#943541 (PyPy3) No.2604 Initial Motion

• 問題: No.2604 Initial Motion
• ユーザー: ニックネーム
• 提出日時: 2024-01-12 22:30:10
• 言語: PyPy3 (7.3.15)
• 結果: AC
• 実行時間: 851 ms / 3,000 ms
• コード長: 6,488 bytes
• コンパイル時間: 271 ms
• コンパイル使用メモリ: 82,540 KB
• 実行使用メモリ: 82,980 KB
• 最終ジャッジ日時: 2024-09-27 23:05:23
• 合計ジャッジ時間: 15,876 ms
• ジャッジサーバーID （参考情報）: judge3 / judge1

ファイルパターン	結果
sample	AC * 3
other	AC * 39

ソースコード

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# 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
from collections import Counter
k,n,m = map(int,input().split())
a = Counter(map(int,input().split()))
b = list(map(int,input().split()))
g = MinCostFlow(n+2)
for i,v in a.items(): g.add_edge(0,i,v,0)
for i,v in enumerate(b,1): g.add_edge(i,n+1,v,0)
for _ in range(m):
    u,v,d = map(int,input().split())
    g.add_edge(u,v,k,d); g.add_edge(v,u,k,d)
print(g.flow(0,n+1)[1])
 
 
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