結果

問題 No.235 めぐるはめぐる (5)
コンテスト
ユーザー terasa
提出日時 2023-01-14 16:05:56
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 6,461 ms / 10,000 ms
コード長 8,717 bytes
コンパイル時間 449 ms
コンパイル使用メモリ 82,048 KB
実行使用メモリ 159,664 KB
最終ジャッジ日時 2024-12-26 01:02:03
合計ジャッジ時間 25,839 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
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ファイルパターン 結果
other AC * 3
権限があれば一括ダウンロードができます

ソースコード

diff # 

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):
    a0, a1 = a >> 32, a & msk
    b0, b1 = b >> 32, b & msk
    x, y = (a0 + b0) % mod, (a1 + b1) % mod
    return x << 32 | y


def mapping(f, x):
    x0, x1 = x >> 32, x & msk
    x, y = (x0 + f * x1) % mod, x1
    return x << 32 | y


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
msk = (1 << 32) - 1

solver = HLD(N, E)
lst = LazySegTree(N, op, 0, mapping, composition, 0)
B = [None] * N
for i in range(N):
    B[solver.get_index(i)] = A[i] << 32 | 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) >> 32
            ans %= mod
        print(ans)
0