結果
| 問題 |
No.1324 Approximate the Matrix
|
| ユーザー |
 shotoyoo
|
| 提出日時 | 2020-12-22 00:23:35 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 335 ms / 2,000 ms |
| コード長 | 6,232 bytes |
| コンパイル時間 | 311 ms |
| コンパイル使用メモリ | 82,240 KB |
| 実行使用メモリ | 89,664 KB |
| 最終ジャッジ日時 | 2024-09-21 13:29:41 |
| 合計ジャッジ時間 | 8,095 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 42 |
ソースコード
import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(2*10**5+10)
write = lambda x: sys.stdout.write(x+"\n")
from typing import NamedTuple, Optional, List, Tuple, cast
from heapq import heappush, heappop
class MCFGraph:
class Edge(NamedTuple):
src: int
dst: int
cap: int
flow: int
cost: int
class _Edge:
def __init__(self, dst: int, cap: int, cost: int) -> None:
self.dst = dst
self.cap = cap
self.cost = cost
self.rev: Optional[MCFGraph._Edge] = None
def __init__(self, n: int, neg=False, negf=None) -> None:
self._neg = neg
if neg:
n += 2
self._negs = n-2
self._negt = n-1
self._negf = negf
self._negfsum = 0
self._negcsum = 0
self._negdone = False
self._n = n
self._g: List[List[MCFGraph._Edge]] = [[] for _ in range(n)]
self._edges: List[MCFGraph._Edge] = []
def add_edge(self, src: int, dst: int, cap: int, cost: int) -> int:
assert 0 <= src < self._n
assert 0 <= dst < self._n
assert 0 <= cap
if cost<0 and self._neg:
if not self._negdone:
global s,t
self._negdone = True
self.add_edge(self._negs, s, self._negf, 0)
self.add_edge(t, self._negt, self._negf, 0)
# 後で指定した流量を流すための処理
# self._inf = 10**12
# self._negE = self.add_edge(self._negt, self._negs, self._negf, -self._inf)
self.add_edge(self._negs, dst, cap, 0)
self.add_edge(src, self._negt, cap, 0)
self.add_edge(dst, src, cap, -cost)
self._negfsum += cap
self._negcsum += cap*cost
else:
m = len(self._edges)
e = MCFGraph._Edge(dst, cap, cost)
re = MCFGraph._Edge(src, 0, -cost)
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(MCFGraph._Edge, e.rev)
return MCFGraph.Edge(
re.dst,
e.dst,
e.cap + re.cap,
re.cap,
e.cost
)
def edges(self) -> List[Edge]:
return [self.get_edge(i) for i in range(len(self._edges))]
def flow(self, s: int, t: int, flow_limit: Optional[int] = None) -> Tuple[int, int]:
if self._neg:
flow_limit += self._negfsum
val = self.slope(self._negs, self._negt, flow_limit)[-1]
return (val[0], val[1] + self._negcsum)
else:
return self.slope(s, t, flow_limit)[-1]
def slope(self, s: int, t: int, flow_limit: Optional[int] = None) -> List[Tuple[int, 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]))
dual = [0] * self._n
prev: List[Optional[Tuple[int, MCFGraph._Edge]]] = [None] * self._n
def refine_dual() -> bool:
pq = [self.enc(0, s)]
visited = [False] * self._n
dist: List[Optional[int]] = [None] * self._n
dist[s] = 0
while pq:
dist_v, v = self.dec(heappop(pq))
if visited[v]:
continue
visited[v] = True
if v == t:
break
dual_v = dual[v]
for e in self._g[v]:
w = e.dst
if visited[w] or e.cap == 0:
continue
reduced_cost = e.cost - dual[w] + dual_v
new_dist = dist_v + reduced_cost
dist_w = dist[w]
if dist_w is None or new_dist < dist_w:
dist[w] = new_dist
prev[w] = v, e
heappush(pq, self.enc(new_dist, w))
else:
return False
dist_t = dist[t]
for v in range(self._n):
if visited[v]:
dual[v] -= cast(int, dist_t) - cast(int, dist[v])
return True
flow = 0
cost = 0
prev_cost_per_flow: Optional[int] = None
result = [(flow, cost)]
while flow < flow_limit:
if not refine_dual():
break
f = flow_limit - flow
v = t
while prev[v] is not None:
u, e = cast(Tuple[int, MCFGraph._Edge], prev[v])
f = min(f, e.cap)
v = u
v = t
while prev[v] is not None:
u, e = cast(Tuple[int, MCFGraph._Edge], prev[v])
e.cap -= f
assert e.rev is not None
e.rev.cap += f
v = u
c = -dual[s]
flow += f
cost += f * c
if c == prev_cost_per_flow:
result.pop()
result.append((flow, cost))
prev_cost_per_flow = c
return result
def enc(self,d,v):
return d*(self._n)+v
def dec(self,val):
return divmod(val,self._n)
n,k = list(map(int, input().split()))
a = list(map(int, input().split()))
b = list(map(int, input().split()))
p = [list(map(int, input().split())) for _ in range(n)]
num = 2*n + 2
# g = MCFGraph(num, neg=True, negf=k)
g = MCFGraph(num)
s = num-2
t = num-1
for i in range(n):
for j in range(n):
for ind in range(min(a[i],b[j])):
cost = -2*p[i][j] + 1 + 2*ind
g.add_edge(i,n+j,1,cost)
# print(i,j,cost)
# g.add_edge(pij(i,j), t, a[i]+b[j], cost) # cost<0のときは？
for i in range(n):
g.add_edge(s, i, a[i], 0)
for j in range(n):
g.add_edge(n+j, t, b[j], 0)
val = g.flow(s,t,k)
ans = sum(p[i][j]**2 for i in range(n) for j in range(n)) + val[1]
print(ans)