【算法总结】树相关

 1 void getroot(int x,int fa)
 2 {
 3     sz[x]=1;mx[x]=0;
 4     for(int i=first[x];i;i=e[i].next)
 5     {
 6         int to=e[i].to;
 7         if(to==fa||vis[to])continue;
 8         getroot(to,x);
 9         sz[x]+=sz[to];
10         mx[x]=max(mx[x],sz[to]);
11     }
12     mx[x]=max(mx[x],sum-sz[x]);
13     if(mx[root]>mx[x])root=x;
14 }
15 void getdeep(int x,int fa)
16 {
17     d[++tot]=deep[x];
18     for(int i=first[x];i;i=e[i].next)
19     {
20         int to=e[i].to;
21         if(to==fa||vis[to])continue;
22         deep[to]=deep[x]+e[i].w;
23         getdeep(to,x);
24     }
25 }
26 int calc(int x)
27 {
28     tot=0;getdeep(x,-1);
29     sort(d+1,d+tot+1);
30     int ans=0,i=1,j=tot;
31     while(i<j)
32     {
33         if(d[i]+d[j]<=K)ans+=j-i,i++;
34         else j--;
35     }
36     return ans;
37 }
38 void dfs(int x)
39 {
40     deep[x]=0;vis[x]=true;ans+=calc(x);
41     for(int i=first[x];i;i=e[i].next)
42     {
43         int to=e[i].to;
44         if(vis[to])continue;
45         deep[to]=e[i].w;
46         ans-=calc(to);
47         sum=sz[to];root=0;
48         getroot(to,-1);dfs(root);
49     }
50 }
51 int main()
52 {
53     root=0;sum=n;mx[0]=inf;
54     getroot(1,-1);dfs(root);
55     printf("%d\n",ans);
56 }

 1 #include<cstdio>
 2 #include<algorithm>
 3 #include<cstring>
 4 using namespace std;
 5 const int N=1e4+5;
 6 const int inf=0x3f3f3f3f;
 7 int n,K,cnt,x,y,w,root,sum,ans,tot;
 8 int sz[N],mx[N],first[N],deep[N],d[N];
 9 bool vis[N];
10 struct edge{int to,next,w;}e[N<<1];
11 int read()
12 {
13     int x=0,f=1;char c=getchar();
14     while(c<‘0‘||c>‘9‘){if(c==‘-‘)f=-1;c=getchar();}
15     while(c>=‘0‘&&c<=‘9‘){x=x*10+c-‘0‘;c=getchar();}
16     return x*f;
17 }
18 void ins(int u,int v,int w){e[++cnt]=(edge){v,first[u],w};first[u]=cnt;}
19 void getroot(int x,int fa)
20 {
21     sz[x]=1;mx[x]=0;
22     for(int i=first[x];i;i=e[i].next)
23     {
24         int to=e[i].to;
25         if(to==fa||vis[to])continue;
26         getroot(to,x);
27         sz[x]+=sz[to];
28         mx[x]=max(mx[x],sz[to]);
29     }
30     mx[x]=max(mx[x],sum-sz[x]);
31     if(mx[root]>mx[x])root=x;
32 }
33 void getdeep(int x,int fa)
34 {
35     d[++tot]=deep[x];
36     for(int i=first[x];i;i=e[i].next)
37     {
38         int to=e[i].to;
39         if(to==fa||vis[to])continue;
40         deep[to]=deep[x]+e[i].w;
41         getdeep(to,x);
42     }
43 }
44 int calc(int x)
45 {
46     tot=0;getdeep(x,-1);
47     sort(d+1,d+tot+1);
48     int ans=0,i=1,j=tot;
49     while(i<j)
50     {
51         if(d[i]+d[j]<=K)ans+=j-i,i++;
52         else j--;
53     }
54     return ans;
55 }
56 void dfs(int x)
57 {
58     deep[x]=0;vis[x]=true;ans+=calc(x);
59     for(int i=first[x];i;i=e[i].next)
60     {
61         int to=e[i].to;
62         if(vis[to])continue;
63         deep[to]=e[i].w;
64         ans-=calc(to);
65         sum=sz[to];root=0;
66         getroot(to,-1);dfs(root);
67     }
68 }
69 int main()
70 {
71     n=read();K=read();
72     while(n||K)
73     {
74         cnt=0;ans=0;
75         memset(first,0,sizeof(first));
76         memset(vis,0,sizeof(vis));
77         for(int i=1;i<n;i++)
78         {
79             x=read();y=read();w=read();
80             ins(x,y,w);ins(y,x,w);
81         }
82         root=0;sum=n;mx[0]=inf;
83         getroot(1,-1);dfs(root);
84         printf("%d\n",ans);
85         n=read();K=read();
86     }
87     return 0;
88 }

 1 #include<cstdio>
 2 #include<algorithm>
 3 #include<cstring>
 4 using namespace std;
 5 const int N=2e4+5;
 6 const int inf=0x3f3f3f3f;
 7 int n,cnt,x,y,w,root,sum,ans;
 8 int t[3],first[N],mx[N],sz[N],deep[N];
 9 bool vis[N];
10 struct edge{int to,next,w;}e[N<<1];
11 int read()
12 {
13     int x=0,f=1;char c=getchar();
14     while(c<‘0‘||c>‘9‘){if(c==‘-‘)f=-1;c=getchar();}
15     while(c>=‘0‘&&c<=‘9‘){x=x*10+c-‘0‘;c=getchar();}
16     return x*f;
17 }
18 void ins(int u,int v,int w){e[++cnt]=(edge){v,first[u],w};first[u]=cnt;}
19 void getroot(int x,int fa)
20 {
21     sz[x]=1;mx[x]=0;
22     for(int i=first[x];i;i=e[i].next)
23     {
24         int to=e[i].to;
25         if(to==fa||vis[to])continue;
26         getroot(to,x);
27         sz[x]+=sz[to];
28         mx[x]=max(mx[x],sz[to]);
29     }
30     mx[x]=max(mx[x],sum-sz[x]);
31     if(mx[root]>mx[x])root=x;
32 }
33 void getdeep(int x,int fa)
34 {
35     t[deep[x]]++;
36     for(int i=first[x];i;i=e[i].next)
37     {
38         int to=e[i].to;
39         if(to==fa||vis[to])continue;
40         deep[to]=(deep[x]+e[i].w)%3;
41         getdeep(to,x);
42     }
43 }
44 int calc(int x)
45 {
46     t[0]=t[1]=t[2]=0;getdeep(x,-1);
47     return t[1]*t[2]*2+t[0]*t[0];
48 }
49 void dfs(int x)
50 {
51     deep[x]=0;vis[x]=true;ans+=calc(x);
52     for(int i=first[x];i;i=e[i].next)
53     {
54         int to=e[i].to;
55         if(vis[to])continue;
56         deep[to]=e[i].w;
57         ans-=calc(to);
58         sum=sz[to];root=0;
59         getroot(to,-1);dfs(root);
60     }
61 }
62 int gcd(int a,int b){return !b?a:gcd(b,a%b);}
63 int main()
64 {
65     n=read();
66     for(int i=1;i<n;i++)
67     {
68         x=read();y=read();w=read()%3;
69         ins(x,y,w);ins(y,x,w);
70     }
71     root=0;sum=n;mx[0]=inf;
72     getroot(1,-1);dfs(root);
73     int g=gcd(ans,n*n);
74     printf("%d/%d\n",ans/g,n*n/g);
75     return 0;
76 }

 1 #include<cstdio>
 2 #include<algorithm>
 3 #include<cstring>
 4 using namespace std;
 5 const int N=2e5+5;
 6 const int inf=0x3f3f3f3f;
 7 int n,K,cnt,x,y,w,root,sum,ans,froot;
 8 int first[N],sz[N],deep[N],dis[N],t[N*5];
 9 bool vis[N];
10 struct edge{int to,next,w;}e[N<<1];
11 int read()
12 {
13     int x=0,f=1;char c=getchar();
14     while(c<‘0‘||c>‘9‘){if(c==‘-‘)f=-1;c=getchar();}
15     while(c>=‘0‘&&c<=‘9‘){x=x*10+c-‘0‘;c=getchar();}
16     return x*f;
17 }
18 void ins(int u,int v,int w){e[++cnt]=(edge){v,first[u],w};first[u]=cnt;}
19 void getroot(int x,int fa)
20 {
21     bool flag=true;sz[x]=1;
22     for(int i=first[x];i;i=e[i].next)
23     {
24         int to=e[i].to;
25         if(to==fa||vis[to])continue;
26         getroot(to,x);
27         sz[x]+=sz[to];
28         if(sz[to]>sum/2)flag=false;
29     }
30     if(sum-sz[x]>sum/2)flag=false;
31     if(flag)root=x,froot=fa;
32 }
33 void getdeep(int x,int fa)
34 {
35     if(dis[x]<=K)ans=min(ans,deep[x]+t[K-dis[x]]);
36     for(int i=first[x];i;i=e[i].next)
37     {
38         int to=e[i].to;
39         if(to==fa||vis[to])continue;
40         dis[to]=dis[x]+e[i].w;
41         deep[to]=deep[x]+1;
42         getdeep(to,x);
43     }
44 }
45 void check(int x,int fa,int flag)
46 {
47     if(dis[x]<=K)
48     {
49         if(flag)t[dis[x]]=min(t[dis[x]],deep[x]);
50         else t[dis[x]]=n;
51     }
52     for(int i=first[x];i;i=e[i].next)
53     {
54         int to=e[i].to;
55         if(to==fa||vis[to])continue;
56         check(to,x,flag);
57     }
58 }
59 void dfs(int x,int s,int fa)
60 {
61     vis[x]=true;dis[x]=deep[x]=0;t[0]=0;
62     for(int i=first[x];i;i=e[i].next)
63     {
64         int to=e[i].to;
65         if(vis[to])continue;
66         deep[to]=1;dis[to]=e[i].w;
67         getdeep(to,x);check(to,x,1);
68     }
69     for(int i=first[x];i;i=e[i].next)
70     {
71         int to=e[i].to;
72         if(vis[to])continue;
73         check(to,x,0);
74     }
75     for(int i=first[x];i;i=e[i].next)
76     {
77         int to=e[i].to;
78         if(vis[to])continue;
79         if(to==fa)sum=s-sz[x];
80         else sum=sz[to];
81         root=0;getroot(to,x);
82         dfs(root,sum,froot);
83     }
84 }
85 int main()
86 {
87     n=read();K=read();
88     for(int i=1;i<=K;i++)t[i]=n;
89     for(int i=1;i<n;i++)
90     {
91         x=read()+1;y=read()+1;w=read();
92         ins(x,y,w);ins(y,x,w);
93     }
94     root=0;sum=n;ans=n;
95     getroot(1,-1);dfs(root,n,froot);
96     if(ans==n)printf("-1\n");
97     else printf("%d\n",ans);
98     return 0;
99 }

 1 #include<cstdio>
 2 #include<algorithm>
 3 #include<cstring>
 4 #define LL long long
 5 using namespace std;
 6 const int N=1e5+5;
 7 const int base=1e5;
 8 const int inf=0x3f3f3f3f;
 9 int n,cnt,x,y,w,sum,root,d;
10 int first[N],sz[N],mx[N],dep[N];
11 int s[N<<1],f[N<<1][2],g[N<<1][2];
12 LL ans;
13 bool vis[N];
14 struct edge{int to,next,w;}e[N<<1];
15 int read()
16 {
17     int x=0,f=1;char c=getchar();
18     while(c<‘0‘||c>‘9‘){if(c==‘-‘)f=-1;c=getchar();}
19     while(c>=‘0‘&&c<=‘9‘){x=x*10+c-‘0‘;c=getchar();}
20     return x*f;
21 }
22 void ins(int u,int v,int w){e[++cnt]=(edge){v,first[u],w};first[u]=cnt;}
23 void getroot(int x,int fa)
24 {
25     sz[x]=1;mx[x]=0;
26     for(int i=first[x];i;i=e[i].next)
27     {
28         int to=e[i].to;
29         if(to==fa||vis[to])continue;
30         getroot(to,x);
31         sz[x]+=sz[to];
32         mx[x]=max(mx[x],sz[to]);
33     }
34     mx[x]=max(mx[x],sum-sz[x]);
35     if(mx[root]>mx[x])root=x;
36 }
37 void getdeep(int x,int fa)
38 {
39     d=max(d,max(dep[x],-dep[x]));
40     if(s[dep[x]+base])g[dep[x]+base][1]++;
41     else g[dep[x]+base][0]++;
42     s[dep[x]+base]++;
43     for(int i=first[x];i;i=e[i].next)
44     {
45         int to=e[i].to;
46         if(to==fa||vis[to])continue;
47         dep[to]=dep[x]+e[i].w;
48         getdeep(to,x);
49     }
50     s[dep[x]+base]--;
51 }
52 void dfs(int x)
53 {
54     vis[x]=true;int dd=0;
55     for(int i=first[x];i;i=e[i].next)
56     {
57         int to=e[i].to;
58         if(vis[to])continue;
59         dep[to]=e[i].w;d=0;
60         getdeep(to,x);dd=max(dd,d);
61         for(int j=base-d;j<=base+d;j++)
62             ans+=1ll*f[base*2-j][0]*g[j][1]+1ll*f[base*2-j][1]*g[j][0]+1ll*f[base*2-j][1]*g[j][1];
63         ans+=1ll*f[base][0]*g[base][0]+g[base][1];
64         for(int j=base-d;j<=base+d;j++)
65             f[j][0]+=g[j][0],f[j][1]+=g[j][1],g[j][0]=g[j][1]=0;
66     }
67     for(int i=base-dd;i<=base+dd;i++)f[i][0]=f[i][1]=0;
68     for(int i=first[x];i;i=e[i].next)
69     {
70         int to=e[i].to;
71         if(vis[to])continue;
72         root=0;sum=sz[to];
73         getroot(to,x);dfs(root);
74     }
75 }
76 int main()
77 {
78     n=read();
79     for(int i=1;i<n;i++)
80     {
81         x=read();y=read();w=read();
82         w=(w==0)?-1:1;ins(x,y,w);ins(y,x,w);
83     }
84     root=0;sum=n;mx[0]=inf;
85     getroot(1,-1);dfs(root);
86     printf("%lld\n",ans);
87     return 0;
88 }

 1 #include<cstdio>
 2 #include<algorithm> 
 3 #include<cstring>
 4 #define LL long long
 5 using namespace std;
 6 const int N=2e5+5;
 7 const int inf=0x3f3f3f3f;
 8 int n,cnt,x,y,root,sum;
 9 int id[N],first[N],sz[N],mx[N];
10 bool vis[N];
11 LL ans[N],mp[(1<<20)+5];
12 char s[N];
13 struct edge{int to,next;}e[N*2];
14 int read()
15 {
16     int x=0,f=1;char c=getchar();
17     while(c<‘0‘||c>‘9‘){if(c==‘-‘)f=-1;c=getchar();}
18     while(c>=‘0‘&&c<=‘9‘){x=x*10+c-‘0‘;c=getchar();}
19     return x*f;
20 }
21 int max(int a,int b){return a>b?a:b;}
22 void ins(int u,int v){e[++cnt]=(edge){v,first[u]};first[u]=cnt;}
23 void getroot(int x,int fa)
24 {
25     sz[x]=1;mx[x]=0;
26     for(int i=first[x];i;i=e[i].next)
27     {
28         int to=e[i].to;
29         if(to==fa||vis[to])continue;
30         getroot(to,x);
31         sz[x]+=sz[to];
32         mx[x]=max(mx[x],sz[to]);
33     }
34     mx[x]=max(mx[x],sum-sz[x]);
35     if(mx[root]>mx[x])root=x;
36 }
37 void getway(int x,int fa,int val,int k)
38 {
39     val^=id[x];mp[val]+=k;
40     for(int i=first[x];i;i=e[i].next)
41     {
42         int to=e[i].to;
43         if(to==fa||vis[to])continue;
44         getway(to,x,val,k);
45     }
46 }
47 LL check(int x,int fa,int val)
48 {
49     val^=id[x];LL num=mp[val];
50     for(int i=0;i<20;i++)num+=mp[(1<<i)^val];
51     for(int i=first[x];i;i=e[i].next)
52     {
53         int to=e[i].to;
54         if(to==fa||vis[to])continue;
55         num+=check(to,x,val);
56     }
57     ans[x]+=num;return num;
58 }
59 void solve(int x)
60 {
61     vis[x]=true;getway(x,-1,0,1);
62     LL num=mp[0];
63     for(int i=0;i<20;i++)num+=mp[1<<i];
64     for(int i=first[x];i;i=e[i].next)
65     {
66         int to=e[i].to;
67         if(vis[to])continue;
68         getway(to,x,id[x],-1);
69         num+=check(to,x,0);
70         getway(to,x,id[x],1);
71     }
72     ans[x]+=num/2;getway(x,-1,0,-1);
73     for(int i=first[x];i;i=e[i].next)
74     {
75         int to=e[i].to;
76         if(vis[to])continue;
77         sum=sz[to];root=0;
78         getroot(to,-1);solve(root);
79     }
80 }
81 int main()
82 {
83     n=read();
84     for(int i=1;i<n;i++)x=read(),y=read(),ins(x,y),ins(y,x);
85     scanf("%s",s+1);
86     for(int i=1;i<=n;i++)id[i]=1<<(s[i]-‘a‘);
87     sum=n;mx[0]=inf;getroot(1,-1);solve(root);
88     for(int i=1;i<=n;i++)printf("%lld ",ans[i]+1);
89     return 0;
90 }

 1 struct LCT
 2 {
 3     int c[N][2],fa[N],sum[N],val[N];
 4     bool rev[N];
 5     bool isroot(int x){return c[fa[x]][0]!=x&&c[fa[x]][1]!=x;}
 6     void update(int x){sum[x]=sum[c[x][0]]+sum[c[x][1]]+val[x];}
 7     void flip(int x){swap(c[x][0],c[x][1]);rev[x]^=1;}
 8     void down(int x){if(rev[x])flip(c[x][0]),flip(c[x][1]),rev[x]=0;}
 9     void rotate(int x)
10     {
11         int y=fa[x],z=fa[y],l,r;
12         if(c[y][0]==x)l=0;else l=1;r=l^1;
13         if(!isroot(y)){if(c[z][0]==y)c[z][0]=x;else c[z][1]=x;}
14         fa[x]=z;fa[y]=x;fa[c[x][r]]=y;
15         c[y][l]=c[x][r];c[x][r]=y;
16         update(y);update(x);
17     }
18     void relax(int x){if(!isroot(x))relax(fa[x]);down(x);}
19     void splay(int x)
20     {
21         relax(x);
22         while(!isroot(x))
23         {
24             int y=fa[x],z=fa[y];
25             if(!isroot(y))
26             {
27                 if((c[y][0]==x)^(c[z][0]==y))rotate(x);
28                 else rotate(y);
29             }
30             rotate(x);
31         }
32     }
33     void access(int x){int t=0;while(x)splay(x),c[x][1]=t,update(x),t=x,x=fa[x];}
34     void makeroot(int x){access(x);splay(x);flip(x);}
35     bool connected(int x,int y)
36     {
37         if(x==y)return true;
38         makeroot(x);access(y);splay(y);return fa[x]!=0;
39     }
40     void modify(int x,int v){splay(x);val[x]=v;update(x);}
41     void link(int x,int y){makeroot(x);fa[x]=y;}
42     void cut(int x,int y){makeroot(x);access(y);splay(y);c[y][0]=fa[x]=0;update(y);}
43     int query(int x,int y){makeroot(x);access(y);splay(y);return sum[y];}
44 }T;

 1 #include<cstdio>
 2 #include<cstring>
 3 #include<algorithm>
 4 #define LL long long
 5 using namespace std;
 6 const int N=3e5+5;
 7 int n,m,op,x,y;
 8 int read()
 9 {
10     int x=0,f=1;char c=getchar();
11     while(c<‘0‘||c>‘9‘){if(c==‘-‘)f=-1;c=getchar();}
12     while(c>=‘0‘&&c<=‘9‘){x=x*10+c-‘0‘;c=getchar();}
13     return x*f;
14 }
15 struct LCT
16 {
17     int c[N][2],fa[N],sum[N],val[N];
18     bool rev[N];
19     bool isroot(int x){return c[fa[x]][0]!=x&&c[fa[x]][1]!=x;}
20     void update(int x){sum[x]=sum[c[x][0]]^sum[c[x][1]]^val[x];}
21     void flip(int x){swap(c[x][0],c[x][1]);rev[x]^=1;}
22     void down(int x){if(rev[x])flip(c[x][0]),flip(c[x][1]),rev[x]=0;}
23     void rotate(int x)
24     {
25         int y=fa[x],z=fa[y],l,r;
26         if(c[y][0]==x)l=0;else l=1;r=l^1;
27         if(!isroot(y)){if(c[z][0]==y)c[z][0]=x;else c[z][1]=x;}
28         fa[x]=z;fa[y]=x;fa[c[x][r]]=y;
29         c[y][l]=c[x][r];c[x][r]=y;
30         update(y);update(x);
31     }
32     void relax(int x){if(!isroot(x))relax(fa[x]);down(x);}
33     void splay(int x)
34     {
35         relax(x);
36         while(!isroot(x))
37         {
38             int y=fa[x],z=fa[y];
39             if(!isroot(y))
40             {
41                 if((c[y][0]==x)^(c[z][0]==y))rotate(x);
42                 else rotate(y);
43             }
44             rotate(x);
45         }
46     }
47     void access(int x){int t=0;while(x){splay(x);c[x][1]=t;update(x);t=x;x=fa[x];}}
48     void makeroot(int x){access(x);splay(x);flip(x);}
49     void modify(int x,int v){splay(x);val[x]=v;update(x);}
50     void link(int x,int y){makeroot(x);fa[x]=y;}
51     void cut(int x,int y){makeroot(x);access(y);splay(y);c[y][0]=fa[x]=0;update(y);}
52     int query(int x,int y){makeroot(x);access(y);splay(y);return sum[y];}
53 }T;
54 int main()
55 {
56     n=read();m=read();
57     for(int i=1;i<=n;i++)T.val[i]=T.sum[i]=read();
58     while(m--)
59     {
60         op=read();x=read();y=read();
61         if(op==0)printf("%d\n",T.query(x,y));
62         if(op==1)T.link(x,y);
63         if(op==2)T.cut(x,y);
64         if(op==3)T.modify(x,y);
65     }
66     return 0;
67 }

 1 #include<cstdio>
 2 #include<cstring>
 3 #include<algorithm>
 4 #define LL long long
 5 using namespace std;
 6 const int N=3e4+5;
 7 int n,m,x,y;
 8 char s[10];
 9 int read()
10 {
11     int x=0,f=1;char c=getchar();
12     while(c<‘0‘||c>‘9‘){if(c==‘-‘)f=-1;c=getchar();}
13     while(c>=‘0‘&&c<=‘9‘){x=x*10+c-‘0‘;c=getchar();}
14     return x*f;
15 }
16 struct LCT
17 {
18     int c[N][2],fa[N],sum[N],val[N];
19     bool rev[N];
20     bool isroot(int x){return c[fa[x]][0]!=x&&c[fa[x]][1]!=x;}
21     void update(int x){sum[x]=sum[c[x][0]]+sum[c[x][1]]+val[x];}
22     void flip(int x){swap(c[x][0],c[x][1]);rev[x]^=1;}
23     void down(int x){if(rev[x])flip(c[x][0]),flip(c[x][1]),rev[x]=0;}
24     void rotate(int x)
25     {
26         int y=fa[x],z=fa[y],l,r;
27         if(c[y][0]==x)l=0;else l=1;r=l^1;
28         if(!isroot(y)){if(c[z][0]==y)c[z][0]=x;else c[z][1]=x;}
29         fa[x]=z;fa[y]=x;fa[c[x][r]]=y;
30         c[y][l]=c[x][r];c[x][r]=y;
31         update(y);update(x);
32     }
33     void relax(int x){if(!isroot(x))relax(fa[x]);down(x);}
34     void splay(int x)
35     {
36         relax(x);
37         while(!isroot(x))
38         {
39             int y=fa[x],z=fa[y];
40             if(!isroot(y))
41             {
42                 if((c[y][0]==x)^(c[z][0]==y))rotate(x);
43                 else rotate(y);
44             }
45             rotate(x);
46         }
47     }
48     void access(int x){int t=0;while(x)splay(x),c[x][1]=t,update(x),t=x,x=fa[x];}
49     void makeroot(int x){access(x);splay(x);flip(x);}
50     bool connected(int x,int y)
51     {
52         if(x==y)return true;
53         makeroot(x);access(y);splay(y);return fa[x]!=0;
54     }
55     void modify(int x,int v){splay(x);val[x]=v;update(x);}
56     void link(int x,int y){makeroot(x);fa[x]=y;}
57     void cut(int x,int y){makeroot(x);access(y);splay(y);c[y][0]=fa[x]=0;update(y);}
58     int query(int x,int y){makeroot(x);access(y);splay(y);return sum[y];}
59 }T;
60 int main()
61 {
62     n=read();
63     for(int i=1;i<=n;i++)T.sum[i]=T.val[i]=read();
64     m=read();
65     while(m--)
66     {
67         scanf("%s",s);x=read();y=read();
68         if(s[0]==‘b‘)
69         {
70             if(T.connected(x,y))printf("no\n");
71             else printf("yes\n"),T.link(x,y);
72         }
73         if(s[0]==‘p‘)T.modify(x,y);
74         if(s[0]==‘e‘)
75         {
76             if(T.connected(x,y))printf("%d\n",T.query(x,y));
77             else printf("impossible\n");
78         }
79     }
80     return 0;
81 }

  1 #include<cstdio>
  2 #include<cstring>
  3 #include<algorithm>
  4 #define LL long long
  5 using namespace std;
  6 const int N=3e4+5;
  7 const int mod=1e4+7;
  8 int n,m,id,k,p,b;
  9 char op[2];
 10 int read()
 11 {
 12     int x=0,f=1;char c=getchar();
 13     while(c<‘0‘||c>‘9‘){if(c==‘-‘)f=-1;c=getchar();}
 14     while(c>=‘0‘&&c<=‘9‘){x=x*10+c-‘0‘;c=getchar();}
 15     return x*f;
 16 }
 17 struct data
 18 {
 19     int k,b;
 20     data(){k=1;b=0;}
 21     int calc(int x){return (k*x+b)%mod;}
 22 };
 23 data operator + (data a,data b)
 24 {
 25     data c;
 26     c.k=a.k*b.k%mod;
 27     c.b=(b.k*a.b%mod+b.b)%mod;
 28     return c;
 29 }
 30 int exgcd(int a,int b,int& x,int& y)
 31 {
 32     if(!b){x=1;y=0;return a;}
 33     int ans=exgcd(b,a%b,x,y);
 34     int tmp=x;x=y;y=tmp-a/b*y;
 35     return ans;
 36 }
 37 struct LCT
 38 {
 39     int c[N][2],fa[N],sfa[N];
 40     bool ins[N],vis[N];
 41     data val[N],sum[N];
 42     bool isroot(int x){return c[fa[x]][0]!=x&&c[fa[x]][1]!=x;}
 43     void update(int x){sum[x]=sum[c[x][0]]+val[x]+sum[c[x][1]];}
 44     void dfs(int x)
 45     {
 46         ins[x]=vis[x]=true;int to=fa[x];
 47         if(ins[to])fa[x]=0,sfa[x]=to;
 48         if(!vis[to])dfs(to);ins[x]=false;
 49     }
 50     void init(int n)
 51     {
 52         int k,b;
 53         for(int i=1;i<=n;i++)
 54         {
 55             k=read();fa[i]=read();b=read();
 56             data tmp;tmp.k=k;tmp.b=b;
 57             val[i]=sum[i]=tmp;
 58         }
 59         for(int i=1;i<=n;i++)if(!vis[i])dfs(i);
 60     }
 61     void rotate(int x)
 62     {
 63         int y=fa[x],z=fa[y],l,r;
 64         if(c[y][0]==x)l=0;else l=1;r=l^1;
 65         if(!isroot(y)){if(c[z][0]==y)c[z][0]=x;else c[z][1]=x;}
 66         fa[x]=z;fa[y]=x;fa[c[x][r]]=y;
 67         c[y][l]=c[x][r];c[x][r]=y;
 68         update(y);update(x);
 69     }
 70     void splay(int x)
 71     {
 72         while(!isroot(x))
 73         {
 74             int y=fa[x],z=fa[y];
 75             if(!isroot(y))
 76             {
 77                 if((c[y][0]==x)^(c[z][0]==y))rotate(x);
 78                 else rotate(y);
 79             }
 80             rotate(x);
 81         }
 82     }
 83     void access(int x){int t=0;while(x)splay(x),c[x][1]=t,update(x),t=x,x=fa[x];}
 84     int findroot(int x)
 85     {
 86         access(x);splay(x);
 87         int t=x;while(c[t][0])t=c[t][0];
 88         splay(t);return t;
 89     }
 90     int query(int x)
 91     {
 92         access(x);splay(x);data v1=sum[x];
 93         int rt=findroot(x),sf=sfa[rt];
 94         access(sf);splay(sf);data v2=sum[sf];
 95         if(v2.k==0)return v1.calc(v2.b);
 96         if(v2.k==1)return v2.b?-1:-2;
 97         int xx,yy;exgcd(v2.k-1,mod,xx,yy);
 98 //        return v1.calc((mod-xx)%mod*v2.b%mod);
 99         return v1.calc((xx%mod+mod)%mod*(((mod-v2.b)%mod+mod)%mod)%mod);
100     }
101     void cut(int x){access(x);splay(x);fa[c[x][0]]=0;c[x][0]=0;update(x);}
102     void link(int x,int f){access(x);splay(x);fa[x]=f;}
103     bool oncircle(int x,int rt)
104     {
105         int sf=sfa[rt];
106         if(x==sf)return true;
107         access(sf);splay(sf);splay(x);
108         return !isroot(sf);
109     }
110     void change(int x,int f,int k,int b)
111     {
112         access(x);splay(x);
113         data tmp;tmp.k=k;tmp.b=b;
114         val[x]=tmp;update(x);
115         int rt=findroot(x);
116         if(x==rt)
117         {
118             int rf=findroot(f);
119             if(rt==rf)sfa[x]=f;
120             else sfa[x]=0,link(x,f);
121         }
122         else
123         {
124             if(oncircle(x,rt))
125             {
126                 cut(x);link(rt,sfa[rt]);sfa[rt]=0;
127                 int rf=findroot(f);
128                 if(x==rf)sfa[x]=f;
129                 else link(x,f);
130             }
131             else
132             {
133                 cut(x);int rf=findroot(f);
134                 if(x==rf)sfa[x]=f;
135                 else link(x,f);
136             }
137         }
138     }
139 }lct;
140 int main()
141 {
142     n=read();lct.init(n);
143     m=read();
144     while(m--)
145     {
146         scanf("%s",op);id=read();
147         if(op[0]==‘A‘)printf("%d\n",lct.query(id));
148         else k=read(),p=read(),b=read(),lct.change(id,p,k,b);
149     }
150     return 0;
151 }

 1 #include<cstdio>
 2 #include<algorithm> 
 3 #include<cstring>
 4 #define LL long long
 5 using namespace std;
 6 const int N=1e5+5;
 7 int n,m,x,y;
 8 char op[2];
 9 int read()
10 {
11     int x=0,f=1;char c=getchar();
12     while(c<‘0‘||c>‘9‘){if(c==‘-‘)f=-1;c=getchar();}
13     while(c>=‘0‘&&c<=‘9‘){x=x*10+c-‘0‘;c=getchar();}
14     return x*f;
15 }
16 struct LCT
17 {
18     int c[N][2],fa[N],sum[N],val[N];
19     bool rev[N];
20     bool isroot(int x){return c[fa[x]][0]!=x&&c[fa[x]][1]!=x;}
21     void update(int x){sum[x]=sum[c[x][0]]+sum[c[x][1]]+val[x]+1;}
22     void flip(int x){swap(c[x][0],c[x][1]);rev[x]^=1;}
23     void down(int x){if(rev[x])flip(c[x][0]),flip(c[x][1]),rev[x]=0;}
24     void rotate(int x)
25     {
26         int y=fa[x],z=fa[y],l,r;
27         if(c[y][0]==x)l=0;else l=1;r=l^1;
28         if(!isroot(y)){if(c[z][0]==y)c[z][0]=x;else c[z][1]=x;}
29         fa[x]=z;fa[y]=x;fa[c[x][r]]=y;
30         c[y][l]=c[x][r];c[x][r]=y;
31         update(y);update(x);
32     }
33     void relax(int x){if(!isroot(x))relax(fa[x]);down(x);}
34     void splay(int x)
35     {
36         relax(x);
37         while(!isroot(x))
38         {
39             int y=fa[x],z=fa[y];
40             if(!isroot(y))
41             {
42                 if((c[y][0]==x)^(c[z][0]==y))rotate(x);
43                 else rotate(y);
44             }
45             rotate(x);
46         }
47     }
48     void access(int x)
49     {
50         int t=0;
51         while(x)
52         {
53             splay(x);val[x]+=sum[c[x][1]]-sum[t];
54             c[x][1]=t;update(x);t=x;x=fa[x];
55         }
56     }
57     void makeroot(int x){access(x);splay(x);flip(x);}
58     void link(int x,int y)
59     {
60         makeroot(x);makeroot(y);
61         fa[x]=y;val[y]+=sum[x];update(y);
62     }
63 }T;
64 int main()
65 {
66     n=read();m=read();
67     for(int i=1;i<=n;i++)T.sum[i]=1;
68     while(m--)
69     {
70         scanf("%s",op);
71         x=read();y=read();
72         if(op[0]==‘A‘)T.link(x,y);
73         else 
74         {
75             T.makeroot(x);T.makeroot(y);
76             printf("%lld\n",1ll*T.sum[x]*(T.sum[y]-T.sum[x]));
77         }
78     }
79     return 0;
80 }

  1 #include<cstdio>
  2 #include<algorithm> 
  3 #include<cstring>
  4 #define LL long long
  5 #define lc(x) x<<1
  6 #define rc(x) x<<1|1
  7 using namespace std;
  8 const int N=1e5+5;
  9 int n,m,x,y,cnt,dfn,rt=1,first[N];
 10 int deep[N],in[N],out[N],fa[N][18];
 11 char op[15];
 12 int read()
 13 {
 14     int x=0,f=1;char c=getchar();
 15     while(c<‘0‘||c>‘9‘){if(c==‘-‘)f=-1;c=getchar();}
 16     while(c>=‘0‘&&c<=‘9‘){x=x*10+c-‘0‘;c=getchar();}
 17     return x*f;
 18 }
 19 struct edge{int to,next;}e[N<<1];
 20 void ins(int u,int v){e[++cnt]=(edge){v,first[u]};first[u]=cnt;}
 21 struct SGT
 22 {
 23     int l[N*4],r[N*4];
 24     LL sum[N*4],tag[N*4];
 25     void build(int x,int L,int R)
 26     {
 27         l[x]=L;r[x]=R;if(L==R)return;
 28         int mid=(L+R)>>1;
 29         build(lc(x),L,mid);build(rc(x),mid+1,R);
 30     }
 31     void up(int x){sum[x]=sum[lc(x)]+sum[rc(x)];}
 32     void qadd(int x,LL w){tag[x]+=w;sum[x]+=w*(r[x]-l[x]+1);}
 33     void down(int x)
 34     {
 35         if(!tag[x])return;
 36         qadd(lc(x),tag[x]);qadd(rc(x),tag[x]);
 37         tag[x]=0;
 38     }
 39     void add(int x,int L,int R,LL w)
 40     {
 41         if(L<=l[x]&&r[x]<=R){qadd(x,w);return;}
 42         down(x);int mid=(l[x]+r[x])>>1;
 43         if(L<=mid)add(lc(x),L,R,w);
 44         if(R>mid)add(rc(x),L,R,w);
 45         up(x);
 46     }
 47     LL query(int x,int L,int R)
 48     {
 49         if(L<=l[x]&&r[x]<=R)return sum[x];
 50         down(x);LL ans=0;
 51         int mid=(l[x]+r[x])>>1;
 52         if(L<=mid)ans+=query(lc(x),L,R);
 53         if(R>mid)ans+=query(rc(x),L,R);
 54         return ans;
 55     }
 56 }sgt;
 57 int find(int x,int y)
 58 {
 59     int d=deep[y]-deep[x]-1;
 60     for(int i=16;i>=0;i--)
 61         if(d&(1<<i))y=fa[y][i];
 62     return y;
 63 }
 64 void addson(int x,LL w)
 65 {
 66     if(x==rt)sgt.add(1,1,n,w);
 67     else if(in[rt]>=in[x]&&out[rt]<=out[x])
 68     {
 69         int t=find(x,rt);
 70         if(in[t]>1)sgt.add(1,1,in[t]-1,w);
 71         if(out[t]<n)sgt.add(1,out[t]+1,n,w);
 72     }
 73     else sgt.add(1,in[x],out[x],w);
 74 }
 75 struct LCT
 76 {
 77     int c[N][2],fa[N],in[N],out[N];
 78     bool rev[N];
 79     bool isroot(int x){return c[fa[x]][0]!=x&&c[fa[x]][1]!=x;}
 80     void flip(int x){swap(c[x][0],c[x][1]);rev[x]^=1;}
 81     void down(int x){if(rev[x])flip(c[x][0]),flip(c[x][1]),rev[x]=0;}
 82     void rotate(int x)
 83     {
 84         int y=fa[x],z=fa[y],l,r;
 85         if(c[y][0]==x)l=0;else l=1;r=l^1;
 86         if(!isroot(y)){if(c[z][0]==y)c[z][0]=x;else c[z][1]=x;}
 87         fa[x]=z;fa[y]=x;fa[c[x][r]]=y;
 88         c[y][l]=c[x][r];c[x][r]=y;
 89     }
 90     void relax(int x){if(!isroot(x))relax(fa[x]);down(x);}
 91     void splay(int x)
 92     {
 93         relax(x);
 94         while(!isroot(x))
 95         {
 96             int y=fa[x],z=fa[y];
 97             if(!isroot(y))
 98             {
 99                 if((c[y][0]==x)^(c[z][0]==y))rotate(x);
100                 else rotate(y);
101             }
102             rotate(x);
103         }
104     }
105     int top(int x){down(x);while(c[x][0])x=c[x][0],down(x);return x;}
106     void access(int x)
107     {
108         int t=0;
109         while(x)
110         {
111             splay(x);
112             if(c[x][1])addson(top(c[x][1]),1);
113             if(t)addson(top(t),-1);
114             c[x][1]=t;t=x;x=fa[x];
115         }
116     }
117     void makeroot(int x){splay(x);rt=x;flip(x);}
118 }lct;
119 void dfs(int x)
120 {
121     in[x]=++dfn;
122     sgt.add(1,in[x],in[x],deep[x]);
123     for(int i=1;(1<<i)<=deep[x];i++)
124         fa[x][i]=fa[fa[x][i-1]][i-1];
125     for(int i=first[x];i;i=e[i].next)
126     {
127         int to=e[i].to;
128         if(to==fa[x][0])continue;
129         fa[to][0]=lct.fa[to]=x;
130         deep[to]=deep[x]+1;dfs(to);
131     }
132     out[x]=dfn;
133 }
134 double request(int x)
135 {
136     if(x==rt)return 1.0*sgt.query(1,1,n)/n;
137     if(in[rt]>=in[x]&&out[rt]<=out[x])
138     {
139         int t=find(x,rt);LL sum=0;
140         if(in[t]>1)sum+=sgt.query(1,1,in[t]-1);
141         if(out[t]<n)sum+=sgt.query(1,out[t]+1,n);
142         return 1.0*sum/(n-(out[t]-in[t]+1));
143     }
144     return 1.0*sgt.query(1,in[x],out[x])/(out[x]-in[x]+1);
145 }
146 int main()
147 {
148     n=read();m=read();
149     for(int i=1;i<n;i++)x=read(),y=read(),ins(x,y),ins(y,x);
150     sgt.build(1,1,n);deep[1]=1;dfs(1);
151     while(m--)
152     {
153         scanf("%s",op);x=read();
154         if(op[2]==‘Q‘)printf("%.10lf\n",request(x));
155         else
156         {
157             lct.access(x);
158             if(op[2]==‘C‘)lct.makeroot(x);
159         }
160     }
161     return 0;
162 }

 1 #include<cstdio>
 2 #include<algorithm> 
 3 #include<cstring>
 4 #define LL long long
 5 using namespace std;
 6 const int N=250005;
 7 const int inf=0x3f3f3f3f;
 8 int n,m,x,y,w,tim,cnt,cntv;
 9 int a[N<<1],first[N],firstv[N],st[N]; 
10 int dfn[N],out[N],deep[N],fa[N][20];
11 LL val[N];
12 bool f[N];
13 struct edge{int to,next,w;}e[N<<1],ev[N<<1];
14 int read()
15 {
16     int x=0,f=1;char c=getchar();
17     while(c<‘0‘||c>‘9‘){if(c==‘-‘)f=-1;c=getchar();}
18     while(c>=‘0‘&&c<=‘9‘){x=x*10+c-‘0‘;c=getchar();}
19     return x*f;
20 }
21 void ins(int u,int v,int w){e[++cnt]=(edge){v,first[u],w};first[u]=cnt;}
22 void insv(int u,int v){ev[++cntv]=(edge){v,firstv[u],0};firstv[u]=cntv;}
23 void dfs(int x)
24 {
25     dfn[x]=++tim;
26     for(int i=1;(1<<i)<=deep[x];i++)
27         fa[x][i]=fa[fa[x][i-1]][i-1];
28     for(int i=first[x];i;i=e[i].next)
29     {
30         int to=e[i].to;
31         if(to==fa[x][0])continue;
32         fa[to][0]=x;
33         deep[to]=deep[x]+1;
34         val[to]=min(val[x],1ll*e[i].w);
35         dfs(to);
36     }
37     out[x]=tim;
38 }
39 int lca(int x,int y)
40 {
41     if(deep[x]<deep[y])swap(x,y);
42     int d=deep[x]-deep[y];
43     for(int i=0;(1<<i)<=d;i++)
44         if((1<<i)&d)x=fa[x][i];
45     if(x==y)return x;
46     for(int i=18;i>=0;i--)
47         if((1<<i)<=deep[x]&&fa[x][i]!=fa[y][i])
48             x=fa[x][i],y=fa[y][i];
49     return fa[x][0];
50 }
51 bool cmp(int a,int b){return dfn[a]<dfn[b];}
52 bool check(int x,int y){return dfn[x]<=out[y];}
53 LL dp(int x)
54 {
55     if(f[x])return val[x];LL sum=0;
56     for(int i=firstv[x];i;i=ev[i].next)sum+=dp(ev[i].to);
57     return min(val[x],sum);
58 }
59 void work()
60 {
61     int k=read(),tmp=k;
62     for(int i=1;i<=k;i++)a[i]=read(),f[a[i]]=true;
63     sort(a+1,a+k+1,cmp);
64     for(int i=1;i<tmp;i++)a[++k]=lca(a[i],a[i+1]);
65     sort(a+1,a+k+1,cmp);
66     k=unique(a+1,a+k+1)-a-1;
67     for(int i=1;i<=k;i++)firstv[a[i]]=0;
68     cntv=0;int top=0;
69     for(int i=1;i<=k;i++)
70     {
71         while(top&&!check(a[i],st[top]))top--;
72         if(top)insv(st[top],a[i]);
73         st[++top]=a[i];
74     }
75     printf("%lld\n",dp(a[1]));
76     for(int i=1;i<=k;i++)f[a[i]]=false;
77 } 
78 int main()
79 {
80     n=read();
81     for(int i=1;i<n;i++)
82     {
83         x=read();y=read();w=read();
84         ins(x,y,w);ins(y,x,w);
85     }
86     val[1]=1e16;dfs(1);
87     m=read();
88     while(m--)work();
89     return 0;
90 }

  1 #include<cstdio>
  2 #include<algorithm> 
  3 #include<cstring>
  4 #define LL long long
  5 using namespace std;
  6 const int N=300005;
  7 int n,m,x,y,cnt,tim,top;
  8 int a[N],b[N],bel[N],first[N],st[N],rem[N],f[N];
  9 int size[N],dfn[N],out[N],deep[N],fa[N][20];
 10 struct edge{int to,next;}e[N<<1];
 11 int read()
 12 {
 13     int x=0,f=1;char c=getchar();
 14     while(c<‘0‘||c>‘9‘){if(c==‘-‘)f=-1;c=getchar();}
 15     while(c>=‘0‘&&c<=‘9‘){x=x*10+c-‘0‘;c=getchar();}
 16     return x*f;
 17 }
 18 void ins(int u,int v){e[++cnt]=(edge){v,first[u]};first[u]=cnt;}
 19 void dfs(int x)
 20 {
 21     dfn[x]=++tim;size[x]=1;
 22     for(int i=1;(1<<i)<=deep[x];i++)
 23         fa[x][i]=fa[fa[x][i-1]][i-1];
 24     for(int i=first[x];i;i=e[i].next)
 25     {
 26         int to=e[i].to;
 27         if(to==fa[x][0])continue;
 28         deep[to]=deep[x]+1;
 29         fa[to][0]=x;dfs(to);
 30         size[x]+=size[to];
 31     }
 32     out[x]=tim;
 33 }
 34 int lca(int x,int y)
 35 {
 36     if(deep[x]<deep[y])swap(x,y);
 37     int d=deep[x]-deep[y];
 38     for(int i=0;(1<<i)<=d;i++)
 39         if((1<<i)&d)x=fa[x][i];
 40     if(x==y)return x;
 41     for(int i=18;i>=0;i--)
 42         if((1<<i)<=deep[x]&&fa[x][i]!=fa[y][i])
 43             x=fa[x][i],y=fa[y][i];
 44     return fa[x][0];
 45 }
 46 bool cmp(int a,int b){return dfn[a]<dfn[b];}
 47 int dis(int a,int b){return deep[a]+deep[b]-2*deep[lca(a,b)];}
 48 bool check(int x,int y){return dfn[x]<=out[y];}
 49 void dfs1(int x)
 50 {
 51     rem[x]=size[x];
 52     for(int i=first[x];i;i=e[i].next)
 53     {
 54         int to=e[i].to;dfs1(to);
 55         if(!bel[to])continue;
 56         int d1=dis(x,bel[to]),d2=dis(x,bel[x]);
 57         if(!bel[x]||d1<d2||(d1==d2&&bel[to]<bel[x]))bel[x]=bel[to];
 58     }
 59 }
 60 void dfs2(int x)
 61 {
 62     for(int i=first[x];i;i=e[i].next)
 63     {
 64         int to=e[i].to;
 65         int d1=dis(to,bel[x]),d2=dis(to,bel[to]);
 66         if(!bel[to]||d1<d2||(d1==d2&&bel[x]<bel[to]))bel[to]=bel[x];
 67         dfs2(to);
 68     }
 69 }
 70 void solve(int a,int b)
 71 {
 72     int x=b,mid=b;
 73     for(int i=18;i>=0;i--)
 74         if(deep[fa[x][i]]>deep[a])x=fa[x][i];
 75     rem[a]-=size[x];
 76     if(bel[a]==bel[b])
 77     {
 78         f[bel[a]]+=size[x]-size[b];
 79         return;
 80     }
 81     for(int i=18;i>=0;i--)
 82     {
 83         int y=fa[mid][i];
 84         if(deep[y]<=deep[a])continue;
 85         int d1=dis(bel[a],y),d2=dis(bel[b],y);
 86         if(d2<d1||(d1==d2&&bel[b]<bel[a]))mid=y;
 87     }
 88     f[bel[a]]+=size[x]-size[mid];
 89     f[bel[b]]+=size[mid]-size[b];
 90 }
 91 void work()
 92 {
 93     int k=read(),tmp=k;
 94     for(int i=1;i<=k;i++)a[i]=b[i]=read();
 95     for(int i=1;i<=k;i++)bel[a[i]]=a[i];
 96     sort(a+1,a+k+1,cmp);
 97     for(int i=1;i<tmp;i++)a[++k]=lca(a[i],a[i+1]);
 98     a[++k]=1;sort(a+1,a+k+1,cmp);
 99     k=unique(a+1,a+k+1)-a-1;
100     cnt=top=0;
101     for(int i=1;i<=k;i++)first[a[i]]=0;
102     for(int i=1;i<=k;i++)
103     {
104         while(top&&!check(a[i],st[top]))top--;
105         if(top)ins(st[top],a[i]);
106         st[++top]=a[i];
107     }
108     dfs1(1);dfs2(1);
109     for(int i=1;i<=k;i++)
110         for(int j=first[a[i]];j;j=e[j].next)
111             solve(a[i],e[j].to);
112     for(int i=1;i<=k;i++)f[bel[a[i]]]+=rem[a[i]];
113     for(int i=1;i<=tmp;i++)printf("%d ",f[b[i]]);
114     printf("\n");
115     for(int i=1;i<=k;i++)f[a[i]]=bel[a[i]]=0;
116 }
117 int main()
118 {
119     n=read();
120     for(int i=1;i<n;i++)
121     {
122         x=read();y=read();
123         ins(x,y);ins(y,x);
124     }
125     dfs(1);m=read();
126     while(m--)work();
127     return 0;
128 }