結果

問題 No.2604 Initial Motion
ユーザー detteiuudetteiuu
提出日時 2024-12-04 00:26:37
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 907 ms / 3,000 ms
コード長 6,532 bytes
コンパイル時間 314 ms
コンパイル使用メモリ 82,392 KB
実行使用メモリ 82,576 KB
最終ジャッジ日時 2024-12-04 00:29:36
合計ジャッジ時間 19,509 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
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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 36 ms
53,856 KB
testcase_01 AC 37 ms
53,552 KB
testcase_02 AC 37 ms
54,728 KB
testcase_03 AC 136 ms
77,492 KB
testcase_04 AC 139 ms
77,328 KB
testcase_05 AC 143 ms
77,776 KB
testcase_06 AC 134 ms
77,588 KB
testcase_07 AC 138 ms
77,376 KB
testcase_08 AC 140 ms
77,928 KB
testcase_09 AC 129 ms
77,716 KB
testcase_10 AC 136 ms
77,384 KB
testcase_11 AC 143 ms
77,824 KB
testcase_12 AC 141 ms
77,944 KB
testcase_13 AC 635 ms
82,332 KB
testcase_14 AC 533 ms
81,412 KB
testcase_15 AC 357 ms
80,408 KB
testcase_16 AC 658 ms
81,772 KB
testcase_17 AC 834 ms
82,556 KB
testcase_18 AC 755 ms
82,576 KB
testcase_19 AC 692 ms
82,412 KB
testcase_20 AC 628 ms
82,056 KB
testcase_21 AC 522 ms
81,652 KB
testcase_22 AC 653 ms
82,412 KB
testcase_23 AC 576 ms
82,236 KB
testcase_24 AC 709 ms
82,040 KB
testcase_25 AC 494 ms
81,504 KB
testcase_26 AC 608 ms
81,876 KB
testcase_27 AC 488 ms
81,252 KB
testcase_28 AC 658 ms
81,660 KB
testcase_29 AC 622 ms
82,452 KB
testcase_30 AC 511 ms
81,908 KB
testcase_31 AC 582 ms
81,536 KB
testcase_32 AC 441 ms
80,992 KB
testcase_33 AC 793 ms
81,644 KB
testcase_34 AC 211 ms
80,520 KB
testcase_35 AC 586 ms
81,936 KB
testcase_36 AC 382 ms
81,520 KB
testcase_37 AC 260 ms
80,112 KB
testcase_38 AC 83 ms
75,916 KB
testcase_39 AC 83 ms
76,376 KB
testcase_40 AC 907 ms
82,184 KB
testcase_41 AC 881 ms
82,020 KB
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ソースコード

diff # 

# https://atcoder.jp/contests/practice2/submissions/33588016
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

INF = 10**9

K, N, M = map(int, input().split())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
edge = [list(map(int, input().split())) for _ in range(M)]

MCF = MinCostFlow(N+2)
for i in range(K):
    MCF.add_edge(N, A[i]-1, 1, 0)
for u, v, d in edge:
    MCF.add_edge(u-1, v-1, INF, d)
    MCF.add_edge(v-1, u-1, INF, d)
for i in range(N):
    MCF.add_edge(i, N+1, B[i], 0)

print(MCF.flow(N, N+1, K)[1])
0