結果

問題 No.2780 The Bottle Imp
ユーザー イルカイルカ
提出日時 2024-06-11 11:04:02
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 648 ms / 2,000 ms
コード長 4,123 bytes
コンパイル時間 376 ms
コンパイル使用メモリ 82,176 KB
実行使用メモリ 273,360 KB
最終ジャッジ日時 2024-06-11 11:04:30
合計ジャッジ時間 11,931 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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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 AC 78 ms
67,456 KB
testcase_01 AC 77 ms
67,584 KB
testcase_02 AC 65 ms
67,456 KB
testcase_03 AC 65 ms
67,584 KB
testcase_04 AC 64 ms
67,584 KB
testcase_05 AC 65 ms
67,584 KB
testcase_06 AC 65 ms
67,456 KB
testcase_07 AC 161 ms
87,936 KB
testcase_08 AC 407 ms
103,488 KB
testcase_09 AC 447 ms
113,664 KB
testcase_10 AC 399 ms
113,180 KB
testcase_11 AC 169 ms
88,052 KB
testcase_12 AC 199 ms
95,360 KB
testcase_13 AC 447 ms
104,508 KB
testcase_14 AC 207 ms
95,868 KB
testcase_15 AC 226 ms
95,996 KB
testcase_16 AC 218 ms
96,804 KB
testcase_17 AC 214 ms
96,120 KB
testcase_18 AC 202 ms
95,620 KB
testcase_19 AC 220 ms
96,500 KB
testcase_20 AC 248 ms
96,116 KB
testcase_21 AC 208 ms
96,320 KB
testcase_22 AC 276 ms
97,152 KB
testcase_23 AC 234 ms
99,456 KB
testcase_24 AC 391 ms
113,980 KB
testcase_25 AC 465 ms
114,808 KB
testcase_26 AC 178 ms
87,936 KB
testcase_27 AC 203 ms
94,464 KB
testcase_28 AC 187 ms
94,464 KB
testcase_29 AC 314 ms
120,624 KB
testcase_30 AC 163 ms
88,692 KB
testcase_31 AC 278 ms
107,452 KB
testcase_32 AC 120 ms
87,424 KB
testcase_33 AC 604 ms
247,372 KB
testcase_34 AC 648 ms
273,360 KB
testcase_35 AC 132 ms
85,888 KB
testcase_36 AC 66 ms
67,328 KB
testcase_37 AC 65 ms
67,584 KB
testcase_38 AC 144 ms
85,888 KB
testcase_39 AC 360 ms
153,900 KB
testcase_40 AC 356 ms
154,028 KB
testcase_41 AC 349 ms
153,984 KB
testcase_42 AC 73 ms
67,456 KB
testcase_43 AC 69 ms
67,584 KB
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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

            low[v] = now_ord
            order[v] = now_ord
            now_ord += 1
            visited.append(v)
            for i in range(g.start[v], g.start[v + 1]):
                to = g.elist[i]
                if order[to] == -1:
                    dfs(to)
                    low[v] = min(low[v], low[to])
                else:
                    low[v] = min(low[v], order[to])

            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

        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) 
if N!=1 and len(graph[0])==0:
	print("No")
	exit()
groups = sccgraph.scc()
if 0 not in groups[0]:
    print("No")
    exit()
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")
"🐬😢"
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