結果

問題 No.2604 Initial Motion
ユーザー ニックネーム
提出日時 2024-01-13 00:31:35
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 2,414 ms / 3,000 ms
コード長 3,534 bytes
コンパイル時間 177 ms
コンパイル使用メモリ 82,416 KB
実行使用メモリ 88,160 KB
最終ジャッジ日時 2024-09-28 00:48:42
合計ジャッジ時間 42,783 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 39
権限があれば一括ダウンロードができます

ソースコード

diff # 

import heapq
class mcf_graph():
    n=1
    pos=[]
    g=[[]]
    def __init__(self,N):
        self.n=N
        self.pos=[]
        self.g=[[] for i in range(N)]
    def add_edge(self,From,To,cap,cost):
        assert 0<=From and From<self.n
        assert 0<=To and To<self.n
        m=len(self.pos)
        self.pos.append((From,len(self.g[From])))
        
        self.g[From].append([To,len(self.g[To]),cap,cost])
        self.g[To].append([From,len(self.g[From])-1,0,-cost])
    def flow(self,s,t,flow_limit=-1-(-1<<63)):
        return self.slope(s,t,flow_limit)[-1]
    def slope(self,s,t,flow_limit=-1-(-1<<63)):
        assert 0<=s and s<self.n
        assert 0<=t and t<self.n
        assert s!=t
        '''
         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
        '''
        dual=[0 for i in range(self.n)]
        dist=[0 for i in range(self.n)]
        pv=[0 for i in range(self.n)]
        pe=[0 for i in range(self.n)]
        vis=[False for i in range(self.n)]
        def dual_ref():
            for i in range(self.n):
                dist[i]=-1-(-1<<63)
                pv[i]=-1
                pe[i]=-1
                vis[i]=False
            que=[]
            heapq.heappush(que,(0,s))
            dist[s]=0
            while(que):
                v=heapq.heappop(que)[1]
                if vis[v]:continue
                vis[v]=True
                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
                '''
                for i in range(len(self.g[v])):
                    e=self.g[v][i]
                    if vis[e[0]] or (not(e[2])):continue
                    '''
                     |-dual[e.to]+dual[v]| <= (n-1)C
                     cost <= C - -(n-1)C + 0 = nC
                    '''
                    cost=e[3]-dual[e[0]]+dual[v]
                    if dist[e[0]]-dist[v]>cost:
                        dist[e[0]]=dist[v]+cost
                        pv[e[0]]=v
                        pe[e[0]]=i
                        heapq.heappush(que,(dist[e[0]],e[0]))
            if not(vis[t]):
                return False
            for v in range(self.n):
                if not(vis[v]):continue
                dual[v]-=dist[t]-dist[v]
            return True
        flow=0
        cost=0
        prev_cost=-1
        result=[(flow,cost)]
        while(flow<flow_limit):
            if not(dual_ref()):
                break
            c=flow_limit-flow
            v=t
            while(v!=s):
                c=min(c,self.g[pv[v]][pe[v]][2])
                v=pv[v]
            v=t
            while(v!=s):
                self.g[pv[v]][pe[v]][2]-=c
                self.g[v][self.g[pv[v]][pe[v]][1]][2]+=c
                v=pv[v]
            d=-dual[s]
            flow+=c
            cost+=c*d
            if(prev_cost==d):
                result.pop()
            result.append((flow,cost))
            prev_cost=cost
        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 = mcf_graph(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])
0