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ID题目提交者结果用时内存语言文件大小提交时间测评时间
#338627#5548. Increase the Toll FeesvwxyzTL 899ms54944kbPython318.6kb2024-02-26 05:02:102024-02-26 05:02:10

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你现在查看的是最新测评结果

  • [2024-02-26 05:02:10]
  • 评测
  • 测评结果:TL
  • 用时:899ms
  • 内存:54944kb
  • [2024-02-26 05:02:10]
  • 提交

answer

from collections import defaultdict

class Graph:
    def __init__(self,V,edges=None,graph=None,directed=False,weighted=False,inf=float("inf")):
        self.V=V
        self.directed=directed
        self.weighted=weighted
        self.inf=inf
        if graph!=None:
            self.graph=graph
            """
            self.edges=[]
            for i in range(self.V):
                if self.weighted:
                    for j,d in self.graph[i]:
                        if self.directed or not self.directed and i<=j:
                            self.edges.append((i,j,d))
                else:
                    for j in self.graph[i]:
                        if self.directed or not self.directed and i<=j:
                            self.edges.append((i,j))
            """
        else:
            self.edges=edges
            self.graph=[[] for i in range(self.V)]
            if weighted:
                for i,j,d in self.edges:
                    self.graph[i].append((j,d))
                    if not self.directed:
                        self.graph[j].append((i,d))
            else:
                for i,j in self.edges:
                    self.graph[i].append(j)
                    if not self.directed:
                        self.graph[j].append(i)

    def Build_HLD(self,s):
        self.hld_parents,size,self.hld_depth=self.SIV_DFS(s,parents=True,subtree_size=True,unweighted_dist=True)
        stack=[s]
        self.hld_tour=[]
        self.hld_path_parents=[None]*self.V
        self.hld_path_parents[s]=s
        while stack:
            x=stack.pop()
            self.hld_tour.append(x)
            max_size=0
            max_size_y=None
            for y in self.graph[x]:
                if self.weighted:
                    y,d=y
                if y==self.hld_parents[x]:
                    continue
                if max_size<size[y]:
                    max_size=size[y]
                    max_size_y=y
            for y in self.graph[x]:
                if self.weighted:
                    y,d=y
                if y==self.hld_parents[x]:
                    continue
                if y!=max_size_y:
                    stack.append(y)
                    self.hld_path_parents[y]=y
            if max_size_y!=None:
                stack.append(max_size_y)
                self.hld_path_parents[max_size_y]=self.hld_path_parents[x]
        self.hld_tour_idx=[None]*self.V
        for i in range(self.V):
            self.hld_tour_idx[self.hld_tour[i]]=i

    def HLD(self,a,b,edge=False):
        L,R=[],[]
        while self.hld_path_parents[a]!=self.hld_path_parents[b]:
            if self.hld_depth[self.hld_path_parents[a]]<self.hld_depth[self.hld_path_parents[b]]:
                R.append((self.hld_tour_idx[self.hld_path_parents[b]],self.hld_tour_idx[b]+1))
                b=self.hld_parents[self.hld_path_parents[b]]
            else:
                L.append((self.hld_tour_idx[a]+1,self.hld_tour_idx[self.hld_path_parents[a]]))
                a=self.hld_parents[self.hld_path_parents[a]]
        if edge:
            if self.hld_depth[a]!=self.hld_depth[b]:
                retu=L+[(self.hld_tour_idx[a]+1,self.hld_tour_idx[b]+1)]+R[::-1]
            else:
                retu=L+R[::-1]
        else:
            if self.hld_depth[a]<self.hld_depth[b]:
                retu=L+[(self.hld_tour_idx[a],self.hld_tour_idx[b]+1)]+R[::-1]
            else:
                retu=L+[(self.hld_tour_idx[a]+1,self.hld_tour_idx[b])]+R[::-1]
        return retu

    def Kruskal(self,maximize=False,spanning_tree=False):
        UF=UnionFind(self.V)
        sorted_edges=sorted(self.edges if self.weighted else [(x,y,1) for x,y in self.edges],key=lambda tpl:tpl[2],reverse=maximize)
        if spanning_tree:
            st=[]
        else:
            cost=0
        for x,y,d in sorted_edges:
            if not UF.Same(x,y):
                UF.Union(x,y)
                if spanning_tree:
                    st.append((x,y,d))
                else:
                    cost+=d
        return st if spanning_tree else cost

    def SIV_DFS(self,s,bipartite_graph=False,cycle_detection=False,directed_acyclic=False,euler_tour=False,linked_components=False,lowlink=False,parents=False,postorder=False,preorder=False,subtree_size=False,topological_sort=False,unweighted_dist=False,weighted_dist=False):
        seen=[False]*self.V
        finished=[False]*self.V
        if directed_acyclic or cycle_detection or topological_sort:
            dag=True
        if euler_tour:
            et=[]
        if linked_components:
            lc=[]
        if lowlink:
            order=[None]*self.V
            ll=[None]*self.V
            idx=0
        if parents or cycle_detection or lowlink or subtree_size:
            ps=[None]*self.V
        if postorder or topological_sort:
            post=[]
        if preorder:
            pre=[]
        if subtree_size:
            ss=[1]*self.V
        if unweighted_dist or bipartite_graph:
            uwd=[self.inf]*self.V
            uwd[s]=0
        if weighted_dist:
            wd=[self.inf]*self.V
            wd[s]=0
        stack=[(s,0)] if self.weighted else [s]
        while stack:
            if self.weighted:
                x,d=stack.pop()
            else:
                x=stack.pop()
            if not seen[x]:
                seen[x]=True
                stack.append((x,d) if self.weighted else x)
                if euler_tour:
                    et.append(x)
                if linked_components:
                    lc.append(x)
                if lowlink:
                    order[x]=idx
                    ll[x]=idx
                    idx+=1
                if preorder:
                    pre.append(x)
                for y in self.graph[x]:
                    if self.weighted:
                        y,d=y
                    if not seen[y]:
                        stack.append((y,d) if self.weighted else y)
                        if parents or cycle_detection or lowlink or subtree_size:
                            ps[y]=x
                        if unweighted_dist or bipartite_graph:
                            uwd[y]=uwd[x]+1
                        if weighted_dist:
                            wd[y]=wd[x]+d
                    elif not finished[y]:
                        if (directed_acyclic or cycle_detection or topological_sort) and dag:
                            dag=False
                            if cycle_detection:
                                cd=(y,x)
            elif not finished[x]:
                finished[x]=True
                if euler_tour:
                    et.append(~x)
                if lowlink:
                    bl=True
                    for y in self.graph[x]:
                        if self.weighted:
                            y,d=y
                        if ps[x]==y and bl:
                            bl=False
                            continue
                        ll[x]=min(ll[x],order[y])
                    if x!=s:
                        ll[ps[x]]=min(ll[ps[x]],ll[x])
                if postorder or topological_sort:
                    post.append(x)
                if subtree_size:
                    for y in self.graph[x]:
                        if self.weighted:
                            y,d=y
                        if y==ps[x]:
                            continue
                        ss[x]+=ss[y]
        if bipartite_graph:
            bg=[[],[]]
            for tpl in self.edges:
                x,y=tpl[:2] if self.weighted else tpl
                if uwd[x]==self.inf or uwd[y]==self.inf:
                    continue
                if not uwd[x]%2^uwd[y]%2:
                    bg=False
                    break
            else:
                for x in range(self.V):
                    if uwd[x]==self.inf:
                        continue
                    bg[uwd[x]%2].append(x)
        retu=()
        if bipartite_graph:
            retu+=(bg,)
        if cycle_detection:
            if dag:
                cd=[]
            else:
                y,x=cd
                cd=self.Route_Restoration(y,x,ps)
            retu+=(cd,)
        if directed_acyclic:
            retu+=(dag,)
        if euler_tour:
            retu+=(et,)
        if linked_components:
            retu+=(lc,)
        if lowlink:
            retu=(ll,)
        if parents:
            retu+=(ps,)
        if postorder:
            retu+=(post,)
        if preorder:
            retu+=(pre,)
        if subtree_size:
            retu+=(ss,)
        if topological_sort:
            if dag:
                tp_sort=post[::-1]
            else:
                tp_sort=[]
            retu+=(tp_sort,)
        if unweighted_dist:
            retu+=(uwd,)
        if weighted_dist:
            retu+=(wd,)
        if len(retu)==1:
            retu=retu[0]
        return retu

class Segment_Tree:
    def __init__(self,N,f,e,lst=None,dynamic=False):
        self.f=f
        self.e=e
        self.N=N
        if dynamic:
            self.segment_tree=defaultdict(lambda:self.e)
        else:
            if lst==None:
                self.segment_tree=[self.e]*2*self.N
            else:
                assert len(lst)<=self.N
                self.segment_tree=[self.e]*self.N+[x for x in lst]+[self.e]*(N-len(lst))
                for i in range(self.N-1,0,-1):
                    self.segment_tree[i]=self.f(self.segment_tree[i<<1],self.segment_tree[i<<1|1])

    def __getitem__(self,i):
        if type(i)==int:
            if -self.N<=i<0:
                return self.segment_tree[i+self.N*2]
            elif 0<=i<self.N:
                return self.segment_tree[i+self.N]
            else:
                raise IndexError("list index out of range")
        else:
            a,b,c=i.start,i.stop,i.step
            if a==None:
                a=self.N
            else:
                a+=self.N
            if b==None:
                b=self.N*2
            else:
                b+=self.N
            return self.segment_tree[slice(a,b,c)]

    def __setitem__(self,i,x):
        if -self.N<=i<0:
            i+=self.N*2
        elif 0<=i<self.N:
            i+=self.N
        else:
            raise IndexError("list index out of range")
        self.segment_tree[i]=x
        while i>1:
            i>>= 1
            self.segment_tree[i]=self.f(self.segment_tree[i<<1],self.segment_tree[i<<1|1])

    def Build(self,lst):
        for i,x in enumerate(lst,self.N):
            self.segment_tree[i]=x
        for i in range(self.N-1,0,-1):
            self.segment_tree[i]=self.f(self.segment_tree[i<<1],self.segment_tree[i<<1|1])

    def Fold(self,L=None,R=None):
        if L==None:
            L=self.N
        else:
            L+=self.N
        if R==None:
            R=self.N*2
        else:
            R+=self.N
        vL=self.e
        vR=self.e
        while L<R:
            if L&1:
                vL=self.f(vL,self.segment_tree[L])
                L+=1
            if R&1:
                R-=1
                vR=self.f(self.segment_tree[R],vR)
            L>>=1
            R>>=1
        return self.f(vL,vR)

    def Fold_Index(self,L=None,R=None):
        if L==None:
            L=self.N
        else:
            L+=self.N
        if R==None:
            R=self.N*2
        else:
            R+=self.N
        if L==R:
            return None
        x=self.Fold(L-self.N,R-self.N)
        while L<R:
            if L&1:
                if self.segment_tree[L]==x:
                    i=L
                    break
                L+=1
            if R&1:
                R-=1
                if self.segment_tree[R]==x:
                    i=R
                    break
            L>>=1
            R>>=1
        while i<self.N:
            if self.segment_tree[i]==self.segment_tree[i<<1]:
                i<<=1
            else:
                i<<=1
                i|=1
        i-=self.N
        return i

    def Bisect_Right(self,L=None,f=None):
        if L==self.N:
            return self.N
        if L==None:
            L=0
        L+=self.N
        vl=self.e
        vr=self.e
        l,r=L,self.N*2
        while l<r:
            if l&1:
                vl=self.f(vl,self.segment_tree[l])
                l+=1
            if r&1:
                r-=1
                vr=self.f(self.segment_tree[r],vr)
            l>>=1
            r>>=1
        if f(self.f(vl,vr)):
            return self.N
        v=self.e
        while True:
            while L%2==0:
                L>>=1
            vv=self.f(v,self.segment_tree[L])
            if f(vv):
                v=vv
                L+=1
            else:
                while L<self.N:
                    L<<=1
                    vv=self.f(v,self.segment_tree[L])
                    if f(vv):
                        v=vv
                        L+=1
                return L-self.N

    def Bisect_Left(self,R=None,f=None):
        if R==0:
            return 0
        if R==None:
            R=self.N
        R+=self.N
        vl=self.e
        vr=self.e
        l,r=self.N,R
        while l<r:
            if l&1:
                vl=self.f(vl,self.segment_tree[l])
                l+=1
            if r&1:
                r-=1
                vr=self.f(self.segment_tree[r],vr)
            l>>=1
            r>>=1
        if f(self.f(vl,vr)):
            return 0
        v=self.e
        while True:
            R-=1
            while R>1 and R%2:
                R>>=1
            vv=self.f(self.segment_tree[R],v)
            if f(vv):
                v=vv
            else:
                while R<self.N:
                    R=2*R+1
                    vv=self.f(self.segment_tree[R],v)
                    if f(vv):
                        v=vv
                        R-=1
                return R+1-self.N

    def __str__(self):
        return "["+", ".join(map(str,self.segment_tree[self.N:]))+"]"

class UnionFind:
    def __init__(self,N,label=None,f=None,weighted=False,rollback=False):
        self.N=N
        self.parents=[None]*self.N
        self.size=[1]*self.N
        self.roots={i for i in range(self.N)}
        self.label=label
        if self.label!=None:
            self.label=[x for x in label]
        self.f=f
        self.weighted=weighted
        if self.weighted:
            self.weight=[0]*self.N
        self.rollback=rollback
        if self.rollback:
            self.operate_list=[]
            self.operate_set=[]

    def Find(self,x):
        stack=[]
        while self.parents[x]!=None:
            stack.append(x)
            x=self.parents[x]
        if not self.rollback:
            if self.weighted:
                w=0
                for y in stack[::-1]:
                    self.parents[y]=x
                    w+=self.weight[y]
                    self.weight[y]=w
            else:
                for y in stack[::-1]:
                    self.parents[y]=x
        return x

    def Union(self,x,y,w=None):
        root_x=self.Find(x)
        root_y=self.Find(y)
        if self.rollback:
            self.operate_list.append([])
            self.operate_set.append([])
        if root_x==root_y:
            if self.weighted:
                if self.weight[y]-self.weight[x]==w:
                    return True
                else:
                    return False
        else:
            if self.size[root_x]<self.size[root_y]:
                x,y=y,x
                root_x,root_y=root_y,root_x
                if self.weighted:
                    w=-w
            if self.rollback:
                self.operate_list[-1].append((self.parents,root_y,self.parents[root_y]))
                self.operate_list[-1].append((self.size,root_x,self.size[root_x]))
                self.operate_set[-1].append(root_y)
                if self.label!=None:
                    self.operate_list[-1]((self.label,root_x,self.label[root_x]))
                if self.weighted:
                    self.operate_list[-1].append((self.weight,root_y,self.weight[root_y]))
            self.parents[root_y]=root_x
            self.size[root_x]+=self.size[root_y]
            self.roots.remove(root_y)
            if self.label!=None:
                self.label[root_x]=self.f(self.label[root_x],self.label[root_y])
            if self.weighted:
                self.weight[root_y]=w+self.weight[x]-self.weight[y]

    def Size(self,x):
        return self.size[self.Find(x)]

    def Same(self,x,y):
        return self.Find(x)==self.Find(y)

    def Label(self,x):
        return self.label[self.Find(x)]

    def Weight(self,x,y):
        root_x=self.Find(x)
        root_y=self.Find(y)
        if root_x!=root_y:
            return None
        return self.weight[y]-self.weight[x]

    def Roots(self):
        return list(self.roots)

    def Linked_Components_Count(self):
        return len(self.roots)

    def Linked_Components(self):
        linked_components=defaultdict(list)
        for x in range(self.N):
            linked_components[self.Find(x)].append(x)
        return linked_components

    def Rollback(self):
        assert self.rollback
        if self.operate_list:
            for lst,x,v in self.operate_list.pop():
                lst[x]=v
            for x in self.operate_set.pop():
                self.roots.add(x)            
            return True
        else:
            return False

    def __str__(self):
        linked_components=defaultdict(list)
        for x in range(self.N):
            linked_components[self.Find(x)].append(x)
        return "\n".join(f"{r}: {linked_components[r]}" for r in sorted(list(linked_components.keys())))

N,M=map(int,input().split())
edges=[]
for m in range(M):
    u,v,w=map(int,input().split())
    u-=1;v-=1
    edges.append((u,v,w))

T0=Graph(N,edges=edges,weighted=True).Kruskal(spanning_tree=True)
set_T0=set(T0)
T1=Graph(N,edges=[(u,v,w) for u,v,w in edges if not(u,v,w) in set_T0],weighted=True).Kruskal(spanning_tree=True)
if len(T1)<N-1:
    ans=-1
else:
    T1=Graph(N,edges=T1,weighted=True)
    T1.Build_HLD(0)
    inf=1<<30
    ST=[-inf]*N
    for u in range(N):
        for v,w in T1.graph[u]:
            if v==T1.hld_parents[u]:
                continue
            ST[T1.hld_tour_idx[v]]=w
    ST=Segment_Tree(N,max,-inf,ST)
    ans=0
    for u,v,w in T0:
        ma=-inf
        for a,b in T1.HLD(u,v,edge=True):
            if a>b:
                a,b=b,a
            ma=max(ma,ST.Fold(a,b))
        ans+=ma+1-w
print(ans)        

详细

Test #1:

score: 100
Accepted
time: 14ms
memory: 10336kb

input:

4 6
1 2 2
1 3 5
1 4 5
2 3 3
2 4 5
3 4 4

output:

9

result:

ok single line: '9'

Test #2:

score: 0
Accepted
time: 14ms
memory: 10352kb

input:

3 4
1 2 3
2 3 4
1 3 5
1 3 10

output:

-1

result:

ok single line: '-1'

Test #3:

score: 0
Accepted
time: 9ms
memory: 10444kb

input:

5 10
1 2 14
1 3 14
1 4 9
1 5 15
2 3 8
2 3 10
2 4 13
3 4 8
4 5 10
4 5 15

output:

21

result:

ok single line: '21'

Test #4:

score: 0
Accepted
time: 14ms
memory: 10484kb

input:

2 1
1 2 1

output:

-1

result:

ok single line: '-1'

Test #5:

score: 0
Accepted
time: 899ms
memory: 54944kb

input:

29171 100000
7223 21138 270743473
5598 27967 847631606
12666 26050 847631606
75 15747 270743473
8522 12955 847631606
6069 23750 270743473
18708 22605 847631606
16814 22169 847631606
11550 27119 847631606
562 15959 847631606
9400 11110 270743473
15325 23805 270743473
19169 24404 270743473
6649 12062 ...

output:

16827826868780

result:

ok single line: '16827826868780'

Test #6:

score: -100
Time Limit Exceeded

input:

47977 200000
10970 47321 440845807
1166 29708 767952745
319 37520 546280762
17581 29425 558321466
22079 26884 344816304
7479 44260 791002634
14685 44163 837529020
1537 10359 330017953
8634 27064 969738917
32950 37192 728271930
34751 42782 63025978
32540 34226 86057211
36786 46050 826927874
30444 436...

output:

-1

result: