結果
| 問題 |
No.529 帰省ラッシュ
|
| コンテスト | |
| ユーザー |
 navel_tos
|
| 提出日時 | 2024-02-12 16:03:22 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 4,197 ms / 4,500 ms |
| コード長 | 10,382 bytes |
| コンパイル時間 | 419 ms |
| コンパイル使用メモリ | 82,552 KB |
| 実行使用メモリ | 266,420 KB |
| 最終ジャッジ日時 | 2024-09-28 18:05:08 |
| 合計ジャッジ時間 | 29,849 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 18 |
ソースコード
#yukicoder 529 帰省ラッシュ
#Lowlink(二重辺連結成分分解)
class Lowlink:
def __init__(self, N, G):
#連結とは限らないグラフGを隣接リストとして受け取る
#articulation[i]: 頂点iが関節点ならTrue 特に、連結成分が1つだけのグラフはFalse
#root[i]: 頂点iが属するDFS木の代表値
#leader[i]: 頂点iが属する二重辺連結成分の代表値 (特に、橋で切ったグラフの代表値)
#size[i]: 頂点iが属する二重辺連結成分の大きさ (同上)
#child[i], bridge[i]: 探索時の有向隣接リスト 特に、それが橋ならbridge[i]へ
self._N = N; self._G = G; self.pre = pre = [N] * N + [0]; self.low = low = [N] * N
self.articulation = A = [False] * N; self.root = root = [-1] * N
self.leader = leader = [-1] * N; self.size = size = [0] * N
self.child = C = [[] for _ in range(N)]; self.bridge = B = [[] for _ in range(N)]
for parent in range(N):
if pre[parent] != N: size[parent] = size[ leader[parent] ]; continue
Q = [(parent, -1)]
while Q:
now, back = Q.pop()
if now >= 0:
if pre[now] == N:
pre[now] = low[now] = pre[-1]; pre[-1] += 1
root[now] = parent; Q.append((~now, back))
else: low[back] = min(low[back], pre[now]); continue
for nxt in G[now]:
if nxt != back: Q.append((nxt, now))
else:
now = ~now
if now == parent: continue
B[back].append(now) if pre[back] < low[now] else C[back].append(now)
low[back] = min(low[back], low[now])
Q = [(parent, -1, parent)]
while Q:
now, back, top = Q.pop(); leader[now] = top; size[top] += 1
for nxt in C[now]:
if pre[now] <= low[nxt]: A[now] = True
Q.append((nxt, now, top))
for nxt in B[now]:
if pre[now] <= low[nxt]: A[now] = True
Q.append((nxt, now, nxt))
if now == parent: A[now] = ( len(C[now]) + len(B[now]) >= 2 )
pre.pop(); return
#Heavy-Light decomposition データ構造を使うならbuild必須なので注意
class HL_decomposition:
class SegmentTree: #前提mod1
def __init__(self, n, identity_e, function): self._n = n; self._size = 1 << (n - 1).bit_length(); self._e = e = identity_e; self._f = function; self._node = [e] * 2 * self._size
def build(self, A):
for i,v in enumerate(A, start = self._size): self._node[i] = v
for i in range(self._size - 1, 0, -1): self._node[i] = self._f(self._node[i<<1], self._node[i<<1|1])
def update(self, index, value):
i = self._size + index; self._node[i] = value
while i - 1: i >>= 1; self._node[i] = self._f(self._node[i<<1], self._node[i<<1|1])
def fold(self, Lt, Rt):
Lt, Rt = Lt + self._size, Rt + self._size; vL = vR = self._e
while Lt < Rt:
if Lt & 1: vL = self._f(vL, self._node[Lt]); Lt += 1
if Rt & 1: Rt -= 1; vR = self._f(self._node[Rt], vR)
Lt >>= 1; Rt >>= 1
return self._f(vL, vR)
class SparseTable: #前提mod2
def __init__(self, n, identity_e, function): self._n = n; self._logn = (n - 1).bit_length(); self._size = 1 << self._logn; self._e = e = identity_e; self._f = function; self._T = [[e] * self._logn for _ in range(self._size)]; self._A = [e] * self._size
def build(self, A):
e, f, T = self._e, self._f, self._T; self._A = A = A + [e] * (self._size - self._n)
for x in range(self._logn):
t = 1 << x
for s in range(t, self._size, t << 1):
T[s][x] = A[s]
for j in range(s + 1, s + t, +1): T[j][x] = f(T[j-1][x], A[j])
for s in range(self._size - t - 1, -1, - t << 1):
T[s][x] = A[s]
for j in range(s - 1, s - t, -1): T[j][x] = f(A[j], T[j+1][x])
def fold(self, Lt, Rt): Lt, Rt = max(0, Lt), min(self._size, Rt) - 1; x = (Lt ^ Rt).bit_length() - 1; return self._e if not 0 <= Lt <= Rt < self._size else self._A[Lt] if Lt == Rt else self._f( self._T[Lt][x], self._T[Rt][x] )
def __init__(self, N, G, identity_e = 0, func = 'add'):
#pos[v] = i, order[i] = v 頂点vのDFS順序がi番目
#leader[i]: Heavy edgeの代表値のDFS順序
#depth[i]: 再帰の深さ parent[i]: ひとつ根側のDFS順序
#A[i]: u - vパスの重みw。DFS順序が遅い頂点v側に入れる。pos[u] < pos[v] = i
self._N = N; self._logN = logN = N.bit_length(); self._e = e = identity_e
self._f = f = (lambda x,y: x + y) if func == 'add' else func
self._G = G = [[(v, e) for v in S] for S in G] if N > 1 and isinstance(G[0][0],int) else G
self._A = A = [e for _ in range(N)]; self.pos = pos = [-1] * N
self.order = order = [-1] * N; self.leader = leader = [-1] * N; size = [1] * N
self.depth = depth = [-1] * N; self.parent = parent = [-1] * N; Q = [(0, -1)]
for now,back in Q: #前処理
for nxt,_ in G[now]:
if nxt != back: Q.append((nxt, now))
while Q: now,back = Q.pop(); size[back] += size[now] if back != -1 else 0
Q.append((0, -1, e, 0, -1)) #HL分解
for i in range(N):
now, back, c, d, t = Q.pop(); pos[now], parent[i]= i, pos[back]
order[i], A[i], depth[i] = now, c, d; leader[i] = t = t if t != -1 else i
if size[now] > 1: #部分木のうち最大サイズのものを最後にappend
s, v, x = 0, now, e
for nxt,w in G[now]:
if nxt == back: continue
if s < size[nxt]:
if s > 0: Q.append((v, now, x, d + 1, -1))
s, v, x = size[nxt], nxt, w
else: Q.append((nxt, now, w, d + 1, -1))
Q.append((v, now, x, d, t))
def build(self, use_SegTree = True, A = 'no need to import'):
N, e, f = self._N, self._e, self._f
if A != 'no need to import': self._A = A
self._ST = ST = self.SegmentTree if use_SegTree else self.SparseTable
self._obvST = obvST = ST(N, e, f); obvST.build(self._A)
self._revST = revST = ST(N, e, f); revST.build(self._A[::-1])
def LCA(self, u, v): #O(logN)
i, j = self.pos[u], self.pos[v]; c, d = self.depth[i], self.depth[j]
if c > d: i, j, c, d = j, i, c, d
s, t = self.leader[i], self.leader[j]
for d in range(d - 1, c - 1, -1): j = self.parent[t]; t = self.leader[j]
while s != t: i, j = self.parent[s], self.parent[t]; s, t = self.leader[i], self.leader[j]
return self.order[ min(i,j) ]
def update(self, index_u, value_v, weight = None):
if weight == None: j, w = self.pos[index_u], value_v
else: i, j, w = self.pos[index_u], self.pos[value_v], weight; i, j = (j, i) if i > j else (i, j); assert self.parent[j] == i, 'not connect Tree edge'
self._A[j] = w; self._obvST.update(j, w); self._revST.update(self._N - 1 - j, w)
def fold(self, u, v, path_query = False): #u→vパスの作用値を取得
Lt = Rt = self._e; f = self._f; i, j = self.pos[u], self.pos[v]
c, d = self.depth[i], self.depth[j]; s, t = self.leader[i], self.leader[j]
for c in range(c - 1, d - 1, -1): Lt = f( Lt, self._revST.fold(N - 1 - i, N - s) ); i = self.parent[s]; s = self.leader[i]
for d in range(d - 1, c - 1, -1): Rt = f( self._obvST.fold(t, j + 1), Rt ); j = self.parent[t]; t = self.leader[j]
while s != t: Lt, Rt = f( Lt, self._revST.fold(N-1-i,N-s) ), f( self._obvST.fold(t,j+1), Rt ); i, j = self.parent[s], self.parent[t]; s, t = self.leader[i], self.leader[j]
if i > j: LCA, Lt = j, f( Lt, self._revST.fold(N - i - 1, N - j - 1) )
elif i < j: LCA, Rt = i, f( self._obvST.fold(i + 1, j + 1), Rt )
else: LCA = i
LCA = self._e if path_query else self._A[LCA]; return f( f(Lt, LCA), Rt )
import heapq
import sys
input = sys.stdin.readline
#入力受取
N,M,Q = map(int,input().split())
G = [[] for _ in range(N)]
for _ in range(M):
a,b = map(lambda x: int(x) - 1, input().split())
G[a].append(b)
G[b].append(a)
query = []
for _ in range(Q):
t,u,v = map(int,input().split())
if t == 1: query.append((t, u-1, v))
if t == 2: query.append((t, u-1, v-1))
#与えられたグラフを二重辺連結成分分解 leaderの値を座標圧縮
L = Lowlink(N, G)
C = sorted(set(L.leader)); C = {j:i for i,j in enumerate(C)}
#座標圧縮後の木を作る
nG = [set() for _ in range(len(C))]
for u in range(N):
for v in G[u]:
if u < v:
nu,nv = C[L.leader[u]], C[L.leader[v]]
if nu != nv:
nG[nu].add(nv); nG[nv].add(nu)
G = [list(S) for S in nG]
N = len(C)
for i in range(Q):
t,u,v = query[i]
if t == 1: query[i] = (t, C[L.leader[u]], v)
if t == 2: query[i] = (t, C[L.leader[u]], C[L.leader[v]])
#座標圧縮後の木をHL分解 SegTreeには(最大の価値, 現在値)を格納
HLD = HL_decomposition(N, G, (0, 0), max)
HLD.build(True, [(0, i) for i in range(N)])
#各連結成分ごとに最大の獲物の価値を格納するheapqを用意 負値で入れるので注意
prey = [[] for _ in range(N)]
#クエリに回答
for t,u,v in query:
if t == 1:
#SegTreeの更新有無を判定
now_max = 0
if len(prey[u]) >= 1: now_max = - prey[u][0]
heapq.heappush(prey[u], - v)
if now_max < v:
HLD.update(u, (v, u))
if t == 2:
#最大の獲物を取得
max_prey, point = HLD.fold(u, v, False)
if max_prey == 0:
print(-1)
continue
else:
print(max_prey)
#獲物を削除する
heapq.heappop(prey[point])
now_max = 0
if len(prey[point]) >= 1: now_max = - prey[point][0]
#更新
HLD.update(point, (now_max, point))