Housewife Wind

【原题链接】

【题意说明】

给一个树，边之间有权值，然后两种操作，第一种：求任意两点的权值和，第二，修改树上某点的权值

【问题分析】

本题就是对树进行单点更新和区域查询，显然可以使用树链剖分来完成。应该是一个比较基础的树链剖分题，注意每当区域查询后，要修改当前所有在的位置。

【参考代码】

#include <cstdio>

#include <cstring>

#include <algorithm>

using namespace std;

#define fr(i) edge[i].from

#define to(i) edge[i].to

#define nt(i) edge[i].next

#define vl(i) edge[i].value

#define hd(i) node[i].head

#define fa(i) node[i].father

#define dp(i) node[i].deep

#define sz(i) node[i].size

#define sn(i) node[i].son

#define cd(i) node[i].code

#define tp(i) node[i].top

#define lt(i) tree[i].left

#define rt(i) tree[i].right

#define vt(i) tree[i].value

#define lson k<<1

#define rson k<<1|1

const int maxN=100010;

struct Tree{

         int left, right, value;

}tree[maxN<<2];

struct Edge{

         int from, to, next, value;

}edge[maxN<<1];

struct Node{

         int head, father, deep, size, son, code, top;

}node[maxN];

int n, q, s, total=0, cnt=0;

void addedge(int, int, int);

void build(int, int, int);

void update(int, int, int);

int query(int, int, int);

int solve(int, int);

void work();

void dfs1(int, int);

void dfs2(int, int);

int main(){

         work();

         return 0;

}

void work(){

         memset(node, 0, sizeof(node));

         memset(edge, 0, sizeof(edge));

         memset(tree, 0, sizeof(tree));

         scanf("%d%d%d", &n, &q, &s);

         for(int i=0; i<n-1; i++){

                   int x, y, w;

                   scanf("%d%d%d", &x, &y, &w);

                   addedge(x, y, w);

                   addedge(y, x, w);

         }

         dfs1(1, 1);

         dfs2(1, 1);

         build(1, 1, total);

         for(int i=1; i<cnt; i+=2){

                   int u=fr(i), v=to(i);

                   if(dp(u)<dp(v)) swap(u, v);

                   update(1, cd(u), vl(i));

         }

         for(int i=0; i<q; i++){

                   int t, u, v, x;

                   scanf("%d%d", &t, &u);

                   if(t){

                            scanf("%d", &x);

                            v=to(u-1<<1|1); u=fr(u-1<<1|1);

                            if(dp(u)<dp(v)) swap(u, v);

                            update(1, cd(u), x);

                   }else{

                            printf("%d ", solve(s, u));

                            s=u;

                   }

         }

}

void addedge(int x, int y, int w){

         fr(++cnt)=x; to(cnt)=y; vl(cnt)=w;

         nt(cnt)=hd(x); hd(x)=cnt;

}

void dfs1(int u, int k){

         sz(u)=1; dp(u)=k;

         for(int i=hd(u); i; i=nt(i)){

                   if(sz(to(i))) continue;

                   fa(to(i))=u;

                   dfs1(to(i), k+1);

                   sz(u)+=sz(to(i));

                   if(sz(sn(u))<sz(to(i))) sn(u)=to(i);

         }       

}

void dfs2(int u, int _tp){

         cd(u)=++total; tp(u)=_tp;

         if(sn(u)) dfs2(sn(u), _tp);

         for(int i=hd(u); i; i=nt(i))

                   if(!cd(to(i))) dfs2(to(i), to(i));

}

void build(int k, int l, int r){

         lt(k)=l; rt(k)=r;

         if(l==r) return;

         int mid=(l+r)>>1;

         build(lson, l, mid);

         if(mid<r) build(rson, mid+1, r);

}

void update(int k, int x, int v){

         if(lt(k)==rt(k)){

                   vt(k)=v;

                   return;

         }

         if(x<=rt(lson)) update(lson, x, v);

         if(x>=lt(rson)) update(rson, x, v);

         vt(k)=vt(lson)+vt(rson);

}

int solve(int u, int v){

         int f1=tp(u), f2=tp(v), ans=0;

         while(f1!=f2){

                   if(dp(f1)<dp(f2)){

                            swap(u, v);

                            swap(f1, f2);

                   }

                   ans+=query(1, cd(f1), cd(u));

                   u=fa(f1); f1=tp(u);

         }

         if(u==v) return ans;

         if(dp(u)<dp(v))  swap(u, v);

         return ans+=query(1, cd(sn(v)), cd(u));

}

int query(int k, int l, int r){

         if(l<=lt(k)&&r>=rt(k)) return vt(k);

         if(r<=rt(lson)) return query(lson, l, r);

         if(l>=lt(rson)) return query(rson, l, r);

         return query(lson, l, rt(lson))+query(rson, lt(rson), r);

}