1 sum[i] = a[1]+...+a[i] + delta[1]*i + delta[2]*(i - 1) + delta[3]*(i - 2)+...+delta[i]*1   // a[i]为原始数组  
2        = sigma( a[x] ) + sigma( delta[x]  *  (i + 1 - x) )  
3        = sigma( a[x] ) + (i + 1) * sigma( delta[x] ) - sigma( delta[x] * x ) 

  1 #include<cstdio>
  2 #include<cstdlib>
  3 #include<cstring>
  4 #include<iostream>
  5 #include<ctime>
  6 #include<queue>
  7 using namespace std;
  8 
  9 const int N=2*100010,S=30,D=20;
 10 struct node{
 11     int x,y,next;
 12 }a[2*N];
 13 struct trnode{
 14     int l,r,lc,rc,d;
 15 }t[2*N];
 16 int n,m,len,num,first[N],dep[N],f[N][S],tot[N],zs[N],dfn[N],top[N],c0[N],c1[N],delta[N];
 17 char s[10];
 18 
 19 void add(int x,int d)
 20 {
 21     for(int i=x;i<=n;i+=(i&(-i))) c0[i]+=d,c1[i]+=d*x;
 22 }
 23 
 24 int getsum(int x)
 25 {
 26     int a0=0,a1=0;
 27     for(int i=x;i>=1;i-=(i&(-i))) a0+=c0[i],a1+=c1[i];
 28     return a0*(x+1)-a1;
 29 }
 30 
 31 
 32 void ins(int x,int y)
 33 {
 34     a[++len].x=x;a[len].y=y;
 35     a[len].next=first[x];first[x]=len;
 36 }
 37 
 38 void dfs(int x,int fa)
 39 {
 40     dep[x]=dep[fa]+1;
 41     f[x][0]=fa;
 42     tot[x]=1;
 43     zs[x]=0;
 44     for(int i=first[x];i;i=a[i].next)
 45     {
 46         int y=a[i].y;
 47         if(y==fa) continue;
 48         dfs(y,x);
 49         tot[x]+=tot[y];
 50         if(zs[x]==0 || tot[y]>tot[zs[x]]) zs[x]=y;
 51     }
 52 }
 53 
 54 void find_top(int x,int fa)
 55 {
 56     dfn[x]=++num;
 57     if(zs[x]) 
 58     {
 59         top[zs[x]]=top[x];
 60         find_top(zs[x],x);
 61     }
 62     for(int i=first[x];i;i=a[i].next)
 63     {
 64         int y=a[i].y;
 65         if(y==fa || y==zs[x]) continue;
 66         top[y]=y;
 67         find_top(y,x);
 68     }
 69 }
 70 
 71 int solve(int x,int y,int tmp)
 72 {
 73     int tx=top[x],ty=top[y],ans=0;
 74     while(tx!=ty)
 75     {
 76         if(dep[tx]<dep[ty]) swap(x,y),swap(tx,ty);
 77         if(tmp==0)
 78         {
 79             add(dfn[tx],1);
 80             add(dfn[x]+1,-1);
 81         }
 82         else ans+=getsum(dfn[x])-getsum(dfn[tx]-1);        
 83         x=f[top[x]][0];tx=top[x];
 84     }
 85     if(x==y) return ans;
 86     else
 87     {
 88         if(dep[x]<dep[y]) swap(x,y);
 89         if(tmp==0)
 90         {
 91             add(dfn[y]+1,1);
 92             add(dfn[x]+1,-1);
 93         }
 94         else ans+=getsum(dfn[x])-getsum(dfn[y]);
 95         return ans;
 96     }
 97 }
 98 
 99 void lca_init()
100 {
101     for(int j=1;j<=D;j++)
102         for(int i=1;i<=n;i++)
103             f[i][j]=f[f[i][j-1]][j-1];
104 }
105 
106 int lca_query(int x,int y)
107 {
108     if(dep[x]<dep[y]) swap(x,y);
109     for(int i=D;i>=0;i--)
110     {
111         if(f[x][i]==0) continue;
112         if(dep[f[x][i]]>=dep[y]) x=f[x][i];
113     }
114     if(x==y) return x;
115     for(int i=D;i>=0;i--)
116     {
117         if(f[x][i]!=f[y][i]) x=f[x][i],y=f[y][i];
118     }
119     return f[x][0];
120 }
121 
122 int main()
123 {
124     freopen("a.in","r",stdin);
125     // freopen("a.out","w",stdout);
126     // freopen("grassplant.in","r",stdin);
127     // freopen("grassplant.out","w",stdout);
128     scanf("%d%d",&n,&m);
129     int x,y,z;len=0;num=0;
130     memset(first,0,sizeof(first));
131     memset(f,0,sizeof(f));
132     memset(c0,0,sizeof(c0));
133     memset(c1,0,sizeof(c1));
134     memset(dep,0,sizeof(dep));
135     memset(tot,0,sizeof(tot));
136     memset(zs,0,sizeof(zs));
137     memset(dfn,0,sizeof(dfn));
138     for(int i=1;i<n;i++)
139     {
140         scanf("%d%d",&x,&y);
141         ins(x,y);
142         ins(y,x);
143     }
144     dfs(1,0);
145     top[1]=1;find_top(1,0);
146     // for(int i=1;i<=n;i++)
147     // {
148         // printf("i = %d  dep = %d  zs = %d  tot = %d  dfn = %d  top = %d\n",i,dep[i],zs[i],tot[i],dfn[i],top[i]);
149     // }
150     lca_init();
151     for(int i=1;i<=m;i++)
152     {
153         scanf("%s",s);
154         scanf("%d%d",&x,&y);
155         if(s[0]==‘P‘)
156         {
157             z=lca_query(x,y);
158             solve(x,z,0);
159             solve(y,z,0);
160         }
161         else
162         {
163             printf("%d\n",solve(x,y,1));
164         }
165     }
166     return 0;
167 }