POJ2763-Housewife Wind-树上单点修改区间求和

这道题可以树链剖分做。但是最近在给学弟搞数据结构复习了LCA树状数组RMQ

然后就搞了一发LCA+树状数组维护。

dis数组维护当前点到根节点的权值和。则dis(u,v) = dis[u]+dis[v]-2*dis[lca(u,v)]

修改的时候，单点修改影响了该点所有儿子的dis，刚好可以用dfs序定位所有儿子，用树状数组改段求点很方便。

http://blog.csdn.net/q573290534/article/details/6664454 树状数组的三种求和（改点求段，改段求点，改段求段）

http://blog.csdn.net/qwe2434127/article/details/49819975 dfs序题目类型

http://www.cnblogs.com/longdouhzt/archive/2011/10/16/2214034.html LCA题目小节

 #include <cstdio>
 #include <cmath>
 #include <cstring>
 #include <algorithm>

 using namespace std;

 const int maxn = 2e5+;

 int N,Q,S;
 //vector <int> G[maxn];

 struct edge{
     int to,next,w;
 }e[*maxn];

 int head[*maxn],tot;
 void add_edge(int u,int v,int w)
 {
     e[tot].to = v;
     e[tot].w = w;
     e[tot].next = head[u];
     head[u] = tot++;

     e[tot].to = u;
     e[tot].w = w;
     e[tot].next = head[v];
     head[v] = tot++;
 }

 int in[maxn],out[maxn],P[*maxn],fa[maxn][],dep[maxn],dis[maxn],cnt;
 void dfs(int u,int _fa,int _dep,int _dis)
 {
     in[u] = ++cnt;
     P[cnt] = u;
     fa[u][] = _fa;
     dis[u] = _dis;
     dep[u] = _dep;
     for(int i=head[u];~i;i=e[i].next)
     {
         int v = e[i].to;
         if(v == _fa) continue;
         dfs(v,u,_dep+,_dis+e[i].w);
     }
     out[u] = ++cnt;
 }
 void debug()
 {
     printf("in:\t");for(int i=;i<=N;i++) printf("%d ",in[i]);puts("");
     printf("out:\t");for(int i=;i<=N;i++) printf("%d ",out[i]);puts("");
     printf("p:\t");for(int i=;i<=cnt;i++) printf("%d ",P[i]);puts("");
     printf("dis:\t");for(int i=;i<=N;i++) printf("%d ",dis[i]);puts("");
     printf("dep:\t");for(int i=;i<=N;i++) printf("%d ",dep[i]);puts("");
     printf("edge:");for(int i=;i<tot;i++) printf("\tto:%d w:%d\n",e[i].to,e[i].w);
 }

 int initLCA()
 {
     int m = (int)log(N)/log()+;
     for(int k=;k<m;k++)
     {
         for(int v=;v<=N;v++)
         {
             if(fa[v][k] < ) {fa[v][k+] = -;continue;}
             else fa[v][k+] = fa[fa[v][k]][k];
         }
     }
 }

 int LCA(int u,int v)
 {
     int m = (int)log(N)/log()+;
     if(dep[v] > dep[u]) swap(u,v);
     for(int k=;k<m;k++)
     {
         if((dep[u]-dep[v])>>k &  )
             u = fa[u][k];
     }
     if(u == v) return u;
     for(int k=m-;k>=;k--)
     {
         if(fa[u][k] != fa[v][k])
         {
             u = fa[u][k];
             v = fa[v][k];
         }
     }
     return fa[u][];
 }

 int c[*maxn];
 int lowbit(int x) {return x&-x;}

 void init()
 {
     memset(head,-,sizeof head);
     memset(fa,-,sizeof fa);
     memset(c,,sizeof c);
     memset(in,,sizeof in);
     memset(out,,sizeof out);
     tot = ;
     cnt = ;
 }

 void add(int x,int d)
 {
     while(x)
     {
         c[x] += d;
         x -= lowbit(x);
     }
 }
 void add_seg(int l,int r,int d)
 {
     add(r,d);
     add(l-,-d);
 }
 int sum(int x)
 {
     int res = ;
     //printf("u:%d ",P[x]);
     while(x <= cnt)
     {
         res += c[x];
         x += lowbit(x);
     }
     //printf("res:%d\n",res);
     return res;
 }
 int dist(int x)
 {
     if(x == -) return ;
     return sum(in[x]) + dis[x];
 }
 int main()
 {
     //freopen("input.txt","r",stdin);
     while(~scanf("%d%d%d",&N,&Q,&S))
     {
         init();
         for(int i=,u,v,w;i<N-;i++)
         {
             scanf("%d%d%d",&u,&v,&w);
             add_edge(u,v,w);
         }
         dfs(,-,,);
         //debug();
         initLCA();
         for(int i=;i<tot;i+=)
         {
             if(dep[e[i].to] < dep[e[i+].to]) swap(e[i].to,e[i+].to);
         }
         int op;
         for(int i=,a,b,c;i<Q;i++)
         {
             scanf("%d",&op);
             if(op == )
             {
                 scanf("%d",&a);
                 int lca = LCA(S,a);
                 //printf("lca:%d\n",lca);

                 printf("%d\n",dist(S)+dist(a)-*(dist(lca)));
                 S = a;
             }else
             {
                 scanf("%d%d",&a,&b);
                 a--;
                 int u = e[a*].to;
                 int dw = b - (dist(u) - dist(fa[u][]));
                 //printf("dw:%d u:%d\n",dw,u);
                 add_seg(in[u],out[u],dw);
             }
         }
     }
 }