結果
問題 | No.1424 Ultrapalindrome |
ユーザー | zkou |
提出日時 | 2021-03-13 13:06:37 |
言語 | PyPy3 (7.3.15) |
結果 |
AC
|
実行時間 | 308 ms / 2,000 ms |
コード長 | 4,435 bytes |
コンパイル時間 | 176 ms |
コンパイル使用メモリ | 82,560 KB |
実行使用メモリ | 121,488 KB |
最終ジャッジ日時 | 2024-04-23 05:39:21 |
合計ジャッジ時間 | 5,590 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge4 |
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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 | 45 ms
56,192 KB |
testcase_01 | AC | 45 ms
56,704 KB |
testcase_02 | AC | 46 ms
56,192 KB |
testcase_03 | AC | 46 ms
56,320 KB |
testcase_04 | AC | 46 ms
56,576 KB |
testcase_05 | AC | 45 ms
56,704 KB |
testcase_06 | AC | 46 ms
56,192 KB |
testcase_07 | AC | 46 ms
56,448 KB |
testcase_08 | AC | 46 ms
56,320 KB |
testcase_09 | AC | 245 ms
92,636 KB |
testcase_10 | AC | 253 ms
92,544 KB |
testcase_11 | AC | 177 ms
86,912 KB |
testcase_12 | AC | 200 ms
90,088 KB |
testcase_13 | AC | 117 ms
80,000 KB |
testcase_14 | AC | 188 ms
89,056 KB |
testcase_15 | AC | 52 ms
63,232 KB |
testcase_16 | AC | 157 ms
84,608 KB |
testcase_17 | AC | 173 ms
87,168 KB |
testcase_18 | AC | 160 ms
83,796 KB |
testcase_19 | AC | 205 ms
87,444 KB |
testcase_20 | AC | 112 ms
78,720 KB |
testcase_21 | AC | 170 ms
85,312 KB |
testcase_22 | AC | 137 ms
82,732 KB |
testcase_23 | AC | 93 ms
78,588 KB |
testcase_24 | AC | 107 ms
78,720 KB |
testcase_25 | AC | 106 ms
78,592 KB |
testcase_26 | AC | 217 ms
89,132 KB |
testcase_27 | AC | 308 ms
100,600 KB |
testcase_28 | AC | 156 ms
91,676 KB |
testcase_29 | AC | 169 ms
94,208 KB |
testcase_30 | AC | 192 ms
121,488 KB |
testcase_31 | AC | 180 ms
112,944 KB |
ソースコード
from collections import deque class LCA: "0-indexed" __slots__ = ["depth", "ancestor"] def __init__(self, adj): N = len(adj) parent = [-1] * N self.depth = [0] * N q = deque([0]) while q: node = q.popleft() for next_node in adj[node]: if parent[node] != next_node: parent[next_node] = node q.append(next_node) self.depth[next_node] = self.depth[node] + 1 self.ancestor = [parent] # self.ancestor[k][u]はuの2**k先の祖先。 k = 1 while (1 << k) < N: anc_k = [0] * N for u in range(N): if self.ancestor[-1][u] == -1: anc_k[u] = -1 else: anc_k[u] = self.ancestor[-1][self.ancestor[-1][u]] self.ancestor.append(anc_k) k += 1 def lca(self, u, v): if self.depth[u] < self.depth[v]: u, v = v, u for k, bit in enumerate(reversed(format(self.depth[u]-self.depth[v], 'b'))): if bit == '1': u = self.ancestor[k][u] if u == v: return u for anc in reversed(self.ancestor): if anc[u] != anc[v]: u = anc[u] v = anc[v] return self.ancestor[0][u] def dist(self, u, v): w = self.lca(u, v) return self.depth[u] + self.depth[v] - 2 * self.depth[w] def slow(N, adj): lca = LCA(adj) leaves = [v for v in range(N) if len(adj[v]) == 1] dist = lca.dist(leaves[0], leaves[1]) for i in range(len(leaves)): for j in range(i + 1, len(leaves)): if dist != lca.dist(leaves[i], leaves[j]): return False return True def dfs(N, adj, root): stack = [root] parent = [-1] * N parent[root] = root depth = [0] * N while stack: v = stack.pop() for nv in adj[v]: if parent[nv] == -1: parent[nv] = v depth[nv] = depth[v] + 1 stack.append(nv) return parent, depth def solve(N, adj): _, depth_0 = dfs(N, adj, 0) root = max(range(N), key=lambda i: depth_0[i]) parent, depth = dfs(N, adj, root) dist = max(depth) leaves = [v for v in range(N) if len(adj[v]) == 1] if dist % 2 == 1: if len(leaves) == 2: return True else: return False else: end = max(range(N), key=lambda i: depth[i]) cent = end for _ in range(dist // 2): cent = parent[cent] parent, dists = dfs(N, adj, cent) used = [False] * N for l in leaves: if dists[l] != dist // 2: return False while l != cent: if used[l]: return False used[l] = True l = parent[l] return True def main(): N = int(input()) adj = [[] for _ in range(N)] for _ in range(N - 1): u, v = map(int, input().split()) u -= 1 v -= 1 adj[u].append(v) adj[v].append(u) print("Yes" if solve(N, adj) else "No") import random def prufer_decode(n, code): "0-indexed. O(n) time." assert len(code) == n - 2 counts = [0] * n for v in code: counts[v] += 1 index = 0 while counts[index]: index += 1 leaf = index edges = [] for v in code: edges.append((leaf, v)) counts[v] -= 1 if counts[v] == 0 and v < index: leaf = v else: index += 1 while counts[index]: index += 1 leaf = index edges.append((leaf, n - 1)) return edges def tree_generator(n): assert n >= 2 code = [random.randrange(n) for _ in range(n - 2)] edges = prufer_decode(n, code) # random.shuffle(edges) return edges def test(t): for _ in range(t): N = random.randint(2, 10 ** 3) edges = tree_generator(N) adj = [[] for _ in range(N)] for u, v in edges: adj[u].append(v) adj[v].append(u) if not slow(N, adj) == solve(N, adj): print(slow(N, adj), solve(N, adj)) print(N) for u, v in edges: print(u + 1, v + 1) raise AssertionError # test(10 ** 3) main()