結果
| 問題 | No.3539 Parentheses Square |
| コンテスト | |
| ユーザー |
 kidodesu
|
| 提出日時 | 2026-05-08 23:22:56 |
| 言語 | PyPy3 (7.3.17) |
| 結果 |
AC
|
| 実行時間 | 1,109 ms / 2,000 ms |
| コード長 | 6,124 bytes |
| 記録 | |
| コンパイル時間 | 227 ms |
| コンパイル使用メモリ | 85,248 KB |
| 実行使用メモリ | 334,560 KB |
| 最終ジャッジ日時 | 2026-05-08 23:23:17 |
| 合計ジャッジ時間 | 16,704 ms |
|
ジャッジサーバーID （参考情報） |
judge1_1 / judge3_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 41 |
ソースコード
class MFGraph:
class Edge:
def __init__(self, src, dst, cap, flow):
self.src = src
self.dst = dst
self.cap = cap
self.flow = flow
class _Edge:
def __init__(self, dst: int, cap: int) -> None:
self.dst = dst
self.cap = cap
self.rev = None
def __init__(self, n: int) -> None:
self._n = n
self._g = [[] for _ in range(n)]
self._edges = []
def add_edge(self, src: int, dst: int, cap: int) -> int:
assert 0 <= src < self._n
assert 0 <= dst < self._n
assert 0 <= cap
m = len(self._edges)
e = MFGraph._Edge(dst, cap)
re = MFGraph._Edge(src, 0)
e.rev = re
re.rev = e
self._g[src].append(e)
self._g[dst].append(re)
self._edges.append(e)
return m
def get_edge(self, i: int) -> Edge:
assert 0 <= i < len(self._edges)
e = self._edges[i]
re = e.rev
return MFGraph.Edge(
re.dst,
e.dst,
e.cap + re.cap,
re.cap
)
def edges(self):
return [self.get_edge(i) for i in range(len(self._edges))]
def change_edge(self, i: int, new_cap: int, new_flow: int) -> None:
assert 0 <= i < len(self._edges)
assert 0 <= new_flow <= new_cap
e = self._edges[i]
e.cap = new_cap - new_flow
assert e.rev is not None
e.rev.cap = new_flow
def flow(self, s: int, t: int, flow_limit = None) -> int:
assert 0 <= s < self._n
assert 0 <= t < self._n
assert s != t
if flow_limit is None:
flow_limit = sum(e.cap for e in self._g[s])
current_edge = [0] * self._n
level = [0] * self._n
def fill(arr, value: int) -> None:
for i in range(len(arr)):
arr[i] = value
def bfs() -> bool:
fill(level, self._n)
queue = []
q_front = 0
queue.append(s)
level[s] = 0
while q_front < len(queue):
v = queue[q_front]
q_front += 1
next_level = level[v] + 1
for e in self._g[v]:
if e.cap == 0 or level[e.dst] <= next_level:
continue
level[e.dst] = next_level
if e.dst == t:
return True
queue.append(e.dst)
return False
def dfs(lim: int) -> int:
stack = []
edge_stack = []
stack.append(t)
while stack:
v = stack[-1]
if v == s:
flow = min(lim, min(e.cap for e in edge_stack))
for e in edge_stack:
e.cap -= flow
assert e.rev is not None
e.rev.cap += flow
return flow
next_level = level[v] - 1
while current_edge[v] < len(self._g[v]):
e = self._g[v][current_edge[v]]
re = e.rev
if level[e.dst] != next_level or re.cap == 0:
current_edge[v] += 1
continue
stack.append(e.dst)
edge_stack.append(re)
break
else:
stack.pop()
if edge_stack:
edge_stack.pop()
level[v] = self._n
return 0
flow = 0
while flow < flow_limit:
if not bfs():
break
fill(current_edge, 0)
while flow < flow_limit:
f = dfs(flow_limit - flow)
flow += f
if f == 0:
break
return flow
n = int(input())
if n % 2: exit(print(-1))
N = n // 2 + 1
S = [input() for _ in range(n)]
E = {}
node = [[] for _ in range(n)]
for i in range(n):
B = [[]]
C = [[0 for _ in range(N)] for _ in range(N)]
C[0][0] = 1
for y in range(N):
for x in range(y+1):
if not C[y][x]:
continue
if y+1 < N and S[i][y+x] != ")":
C[y+1][x] = 1
if x+1 < N and S[i][y+x] != "(":
C[y][x+1] = 1
if not C[-1][-1]: exit(print(-1))
C[-1][-1] = 2
for y in range(N-1, -1, -1):
for x in range(y, -1, -1):
if C[y][x] != 2: continue
if y and S[i][y+x-1] != ")" and C[y-1][x]:
C[y-1][x] = 2
if x and S[i][y+x-1] != "(" and C[y][x-1]:
C[y][x-1] = 2
for y in range(N):
for x in range(N):
if y < x:
C[y][x] = 0
if C[y][x] <= 1:
C[y][x] = 0
D = [[[] for _ in range(N)] for _ in range(N)]
D[0][0].append("")
for le in range(n):
cnt = 200
for y in range(le+1):
x = le - y
if not (0 <= y < N and 0 <= x < N): continue
if not C[y][x]: continue
for s in D[y][x]:
if y+1 < N and S[i][y+x] != ")" and C[y+1][x] and cnt:
cnt -= 1
D[y+1][x].append(s+"(")
if x+1 < N and S[i][y+x] != "(" and C[y][x+1] and cnt:
cnt -= 1
D[y][x+1].append(s+")")
for d in D[-1][-1]:
if not d in E:
E[d] = len(E)
ei = E[d]
else:
ei = E[d]
node[i].append(ei)
Ei = [""] * len(E)
for d in E:
Ei[E[d]] = d
mf = MFGraph(n+len(E)+2)
s = n+len(E)
t = s+1
for i in range(n):
mf.add_edge(s, i, 1)
for j in node[i]:
mf.add_edge(i, n+j, 1)
for i in range(len(E)):
mf.add_edge(n+i, t, 1)
ans = mf.flow(s, t, n)
if ans < n:
print(-1)
else:
Ans = ["" for _ in range(n)]
for e in mf.edges():
if e.flow == 1 and e.src < n:
Ans[e.src] = Ei[e.dst-n]
for ans in Ans:
print(ans)