結果

問題 No.1023 Cyclic Tour
ユーザー gew1fw
提出日時 2025-06-12 18:51:50
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 949 ms / 2,000 ms
コード長 3,308 bytes
コンパイル時間 235 ms
コンパイル使用メモリ 82,044 KB
実行使用メモリ 280,312 KB
最終ジャッジ日時 2025-06-12 18:52:42
合計ジャッジ時間 33,293 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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ファイルパターン 結果
sample AC * 4
other AC * 49
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 # 

import sys
from sys import stdin
from collections import defaultdict
sys.setrecursionlimit(1 << 25)

def main():
    input = sys.stdin.read().split()
    ptr = 0
    N = int(input[ptr])
    ptr += 1
    M = int(input[ptr])
    ptr += 1

    roads = []
    edges = defaultdict(list)
    for i in range(M):
        a = int(input[ptr])
        ptr += 1
        b = int(input[ptr])
        ptr += 1
        c = int(input[ptr])
        ptr += 1
        roads.append((a, b, c))
        if c == 1:
            edges[(a, b)].append(i)
            edges[(b, a)].append(i)
        else:
            edges[(a, b)].append(i)

    # Step 1: Check for pairs of edges in opposite directions from different roads
    found = False
    for i in range(M):
        a, b, c = roads[i]
        reverse_roads = edges.get((b, a), [])
        for r in reverse_roads:
            if r != i:
                found = True
                break
        if found:
            break
    if found:
        print("Yes")
        return

    # Step 2: Build the directed graph for SCC computation
    graph = [[] for _ in range(N + 1)]
    for a, b, c in roads:
        graph[a].append(b)
        if c == 1:
            graph[b].append(a)

    # Compute SCC using Tarjan's algorithm
    index = 0
    indices = [0] * (N + 1)
    low = [0] * (N + 1)
    on_stack = [False] * (N + 1)
    stack = []
    scc = []

    def strongconnect(v):
        nonlocal index
        indices[v] = index
        low[v] = index
        index += 1
        stack.append(v)
        on_stack[v] = True
        for w in graph[v]:
            if indices[w] == 0:
                strongconnect(w)
                low[v] = min(low[v], low[w])
            elif on_stack[w]:
                low[v] = min(low[v], indices[w])
        if low[v] == indices[v]:
            component = []
            while True:
                w = stack.pop()
                on_stack[w] = False
                component.append(w)
                if w == v:
                    break
            scc.append(component)

    for v in range(1, N + 1):
        if indices[v] == 0:
            strongconnect(v)

    node_component = [0] * (N + 1)
    for i, component in enumerate(scc):
        for node in component:
            node_component[node] = i

    # Step 3: Check unidirectional roads
    for i in range(M):
        a, b, c = roads[i]
        if c == 2:
            if node_component[a] == node_component[b]:
                print("Yes")
                return

    # Step 4: Check for cycles in the undirected graph of bidirectional roads using DSU
    parent = list(range(N + 1))

    def find(u):
        while parent[u] != u:
            parent[u] = parent[parent[u]]
            u = parent[u]
        return u

    def union(u, v):
        u_root = find(u)
        v_root = find(v)
        if u_root == v_root:
            return False
        parent[v_root] = u_root
        return True

    cycle_found = False
    parent = list(range(N + 1))
    for i in range(M):
        a, b, c = roads[i]
        if c == 1:
            x = find(a)
            y = find(b)
            if x == y:
                cycle_found = True
                break
            union(x, y)
    if cycle_found:
        print("Yes")
        return

    print("No")

if __name__ == "__main__":
    main()
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