結果
| 問題 |
No.2604 Initial Motion
|
| コンテスト | |
| ユーザー |
 miya145592
|
| 提出日時 | 2024-01-13 02:01:59 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 744 ms / 3,000 ms |
| コード長 | 6,645 bytes |
| コンパイル時間 | 380 ms |
| コンパイル使用メモリ | 82,080 KB |
| 実行使用メモリ | 82,336 KB |
| 最終ジャッジ日時 | 2024-09-28 01:09:24 |
| 合計ジャッジ時間 | 15,241 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 39 |
ソースコード
# https://atcoder.jp/contests/practice2/submissions/33588016
import heapq
from heapq import heappush, heappop
class MinCostFlow:
"""
https://github.com/atcoder/ac-library/blob/master/atcoder/internal_csr.hpp
https://github.com/atcoder/ac-library/blob/master/atcoder/mincostflow.hpp
https://github.com/atcoder/ac-library/blob/master/document_en/mincostflow.md
https://github.com/atcoder/ac-library/blob/master/document_ja/mincostflow.md
"""
def __init__(self, n):
self.n = n
self._edges = []
def add_edge(self, fr, to, cap, cost):
assert 0 <= fr < self.n
assert 0 <= to < self.n
assert 0 <= cap
assert 0 <= cost
self._edges.append(self.edge(fr, to, cap, cost))
return len(self._edges) - 1
class edge:
def __init__(self, fr, to, cap, cost):
self.fr = fr
self.to = to
self.cap = cap
self.flow = 0
self.cost = cost
def get_edge(self, i):
assert 0 <= i < len(self._edges)
return self._edges[i]
def edges(self):
return self._edges
def flow(self, s, t, flow_limit=1<<60):
return self.slope(s, t, flow_limit)[-1]
def __csr(self, edges):
# Compressed Sparse Row
self.start = [0] * (self.n + 1)
for fr, _ in edges:
self.start[fr + 1] += 1
for i in range(self.n):
self.start[i + 1] += self.start[i]
counter = self.start.copy()
self.elist = [0] * len(edges)
for fr, e in edges:
self.elist[counter[fr]] = e
counter[fr] += 1
class _edge:
def __init__(self, to, rev, cap, cost):
self.to = to
self.rev = rev
self.cap = cap
self.cost = cost
def __g(self):
degree = [0] * self.n
redge_idx = [0] * self.m
elist = [(0, None)] * (2 * self.m)
now_elist = 0
for i in range(self.m):
e = self._edges[i]
self.edge_idx[i] = degree[e.fr]
degree[e.fr] += 1
redge_idx[i] = degree[e.to]
degree[e.to] += 1
elist[now_elist] = (e.fr, self._edge(e.to, -1, e.cap - e.flow, e.cost))
now_elist += 1
elist[now_elist] = (e.to, self._edge(e.fr, -1, e.flow, -e.cost))
now_elist += 1
self.__csr(elist)
for i in range(self.m):
e = self._edges[i]
self.edge_idx[i] += self.start[e.fr]
redge_idx[i] += self.start[e.to]
self.elist[self.edge_idx[i]].rev = redge_idx[i]
self.elist[redge_idx[i]].rev = self.edge_idx[i]
def slope(self, s, t, flow_limit=1<<60):
assert 0 <= s < self.n
assert 0 <= t < self.n
assert s != t
self.m = len(self._edges)
self.edge_idx = [0] * self.m
self.__g()
result = self.__slope(s, t, flow_limit)
for i in range(self.m):
e = self.elist[self.edge_idx[i]]
self._edges[i].flow = self._edges[i].cap - e.cap
return result
def __dual_ref(self, s, t):
log = self.n.bit_length()
mask = (1<<log) - 1
dist = [1<<60] * self.n
vis = [0] * self.n
que_min = []
que = []
dist[s] = 0
que_min.append(s)
while que_min or que:
if que_min:
v = que_min.pop()
else:
v = heappop(que) & mask
if vis[v]:
continue
vis[v] = 1
if v == t:
break
# dist[v] = shortest(s, v) + dual[s] - dual[v]
# dist[v] >= 0 (all reduced cost are positive)
# dist[v] <= (n-1)C
dual_v = self.dual[v]
dist_v = dist[v]
for i in range(self.start[v], self.start[v+1]):
e = self.elist[i]
if not e.cap:
continue
# |-dual[e.to] + dual[v]| <= (n-1)C
# cost <= C - -(n-1)C + 0 = nC
cost = e.cost - self.dual[e.to] + dual_v
if dist[e.to] - dist_v > cost:
dist_to = dist_v + cost
dist[e.to] = dist_to
self.prev_e[e.to] = e.rev
if dist_to == dist_v:
que_min.append(e.to)
else:
heappush(que, dist_to<<log | e.to)
if not vis[t]:
return False
for v in range(self.n):
if not vis[v]:
continue
# dual[v]
# = dual[v] - dist[t] + dist[v]
# = dual[v] - (shortest(s, t) + dual[s] - dual[t]) + (shortest(s, v) + dual[s] - dual[v])
# = - shortest(s, t) + dual[t] + shortest(s, v)
# = shortest(s, v) - shortest(s, t)
# >= 0 - (n-1)C
self.dual[v] -= dist[t] - dist[v]
return True
def __slope(self, s, t, flow_limit):
# variants (C = maxcost):
# -(n-1)C <= dual[s] <= dual[i] <= dual[t] = 0
# reduced cost (= e.cost + dual[e.from] - dual[e.to]) >= 0 for all edge
self.dual = [0] * self.n
self.prev_e = [0] * self.n
flow = 0
cost = 0
prev_cost_per_flow = -1
result = [(0, 0)]
while flow < flow_limit:
if not self.__dual_ref(s, t):
break
c = flow_limit - flow
v = t
while v != s:
c = min(c, self.elist[self.elist[self.prev_e[v]].rev].cap)
v = self.elist[self.prev_e[v]].to
v = t
while v != s:
e = self.elist[self.prev_e[v]]
e.cap += c
self.elist[e.rev].cap -= c
v = self.elist[self.prev_e[v]].to
d = -self.dual[s]
flow += c
cost += c * d
if prev_cost_per_flow == d:
result.pop()
result.append((flow, cost))
prev_cost_per_flow = d
return result
import sys
input = sys.stdin.readline
K, N, M = map(int, input().split())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
MCF = MinCostFlow(N+2)
INF = 10**5
C = [0 for _ in range(N)]
for a in A:
a-=1
C[a]+=1
for i in range(N):
if C[i]>0:
MCF.add_edge(0, i+1, C[i], 0)
if B[i]>0:
MCF.add_edge(i+1, N+1, B[i], 0)
for _ in range(M):
u, v, d = map(int, input().split())
MCF.add_edge(u, v, INF, d)
MCF.add_edge(v, u, INF, d)
ans = MCF.flow(0, N+1, K)
print(ans[1])