#944596 (PyPy3) No.2604 Initial Motion

提出ソース

結果

問題	No.2604 Initial Motion
ユーザー	rlangevin
提出日時	2024-01-19 12:22:59
言語	PyPy3 (7.3.15)
結果	AC
実行時間	1,024 ms / 3,000 ms
コード長	6,497 bytes
コンパイル時間	228 ms
コンパイル使用メモリ	82,352 KB
実行使用メモリ	83,720 KB
最終ジャッジ日時	2024-09-28 03:24:43
合計ジャッジ時間	20,914 ms
ジャッジサーバーID （参考情報）	judge2 / judge1

このコードへのチャレンジ
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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	46 ms 54,876 KB
testcase_01	AC	43 ms 55,324 KB
testcase_02	AC	45 ms 54,476 KB
testcase_03	AC	146 ms 77,268 KB
testcase_04	AC	145 ms 77,468 KB
testcase_05	AC	142 ms 77,788 KB
testcase_06	AC	145 ms 77,160 KB
testcase_07	AC	145 ms 77,432 KB
testcase_08	AC	149 ms 77,488 KB
testcase_09	AC	143 ms 77,228 KB
testcase_10	AC	147 ms 77,784 KB
testcase_11	AC	144 ms 77,788 KB
testcase_12	AC	140 ms 77,124 KB
testcase_13	AC	746 ms 82,608 KB
testcase_14	AC	606 ms 81,836 KB
testcase_15	AC	387 ms 80,460 KB
testcase_16	AC	680 ms 82,668 KB
testcase_17	AC	820 ms 83,088 KB
testcase_18	AC	771 ms 83,720 KB
testcase_19	AC	771 ms 82,704 KB
testcase_20	AC	703 ms 82,432 KB
testcase_21	AC	613 ms 81,452 KB
testcase_22	AC	749 ms 82,696 KB
testcase_23	AC	652 ms 81,900 KB
testcase_24	AC	713 ms 82,200 KB
testcase_25	AC	572 ms 82,020 KB
testcase_26	AC	649 ms 81,940 KB
testcase_27	AC	580 ms 81,764 KB
testcase_28	AC	674 ms 82,096 KB
testcase_29	AC	707 ms 82,212 KB
testcase_30	AC	593 ms 81,744 KB
testcase_31	AC	659 ms 81,836 KB
testcase_32	AC	465 ms 81,248 KB
testcase_33	AC	1,024 ms 82,216 KB
testcase_34	AC	231 ms 81,300 KB
testcase_35	AC	755 ms 82,768 KB
testcase_36	AC	464 ms 82,256 KB
testcase_37	AC	337 ms 80,284 KB
testcase_38	AC	93 ms 76,576 KB
testcase_39	AC	93 ms 76,240 KB
testcase_40	AC	893 ms 82,712 KB
testcase_41	AC	873 ms 82,880 KB

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ソースコード

raw source code

import sys
input = sys.stdin.readline
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
    
    
K, N, M = map(int, input().split())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
G = MinCostFlow(N + 2)
s, g = 0, N + 1
for i in range(M):
    u, v, d = map(int, input().split())
    G.add_edge(u, v, K, d)
    G.add_edge(v, u, K, d)
    
for i in range(K):
    G.add_edge(s, A[i], 1, 0)
for i in range(N):
    G.add_edge(i + 1, g, B[i], 0)
    
print(G.flow(s, g, K)[1])

yukicoder

結果

テストケース

ソースコード