結果
| 問題 |
No.1744 Selfish Spies 1 (à la Princess' Perfectionism)
|
| コンテスト | |
| ユーザー |
 vwxyz
|
| 提出日時 | 2023-08-09 02:51:10 |
| 言語 | Python3 (3.13.1 + numpy 2.2.1 + scipy 1.14.1) |
| 結果 |
AC
|
| 実行時間 | 2,015 ms / 5,000 ms |
| コード長 | 8,626 bytes |
| コンパイル時間 | 314 ms |
| コンパイル使用メモリ | 13,696 KB |
| 実行使用メモリ | 77,720 KB |
| 最終ジャッジ日時 | 2024-11-14 08:12:37 |
| 合計ジャッジ時間 | 16,334 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 39 |
ソースコード
import sys
readline=sys.stdin.readline
from typing import NamedTuple, Optional, List, cast
class MFGraph:
class Edge(NamedTuple):
src: int
dst: int
cap: int
flow: int
class _Edge:
def __init__(self, dst: int, cap: int) -> None:
self.dst = dst
self.cap = cap
self.rev: Optional[MFGraph._Edge] = None
def __init__(self, n: int) -> None:
self._n = n
self._g: List[List[MFGraph._Edge]] = [[] for _ in range(n)]
self._edges: List[MFGraph._Edge] = []
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 = cast(MFGraph._Edge, e.rev)
return MFGraph.Edge(
re.dst,
e.dst,
e.cap + re.cap,
re.cap
)
def edges(self) -> List[Edge]:
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: Optional[int] = None) -> int:
assert 0 <= s < self._n
assert 0 <= t < self._n
assert s != t
if flow_limit is None:
flow_limit = cast(int, sum(e.cap for e in self._g[s]))
current_edge = [0] * self._n
level = [0] * self._n
def fill(arr: List[int], 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: List[MFGraph._Edge] = []
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 = cast(MFGraph._Edge, 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
def min_cut(self, s: int) -> List[bool]:
visited = [False] * self._n
stack = [s]
visited[s] = True
while stack:
v = stack.pop()
for e in self._g[v]:
if e.cap > 0 and not visited[e.dst]:
visited[e.dst] = True
stack.append(e.dst)
return visited
def SCC(N,edges):
start = [0] * (N + 1)
elist = [0] * len(edges)
for e in edges:
start[e[0] + 1] += 1
for i in range(1, N + 1):
start[i] += start[i - 1]
counter = start[:]
for e in edges:
elist[counter[e[0]]] = e[1]
counter[e[0]] += 1
N = N
now_ord = group_num = 0
visited = []
low = [0] * N
order = [-1] * N
ids = [0] * N
parent = [-1] * N
stack = []
for i in range(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(start[v], start[v + 1]):
to = 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] = 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
groups = [[] for _ in range(group_num)]
for i, x in enumerate(ids):
groups[x].append(i)
return groups
def DM_Decomposition(N,M,edges):
s=0
t=N+M+1
MFG=MFGraph(N+M+2)
for n,m in edges:
MFG.add_edge(1+n,1+m,1)
for n in range(N):
MFG.add_edge(s,1+n,1)
for m in range(M):
MFG.add_edge(1+N+m,t,1)
MFG.flow(s,t)
graph=[[] for x in range(N+M)]
graph_rev=[[] for x in range(N+M)]
covering=[False]*(N+M)
for e in MFG.edges():
if 1<=e.src<1+N and 1+N<=e.dst<1+N+M:
x=e.src-1
y=e.dst-1
if e.flow:
graph[x].append(y)
graph[y].append(x)
graph_rev[x].append(y)
graph_rev[y].append(x)
covering[x]=True
covering[y]=True
else:
graph[x].append(y)
graph_rev[y].append(x)
retu=[[]]
seen=[False]*(N+M)
stack=[]
for m in range(M):
if not covering[m+N]:
stack.append(m+N)
seen[m+N]=True
while stack:
x=stack.pop()
retu[0].append(x)
for y in graph_rev[x]:
if not seen[y]:
stack.append(y)
seen[y]=True
stack=[]
V_inf=[]
for n in range(N):
if not covering[n]:
seen[n]=True
stack.append(n)
while stack:
x=stack.pop()
V_inf.append(x)
for y in graph[x]:
if not seen[y]:
stack.append(y)
seen[y]=True
scc_edges=[]
for e in MFG.edges():
if 1<=e.src<1+N and 1+N<=e.dst<1+N+M:
x=e.src-1
y=e.dst-1
if not seen[x] and not seen[y]:
if e.flow:
scc_edges.append((x,y))
scc_edges.append((y,x))
else:
scc_edges.append((x,y))
scc=SCC(N+M,scc_edges)
for lst in scc:
if seen[lst[0]]:
continue
retu.append(lst)
retu.append(V_inf)
return retu
N,M,L=map(int,readline().split())
edges=[]
for l in range(L):
x,y=map(int,readline().split())
x-=1;y-=1
edges.append((x,y+N))
dm=DM_Decomposition(N,M,edges)
idx=[None]*(N+M)
for i,lst in enumerate(dm):
for x in lst:
idx[x]=i
for x,y in edges:
if idx[x]==idx[y] and len(dm[idx[x]])==2:
ans="No"
else:
ans="Yes"
print(ans)