結果
| 問題 | No.1914 Directed by Two Sequences |
| ユーザー |
 chineristAC
|
| 提出日時 | 2021-11-05 20:13:09 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
WA
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 10,630 bytes |
| コンパイル時間 | 277 ms |
| コンパイル使用メモリ | 81,792 KB |
| 実行使用メモリ | 201,100 KB |
| 最終ジャッジ日時 | 2024-05-09 12:19:53 |
| 合計ジャッジ時間 | 52,773 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 | 51 ms
68,480 KB |
| testcase_01 | AC | 52 ms
68,480 KB |
| testcase_02 | AC | 517 ms
102,644 KB |
| testcase_03 | AC | 527 ms
105,820 KB |
| testcase_04 | AC | 501 ms
104,960 KB |
| testcase_05 | AC | 509 ms
104,884 KB |
| testcase_06 | AC | 480 ms
103,580 KB |
| testcase_07 | AC | 513 ms
100,904 KB |
| testcase_08 | AC | 529 ms
101,656 KB |
| testcase_09 | AC | 519 ms
102,428 KB |
| testcase_10 | AC | 1,291 ms
163,272 KB |
| testcase_11 | AC | 1,305 ms
167,068 KB |
| testcase_12 | AC | 1,290 ms
166,896 KB |
| testcase_13 | AC | 1,318 ms
158,348 KB |
| testcase_14 | AC | 1,276 ms
162,636 KB |
| testcase_15 | AC | 1,355 ms
160,888 KB |
| testcase_16 | AC | 1,246 ms
171,952 KB |
| testcase_17 | AC | 1,254 ms
165,648 KB |
| testcase_18 | AC | 1,254 ms
166,904 KB |
| testcase_19 | AC | 868 ms
129,436 KB |
| testcase_20 | AC | 824 ms
129,016 KB |
| testcase_21 | AC | 939 ms
141,676 KB |
| testcase_22 | AC | 1,283 ms
163,636 KB |
| testcase_23 | AC | 1,220 ms
164,068 KB |
| testcase_24 | AC | 1,266 ms
168,032 KB |
| testcase_25 | AC | 1,340 ms
157,404 KB |
| testcase_26 | AC | 1,199 ms
158,028 KB |
| testcase_27 | AC | 1,497 ms
158,300 KB |
| testcase_28 | AC | 1,427 ms
162,428 KB |
| testcase_29 | AC | 1,385 ms
157,116 KB |
| testcase_30 | AC | 1,388 ms
157,068 KB |
| testcase_31 | AC | 1,554 ms
185,092 KB |
| testcase_32 | AC | 1,622 ms
156,216 KB |
| testcase_33 | AC | 581 ms
117,184 KB |
| testcase_34 | WA | - |
| testcase_35 | AC | 797 ms
142,404 KB |
| testcase_36 | AC | 1,363 ms
176,256 KB |
| testcase_37 | AC | 1,300 ms
173,436 KB |
| testcase_38 | AC | 1,539 ms
188,012 KB |
| testcase_39 | AC | 1,747 ms
201,100 KB |
ソースコード
class SegmentTree:
def __init__(self, init_val, segfunc, ide_ele):
n = len(init_val)
self.segfunc = segfunc
self.ide_ele = ide_ele
self.num = 1 << (n - 1).bit_length()
self.tree = [ide_ele] * 2 * self.num
self.size = n
for i in range(n):
self.tree[self.num + i] = init_val[i]
for i in range(self.num - 1, 0, -1):
self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1])
def update(self, k, x):
k += self.num
self.tree[k] = x
while k > 1:
k >>= 1
self.tree[k] = self.segfunc(self.tree[2*k], self.tree[2*k+1])
def query(self, l, r):
if r==self.size:
r = self.num
res = self.ide_ele
l += self.num
r += self.num
right = []
while l < r:
if l & 1:
res = self.segfunc(res, self.tree[l])
l += 1
if r & 1:
right.append(self.tree[r-1])
l >>= 1
r >>= 1
for e in right[::-1]:
res = self.segfunc(res,e)
return res
class _csr:
def __init__(self, n, edges):
self.start = [0] * (n + 1)
self.elist = [0] * len(edges)
for v, _ in edges:
self.start[v + 1] += 1
for i in range(1, n + 1):
self.start[i] += self.start[i - 1]
counter = self.start.copy()
for v, e in edges:
self.elist[counter[v]] = e
counter[v] += 1
class scc_graph:
"""It calculates the strongly connected components of directed graphs.
"""
def __init__(self, n):
"""It creates a directed graph with n vertices and 0 edges.
Constraints
-----------
> 0 <= n <= 10 ** 8
Complexity
----------
> O(n)
"""
self.n = n
self.edges = []
def add_edge(self, from_, to):
"""It adds a directed edge from the vertex `from_` to the vertex `to`.
Constraints
-----------
> 0 <= from_ < n
> 0 <= to < n
Complexity
----------
> O(1) amortized
"""
# assert 0 <= from_ < self.n
# assert 0 <= to < self.n
self.edges.append((from_, to))
def _scc_ids(self):
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
parent = [-1] * self.n
stack = []
for i in range(self.n):
if order[i] == -1:
stack.append(i)
stack.append(i)
while stack:
v = stack.pop()
if order[v] == -1:
low[v] = 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:
stack.append(to)
stack.append(to)
parent[to] = v
else:
low[v] = min(low[v], order[to])
else:
if low[v] == order[v]:
while True:
u = visited.pop()
order[u] = self.n
ids[u] = group_num
if u == v:
break
group_num += 1
if parent[v] != -1:
low[parent[v]] = min(low[parent[v]], low[v])
for i, x in enumerate(ids):
ids[i] = group_num - 1 - x
return group_num, ids
def scc(self):
"""It returns the list of the "list of the vertices" that satisfies the following.
> Each vertex is in exactly one "list of the vertices".
> Each "list of the vertices" corresponds to the vertex set of a strongly connected component.
The order of the vertices in the list is undefined.
> The list of "list of the vertices" are sorted in topological order,
i.e., for two vertices u, v in different strongly connected components,
if there is a directed path from u to v,
the list contains u appears earlier than the list contains v.
Complexity
----------
> O(n + m), where m is the number of added edges.
"""
group_num, ids = self._scc_ids()
groups = [[] for _ in range(group_num)]
for i, x in enumerate(ids):
groups[x].append(i)
return groups
def popcount(x):
'''xの立っているビット数をカウントする関数
(xは64bit整数)'''
# 2bitごとの組に分け、立っているビット数を2bitで表現する
x = x - ((x >> 1) & 0x5555555555555555)
# 4bit整数に 上位2bit + 下位2bit を計算した値を入れる
x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333)
x = (x + (x >> 4)) & 0x0f0f0f0f0f0f0f0f # 8bitごと
x = x + (x >> 8) # 16bitごと
x = x + (x >> 16) # 32bitごと
x = x + (x >> 32) # 64bitごと = 全部の合計
return x & 0x0000007f
popcnt = [popcount(i) for i in range(2**20)]
def solve(N,A,B,M,E):
A = [a-1 for a in A]
B = [b-1 for b in B]
G = scc_graph(N)
edge = [[] for v in range(N)]
for u,v in E:
edge[u-1].append(v-1)
edge[v-1].append(u-1)
group = [-1 for v in range(N)]
for v in range(N):
mex = [False for i in range(len(edge[v])+1)]
for nv in edge[v]:
if nv < v and group[nv] < len(mex):
mex[group[nv]] = True
for i in range(len(mex)):
if not mex[i]:
group[v] = i
break
n = max(group) + 1
clique = [[] for g in range(n)]
for v in range(N):
clique[group[v]].append(v)
def direct(i,j):
if i < j:
return A[i] < B[j]
else:
return B[i] < A[j]
def hamilton_path(V):
n = len(V)
if n <= 1:
return V
A = hamilton_path(V[:n//2])
B = hamilton_path(V[n//2:])
res = []
bi = 0
for ai in range(len(A)):
while bi<len(B) and direct(B[bi],A[ai]):
res.append(B[bi])
bi += 1
res.append(A[ai])
res += B[bi:]
return res
idx = [-1 for v in range(N)]
for g in range(n):
clique[g] = hamilton_path(clique[g])
for i in range(len(clique[g])):
idx[clique[g][i]] = i
for u,v in zip(clique[g],clique[g][1:]):
G.add_edge(u,v)
memo_to = [N for v in range(N)]
memo_from = [-1 for v in range(N)]
ci = [i for i in range(n)]
ci.sort(lambda g:len(clique[g]))
idx_on_ci = [-1 for i in range(n)]
for i in range(n):
idx_on_ci[ci[i]] = i
ban = [[] for v in range(N)]
Vs = []
seg_to_large = SegmentTree([N]*2*N,min,N)
seg_to_small = SegmentTree([N]*2*N,min,N)
seg_from_large = SegmentTree([-1]*2*N,max,-1)
seg_from_small = SegmentTree([-1]*2*N,max,-1)
for i in range(n):
target = ci[i]
Vs += clique[target]
Vs.sort()
for nv in clique[target]:
for v in edge[nv]:
if idx_on_ci[group[v]] <= i:
ban[v].append(nv)
for v in Vs[::-1]:
for nv in ban[v]:
if v < nv:
seg_to_large.update(B[nv],N)
memo_to[v] = min(memo_to[v],seg_to_large.query(A[v],2*N))
for nv in ban[v]:
if v < nv:
seg_to_large.update(B[nv],idx[nv])
if group[v]==target:
seg_to_large.update(B[v],idx[v])
for v in Vs:
for nv in ban[v]:
if nv < v:
seg_to_small.update(A[nv],N)
memo_to[v] = min(memo_to[v],seg_to_small.query(B[v],2*N))
for nv in ban[v]:
if nv < v:
seg_to_small.update(A[nv],idx[nv])
if group[v]==target:
seg_to_small.update(A[v],idx[v])
for v in Vs[::-1]:
for nv in ban[v]:
if v < nv:
seg_from_large.update(B[nv],-1)
memo_from[v] = max(memo_from[v],seg_from_large.query(0,A[v]))
for nv in ban[v]:
if v < nv:
seg_from_large.update(B[nv],idx[nv])
if group[v]==target:
seg_from_large.update(B[v],idx[v])
for v in Vs:
for nv in ban[v]:
if nv < v:
seg_from_small.update(A[nv],-1)
memo_from[v] = max(memo_from[v],seg_from_small.query(0,B[v]))
for nv in ban[v]:
if nv < v:
seg_from_small.update(A[nv],idx[nv])
if group[v]==target:
seg_from_small.update(A[v],idx[v])
for v in Vs:
if memo_to[v]!=N:
nv = clique[target][memo_to[v]]
G.add_edge(v,nv)
memo_to[v] = N
if memo_from[v]!=-1:
pv = clique[target][memo_from[v]]
G.add_edge(pv,v)
memo_from[v] = -1
ban[v] = []
if group[v]==target:
seg_to_large.update(B[v],N)
seg_to_small.update(A[v],N)
seg_from_large.update(B[v],-1)
seg_from_small.update(A[v],-1)
group_num,ids = G._scc_ids()
res = []
SCC = [[] for g in range(group_num)]
for v in range(N):
SCC[ids[v]].append(v)
for g in range(group_num):
for u,v in zip(SCC[g],SCC[g][1:]):
res.append((u+1,v+1))
if len(SCC[g])!=1:
u,v = SCC[g][-1],SCC[g][0]
res.append((u+1,v+1))
for u,v in G.edges:
if ids[u] < ids[v]:
res.append((u+1,v+1))
print(len(res))
for u,v in res:
print(u,v)
import sys
input = lambda :sys.stdin.buffer.readline()
mi = lambda :map(int,input().split())
li = lambda :list(mi())
N,M = mi()
A = li()
B = li()
E = [tuple(mi()) for i in range(M)]
solve(N,A,B,M,E)