結果

問題 No.2780 The Bottle Imp
コンテスト
ユーザー イルカ
提出日時 2024-06-11 10:44:08
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 4,893 bytes
コンパイル時間 290 ms
コンパイル使用メモリ 82,176 KB
実行使用メモリ 279,108 KB
最終ジャッジ日時 2024-06-11 10:44:23
合計ジャッジ時間 11,480 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 4
other AC * 8 TLE * 1 -- * 31
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 # 

# SCC→強連結成分をノードとみなしてDFSで訪問可能判定？

from collections import defaultdict
#from atcoder.scc import SCCGraph

###
# https://github.com/not522/ac-library-python
import sys
import typing


class CSR:
    def __init__(
            self, n: int, edges: typing.List[typing.Tuple[int, int]]) -> None:
        self.start = [0] * (n + 1)
        self.elist = [0] * len(edges)

        for e in edges:
            self.start[e[0] + 1] += 1

        for i in range(1, n + 1):
            self.start[i] += self.start[i - 1]

        counter = self.start.copy()
        for e in edges:
            self.elist[counter[e[0]]] = e[1]
            counter[e[0]] += 1


class SCCGraph:
    '''
    Reference:
    R. Tarjan,
    Depth-First Search and Linear Graph Algorithms
    '''

    def __init__(self, n: int) -> None:
        self._n = n
        self._edges: typing.List[typing.Tuple[int, int]] = []

    def num_vertices(self) -> int:
        return self._n

    def add_edge(self, from_vertex: int, to_vertex: int) -> None:
        self._edges.append((from_vertex, to_vertex))

    def scc_ids(self) -> typing.Tuple[int, typing.List[int]]:
        g = CSR(self._n, self._edges)
        now_ord = 0
        group_num = 0
        visited = []
        low = [0] * self._n
        order = [-1] * self._n
        ids = [0] * self._n

        sys.setrecursionlimit(max(self._n + 1000, sys.getrecursionlimit()))

        def dfs(v: int) -> None:
          nonlocal now_ord
          nonlocal group_num
          nonlocal visited
          nonlocal low
          nonlocal order
          nonlocal ids


          stack = []
          for start in range(self._n):
              if order[start] != -1:
                  continue
              
              stack.append((start, 'visit'))
              parent = [-1] * self._n  # 親を記録するリスト

              while stack:
                  v, action = stack.pop()

                  if action == 'visit':
                      if order[v] == -1:
                          low[v] = now_ord
                          order[v] = now_ord
                          now_ord += 1
                          visited.append(v)
                          stack.append((v, 'process'))

                          for i in range(g.start[v], g.start[v + 1]):
                              to = g.elist[i]
                              if order[to] == -1:
                                  parent[to] = v
                                  stack.append((to, 'visit'))
                              else:
                                  low[v] = min(low[v], order[to])
                  elif action == 'process':
                      if parent[v] != -1:
                          low[parent[v]] = min(low[parent[v]], low[v])

                      if low[v] == order[v]:
                          while True:
                              u = visited[-1]
                              visited.pop()
                              order[u] = self._n
                              ids[u] = group_num
                              if u == v:
                                  break
                          group_num += 1

          return ids

        for i in range(self._n):
            if order[i] == -1:
                dfs(i)

        for i in range(self._n):
            ids[i] = group_num - 1 - ids[i]

        return group_num, ids

    def scc(self) -> typing.List[typing.List[int]]:
        ids = self.scc_ids()
        group_num = ids[0]
        counts = [0] * group_num
        for x in ids[1]:
            counts[x] += 1
        groups: typing.List[typing.List[int]] = [[] for _ in range(group_num)]
        for i in range(self._n):
            groups[ids[1][i]].append(i)

        return groups

###


N = int(input())
sccgraph = SCCGraph(N)
graph = defaultdict(list)
for i in range(1,N+1):
    A = list(map(int, input().split()))[1:]
    for a in A:
        sccgraph.add_edge(i-1, a-1)
        graph[i-1].append(a-1) 
groups = sccgraph.scc()

num_groups = len(groups)
node_to_group = [0] * N

# 各ノードがどの強連結成分に属するかを記録する
for group_index, nodes in enumerate(groups):
    for node in nodes:
        node_to_group[node] = group_index

group_connections = [set() for _ in range(num_groups)]

# グラフ内のノード間の接続を強連結成分間の接続に変換する
for node in range(N):
    current_group = node_to_group[node]
    for neighbor in graph[node]:
        neighbor_group = node_to_group[neighbor]
        if neighbor_group == current_group:
            continue
        group_connections[current_group].add(neighbor_group)

# 各強連結成分が次の強連結成分と直接接続されているかを確認する
for group in range(num_groups - 1):
    if group + 1 not in group_connections[group]:
        print("No")
        exit()
print("Yes")
0