結果
| 問題 |
No.529 帰省ラッシュ
|
| コンテスト | |
| ユーザー |
 terasa
|
| 提出日時 | 2023-01-14 12:44:45 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 11,181 bytes |
| コンパイル時間 | 297 ms |
| コンパイル使用メモリ | 82,176 KB |
| 実行使用メモリ | 201,856 KB |
| 最終ジャッジ日時 | 2024-12-25 20:19:36 |
| 合計ジャッジ時間 | 21,338 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 9 RE * 9 |
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()))
class SegTree:
def __init__(self, N, func, e):
self.N = N
self.func = func
self.X = [e] * (N << 1)
self.e = e
def build(self, seq):
for i in range(self.N):
self.X[self.N + i] = seq[i]
for i in range(self.N)[::-1]:
self.X[i] = self.func(self.X[i << 1], self.X[i << 1 | 1])
def get(self, i):
i += self.N
return self.X[i]
def add(self, i, x):
i += self.N
self.X[i] += x
while i > 1:
i >>= 1
self.X[i] = self.func(self.X[i << 1], self.X[i << 1 | 1])
def update(self, i, x):
i += self.N
self.X[i] = x
while i > 1:
i >>= 1
self.X[i] = self.func(self.X[i << 1], self.X[i << 1 | 1])
def query(self, l, r):
l += self.N
r += self.N
vl = self.e
vr = self.e
while l < r:
if l & 1:
vl = self.func(vl, self.X[l])
l += 1
if r & 1:
r -= 1
vr = self.func(self.X[r], vr)
l >>= 1
r >>= 1
return self.func(vl, vr)
class DFSTree:
# cf: https://codeforces.com/blog/entry/68138
def __init__(self, N: int):
self.N = N
self.edges = []
self.E = [[] for _ in range(self.N)]
# span-edge and back-edge (directed)
self.span_edge = [[] for _ in range(self.N)]
self.back_edge = [[] for _ in range(self.N)]
self.ord = [-1] * self.N
self.low = [-1] * self.N
self.par = [None] * self.N
self.is_art = [False] * self.N
self.is_bridge = []
self.built = False
def add_edge(self, u: int, v: int) -> None:
"""add edge"""
eid = len(self.edges)
self.edges.append((u, v))
self.E[u].append((v, eid))
self.E[v].append((u, eid))
self.is_bridge.append(False)
def build(self) -> None:
"""build dfs tree"""
cnt = 0
self.tecc_id = [-1] * self.N
self.tvcc_id = [-1] * len(self.edges)
self.bcc_num = 0
for i in range(self.N):
if ~self.ord[i]:
continue
stack = [(i, -1, -1)]
estack = []
while stack:
v, p, p_eid = stack.pop()
if v < 0:
v = ~v
for d, i in self.span_edge[v]:
if d == p:
continue
self.low[v] = min(self.low[v], self.low[d])
if ~p and self.ord[p] <= self.low[v]:
while True:
eid = estack.pop()
self.tvcc_id[eid] = self.bcc_num
if eid == p_eid:
break
self.bcc_num += 1
else:
if ~self.ord[v]:
continue
self.ord[v] = cnt
self.low[v] = cnt
cnt += 1
# p -> v is span-edge.
if ~p:
self.par[v] = (p, p_eid)
self.span_edge[p].append((v, p_eid))
estack.append(p_eid)
stack.append((~v, p, p_eid))
for d, eid in self.E[v][::-1]:
if eid == p_eid:
continue
if ~self.ord[d]:
# v -> d is back-edge since d is already visited.
self.back_edge[v].append((d, eid))
self.low[v] = min(self.low[v], self.ord[d])
estack.append(eid)
continue
stack.append((d, v, eid))
self._search_bridge()
self._search_articulation_points()
self.built = True
def bridges(self) -> List[Tuple[int, int]]:
"""return list of edges that are bridges"""
assert self.built
return [e for i, e in enumerate(self.edges) if self.is_bridge[i]]
def articulation_points(self) -> List[int]:
"""return list of vertices that are articulation points"""
assert self.built
return [i for i in range(self.N) if self.is_art[i]]
def two_edge_connected_components(self) -> List[List[int]]:
assert self.built
cnt = 0
for i in range(self.N):
if ~self.tecc_id[i]:
continue
stack = [i]
while stack:
v = stack.pop()
if ~self.tecc_id[v]:
continue
self.tecc_id[v] = cnt
for d, eid in self.E[v]:
if ~self.tecc_id[d] or self.is_bridge[eid]:
continue
stack.append(d)
cnt += 1
ret = [[] for _ in range(cnt)]
for i, tid in enumerate(self.tecc_id):
assert ~tid
ret[tid].append(i)
return ret
def biconnected_components(self) -> List[List[int]]:
assert self.built
ret = [set() for _ in range(self.bcc_num)]
for eid, tid in enumerate(self.tvcc_id):
assert ~tid
u, v = self.edges[eid]
ret[tid].add(u)
ret[tid].add(v)
ret = [list(s) for s in ret]
for i in range(self.N):
if not self.E[i]:
ret.append([i])
return ret
def _search_bridge(self) -> None:
for u in range(self.N):
for v, i in self.span_edge[u]:
# (u, v) is bridge if vertex u has child v
# that does not have lowlink to pass over its parent
self.is_bridge[i] = self.ord[u] < self.low[v]
def _search_articulation_points(self) -> None:
for u in range(self.N):
if self.par[u] is None:
self.is_art[u] = len(self.span_edge[u]) >= 2
else:
for v, _ in self.span_edge[u]:
if self.ord[u] <= self.low[v]:
self.is_art[u] = True
break
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[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))
N, M, Q = readints()
dfs_tree = DFSTree(N)
E = [[] for _ in range(N)]
for _ in range(M):
a, b = readints()
a -= 1
b -= 1
E[a].append(b)
E[b].append(a)
dfs_tree.add_edge(a, b)
dfs_tree.build()
T = dfs_tree.two_edge_connected_components()
NE = [[] for _ in range(len(T))]
for u in range(N):
for v in E[u]:
s, t = dfs_tree.tecc_id[u], dfs_tree.tecc_id[v]
if s == t:
continue
NE[s].append(t)
NE[t].append(s)
NE = [list(set(ne)) for ne in NE]
solver = HLD(len(T), NE)
st = SegTree(len(T), max, (0, -1))
st.build([(0, i) for i in range(len(T))])
H = [[] for _ in range(len(T))]
for _ in range(Q):
t, *q = readints()
if t == 1:
u, w = q
u -= 1
idx = solver.get_index(dfs_tree.tecc_id[u])
heapq.heappush(H[idx], -w)
v = -H[idx][0]
st.update(idx, (v, idx))
else:
u, v = q
u -= 1
v -= 1
s, t = dfs_tree.tecc_id[u], dfs_tree.tecc_id[v]
e = (0, len(T))
ma = e
for l, r in solver.path_query_range(s, t):
v = st.query(l, r)
ma = max(ma, v)
if ma == e:
print(-1)
continue
max_value, idx = ma
heapq.heappop(H[idx])
nxt = -H[idx][0] if H[idx] else 0
st.update(idx, (nxt, idx))
print(max_value)