QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#338636#5548. Increase the Toll FeesvwxyzTL 901ms96520kbPython320.5kb2024-02-26 05:40:512024-02-26 05:40:52

Judging History

你现在查看的是最新测评结果

  • [2024-02-26 05:40:52]
  • 评测
  • 测评结果:TL
  • 用时:901ms
  • 内存:96520kb
  • [2024-02-26 05:40:51]
  • 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 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

    def Build_LCA(self,s,segment_tree=False):
        self.lca_segment_tree=segment_tree
        if self.lca_segment_tree:
            self.lca_euler_tour,self.lca_parents,depth=self.SIV_DFS(s,euler_tour=True,parents=True,unweighted_dist=True)
            self.lca_dfs_in_index=[None]*self.V
            self.lca_dfs_out_index=[None]*self.V
            for i,x in enumerate(self.lca_euler_tour):
                if x>=0:
                    self.lca_dfs_in_index[x]=i
                else:
                    self.lca_dfs_out_index[~x]=i
            self.ST=Segment_Tree(2*self.V,lambda x,y:min(x,y),self.V)
            lst=[None]*(2*self.V)
            for i in range(2*self.V-1):
                if self.lca_euler_tour[i]>=0:
                    lst[i]=depth[self.lca_euler_tour[i]]
                else:
                    lst[i]=depth[self.lca_parents[~self.lca_euler_tour[i]]]
            lst[2*self.V-1]=-1
            self.ST.Build(lst)
        else:
            self.lca_parents,self.lca_depth=self.SIV_DFS(s,parents=True,unweighted_dist=True)
            self.lca_PD=Path_Doubling(self.V,self.lca_parents)
            self.lca_PD.Build_Next(self.V)

    def LCA(self,a,b):
        if self.lca_segment_tree:
            m=min(self.lca_dfs_in_index[a],self.lca_dfs_in_index[b])
            M=max(self.lca_dfs_in_index[a],self.lca_dfs_in_index[b])
            x=self.lca_euler_tour[self.ST.Fold_Index(m,M+1)]
            if x>=0:
                lca=x
            else:
                lca=self.lca_parents[~x]
        else:
            if self.lca_depth[a]>self.lca_depth[b]:
                a,b=b,a
            b=self.lca_PD.Permutation_Doubling(b,self.lca_depth[b]-self.lca_depth[a])
            if a!=b:
                for k in range(self.lca_PD.k-1,-1,-1):
                    if self.lca_PD.permutation_doubling[k][a]!=self.lca_PD.permutation_doubling[k][b]:
                        a,b=self.lca_PD.permutation_doubling[k][a],self.lca_PD.permutation_doubling[k][b]
                a,b=self.lca_PD.permutation_doubling[0][a],self.lca_PD.permutation_doubling[0][b]
            lca=a
        return lca

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())))

class Path_Doubling:
    def __init__(self,N,permutation,lst=None,f=None,e=None):
        self.N=N
        self.permutation=permutation
        self.lst=lst
        self.f=f
        self.e=e

    def Build_Next(self,K=None):
        if K==None:
            K=self.N
        self.k=K.bit_length()
        self.permutation_doubling=[[None]*self.N for k in range(self.k)]
        for n in range(self.N):
            self.permutation_doubling[0][n]=self.permutation[n]
        if self.lst!=None:
            self.doubling=[[self.e]*self.N for k in range(self.k)]
            for n in range(self.N):
                self.doubling[0][n]=self.lst[n]
        for k in range(1,self.k):
            for n in range(self.N):
                if self.permutation_doubling[k-1][n]!=None:
                    self.permutation_doubling[k][n]=self.permutation_doubling[k-1][self.permutation_doubling[k-1][n]]
                    if self.f!=None:
                        self.doubling[k][n]=self.f(self.doubling[k-1][n],self.doubling[k-1][self.permutation_doubling[k-1][n]])

    def Permutation_Doubling(self,N,K):
        if K<0 or 1<<self.k<=K:
            return None
        for k in range(self.k):
            if K>>k&1 and N!=None:
                N=self.permutation_doubling[k][N]
        return N

    def Doubling(self,N,K):
        if K<0:
            return self.e
        retu=self.e
        for k in range(self.k):
            if K>>k&1:
                if self.permutation_doubling[k][N]==None:
                    return None
                retu=self.f(retu,self.doubling[k][N])
                N=self.permutation_doubling[k][N]
        return N,retu

    def Bisect(self,x,is_ok):
        if not is_ok(x):
            return -1,None
        K=0
        for k in range(self.k-1,-1,-1):
            if is_ok(self.permutation_doubling[k][x]):
                K|=1<<k
                x=self.permutation_doubling[k][x]
        return K,x

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_LCA(0)
    depth=T1.lca_depth
    parents=[0]+T1.lca_parents[1:]
    inf=1<<30
    lst=[-inf]*N
    for u in range(N):
        for v,w in T1.graph[u]:
            if v==parents[u]:
                continue
            lst[v]=w
    PD=Path_Doubling(N,permutation=parents,lst=lst,f=max,e=-inf)
    PD.Build_Next()
    ans=0
    for u,v,w in T0:
        lca=T1.LCA(u,v)
        ma=max(PD.Doubling(u,depth[u]-depth[lca])[1],PD.Doubling(v,depth[v]-depth[lca])[1])
        ans+=ma+1-w

print(ans)

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 5ms
memory: 10244kb

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: 12ms
memory: 10168kb

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: 6ms
memory: 10156kb

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: 6ms
memory: 10384kb

input:

2 1
1 2 1

output:

-1

result:

ok single line: '-1'

Test #5:

score: 0
Accepted
time: 756ms
memory: 62472kb

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: 0
Accepted
time: 901ms
memory: 96520kb

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:

ok single line: '-1'

Test #7:

score: 0
Accepted
time: 712ms
memory: 46248kb

input:

28825 57648
9446 22014 286256842
14902 20222 14175
3246 20218 80493268
1783 13768 931622563
11107 24862 918832025
25070 27312 98899079
8535 20222 16037
9184 17491 294248461
8799 17834 456827944
1152 11687 960740527
17849 23045 9706
5774 21436 444202963
5417 23045 3092
20222 20370 11232
16585 20222 1...

output:

28822649262260

result:

ok single line: '28822649262260'

Test #8:

score: -100
Time Limit Exceeded

input:

22253 200000
46 10310 674985053
2403 19582 788128238
5203 7897 985236456
2709 9034 824557880
14337 20524 230824854
19901 22177 99959362
5067 8568 570267383
13707 21474 610729058
7494 7860 109319713
14473 16182 794578653
21 17055 852110939
19320 21640 844993191
2443 21673 170358534
5941 9705 16465049...

output:

3270266304988

result: