結果

問題 No.828 全方位神童数
ユーザー vwxyzvwxyz
提出日時 2024-04-08 08:39:28
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 841 ms / 2,000 ms
コード長 10,493 bytes
コンパイル時間 373 ms
コンパイル使用メモリ 82,304 KB
実行使用メモリ 174,356 KB
最終ジャッジ日時 2024-10-01 04:59:42
合計ジャッジ時間 23,212 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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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 41 ms
55,936 KB
testcase_01 AC 42 ms
56,064 KB
testcase_02 AC 43 ms
56,380 KB
testcase_03 AC 219 ms
82,316 KB
testcase_04 AC 149 ms
79,052 KB
testcase_05 AC 194 ms
81,796 KB
testcase_06 AC 135 ms
78,556 KB
testcase_07 AC 125 ms
78,396 KB
testcase_08 AC 141 ms
78,916 KB
testcase_09 AC 89 ms
76,800 KB
testcase_10 AC 204 ms
81,220 KB
testcase_11 AC 89 ms
76,928 KB
testcase_12 AC 218 ms
81,528 KB
testcase_13 AC 389 ms
108,560 KB
testcase_14 AC 642 ms
151,572 KB
testcase_15 AC 338 ms
101,380 KB
testcase_16 AC 394 ms
110,324 KB
testcase_17 AC 361 ms
104,064 KB
testcase_18 AC 499 ms
125,572 KB
testcase_19 AC 795 ms
170,364 KB
testcase_20 AC 577 ms
130,972 KB
testcase_21 AC 706 ms
153,620 KB
testcase_22 AC 288 ms
94,008 KB
testcase_23 AC 208 ms
82,052 KB
testcase_24 AC 479 ms
117,624 KB
testcase_25 AC 319 ms
94,900 KB
testcase_26 AC 734 ms
162,316 KB
testcase_27 AC 660 ms
152,200 KB
testcase_28 AC 733 ms
161,636 KB
testcase_29 AC 704 ms
155,316 KB
testcase_30 AC 462 ms
119,592 KB
testcase_31 AC 459 ms
117,816 KB
testcase_32 AC 765 ms
161,344 KB
testcase_33 AC 831 ms
169,720 KB
testcase_34 AC 654 ms
150,544 KB
testcase_35 AC 484 ms
119,724 KB
testcase_36 AC 572 ms
133,488 KB
testcase_37 AC 431 ms
115,012 KB
testcase_38 AC 549 ms
127,984 KB
testcase_39 AC 758 ms
161,132 KB
testcase_40 AC 436 ms
112,928 KB
testcase_41 AC 401 ms
109,348 KB
testcase_42 AC 841 ms
174,356 KB
testcase_43 AC 419 ms
171,424 KB
testcase_44 AC 220 ms
101,552 KB
testcase_45 AC 297 ms
125,564 KB
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 # 

from collections import defaultdict

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 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 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

N=int(input())
R=list(map(int,input().split()))
graph=[[] for x in range(N)]
for i in range(N-1):
    u,v=map(int,input().split())
    u-=1;v-=1
    if u>v:
        u,v=v,u
    graph[v].append(u)
cnt=[0]*N
UF=UnionFind(N,label=[x for x in range(N)],f=max)
edges=[]
for x in range(N):
    for y in graph[x]:
        edges.append((UF.Label(x),UF.Label(y)))
        UF.Union(x,y)
    cnt[UF.Label(x)]+=1
G=Graph(N,edges=edges)
parents,tour=G.SIV_DFS(UF.Label(N-1),parents=True,preorder=True)
for x in tour:
    for y in G.graph[x]:
        if y==parents[x]:
            continue
        cnt[y]+=cnt[x]
ans=1
mod=10**9+7
for x in range(N):
    ans*=R[x]+cnt[x]
    ans%=mod
print(ans)
0