> dst is heavy path otherwise dst itself
self.top[dst] = self.top[v] if i == heavy_path_idx else dst
stack.append((dst, v))
def op(a, b):
return ((a[0] + b[0]) % mod, (a[1] + b[1]) % mod)
def mapping(f, x):
return ((x[0] + f * x[1]) % mod, x[1])
def composition(f, g):
return (f + g) % mod
N = int(input())
A = readlist()
C = readlist()
E = [[] for _ in range(N)]
for _ in range(N - 1):
a, b = readints()
a -= 1
b -= 1
E[a].append(b)
E[b].append(a)
mod = 10 ** 9 + 7
solver = HLD(N, E)
lst = LazySegTree(N, op, (0, 0), mapping, composition, 0)
B = [None] * N
for i in range(N):
B[solver.get_index(i)] = (A[i], C[i])
lst.build(B)
Q = int(input())
for _ in range(Q):
t, *q = readints()
if t == 0:
x, y, z = q
x -= 1
y -= 1
for l, r in solver.path_query_range(x, y):
lst.apply(l, r, z)
else:
x, y = q
x -= 1
y -= 1
ans = 0
for l, r in solver.path_query_range(x, y):
ans += lst.prod(l, r)[0]
print(ans)