wushen部落格：wuyiqi

思路：

邊權轉點權：

由於線段樹中的點是節點，則把題目給的邊權值作為 邊一端 距離根更遠的節點的點權值。

直接設定根權值為0 這樣不會影響題意。

因為求的的是兩點間所有的點權和，所以要減去 LCA(u,v)，因為這個點所代表的邊是沒有在路徑上的。

#include<stdio.h>
#include<iostream>
#include<string.h>
using namespace std;
#define N 50050
#define L(x) (x<<1)
#define R(x) (x<<1|1)
#define Mid(x,y) ((x+y)>>1)
#define ll __int64
struct Edge{
	ll from, to, dis,nex;
	bool yes;
}edge[N<<1];
ll head[N], edgenum;
ll dis[N];
void addedge(ll u, ll v, ll d){
	Edge E={u,v,d,head[u],false};
	edge[edgenum] = E;
	head[u] = edgenum++;
}
ll son[N];
ll top[N];
ll fp[N];
ll p[N];
ll siz[N];
ll dep[N];
ll fa[N];
ll tree_id;
void dfs(ll u, ll father, ll deep){
	fa[u] = father; dep[u] = deep;
	siz[u] = 1;
	for(ll i = head[u]; ~i; i = edge[i].nex){
		ll v = edge[i].to; if(v == father)continue;
		dfs(v, u, deep+1);
		siz[u] += siz[v];
		if(son[u] == -1 || siz[son[u]]<siz[v])son[u] = v;
		dis[v] = edge[i].dis;
		edge[i].yes = true;
	}
}
void getpos(ll u, ll toppos){
	p[u] = tree_id++; fp[p[u]] = u;
	top[u] = toppos;
	if(son[u] == -1)return;
	if(u==0)getpos(son[u],son[u]);
	else getpos(son[u], toppos);
	for(int i = head[u]; ~i; i = edge[i].nex)
	{
		int v = edge[i].to; if(v == fa[u] || v == son[u])continue;
		getpos(v,v);
	}
}
struct node{
	ll l, r;
	ll sum;
}tree[N*8];
void updata_up(ll id){
	tree[id].sum = tree[L(id)].sum+tree[R(id)].sum;
}
void build(ll l, ll r, ll id){
	tree[id].l = l, tree[id].r = r;
	tree[id].sum = 0;
	if(l == r)return ;
	int mid = Mid(l,r);
	build(l,mid,L(id)), build(mid+1,r,R(id));
}
void updata(ll pos, ll val, ll id){
	if(tree[id].l == tree[id].r)
	{
		tree[id].sum = val;
		return;
	}
	ll mid = Mid(tree[id].l,tree[id].r);
	if(pos <= mid)updata(pos, val, L(id));
	else updata(pos, val, R(id));
	updata_up(id);
}
ll query(ll l, ll r, ll id){
	if(l <= tree[id].l && tree[id].r <= r)return tree[id].sum;
	ll mid = Mid(tree[id].l, tree[id].r);
	ll ans = 0;
	if(l <= mid)ans+=query(l,r,L(id));
	if(r >  mid)ans+=query(l,r,R(id));
	return ans;
}
ll Query(ll x,ll y){ //讓x在y下面
	ll f1 = top[x], f2 = top[y];
	ll ans = 0;
	while(f1 != f2)
	{
		if(dep[f1]<dep[f2])swap(f1,f2),swap(x,y);

		ans += query(p[f1],p[x],1);
		x = fa[f1];
		f1 = top[x];
	}
	if(dep[x] > dep[y])swap(x,y);
	return ans + query(p[x],p[y],1) - query(p[x],p[x],1);;
}
void change(ll pos, ll val){
	Edge &E = edge[pos<<1]; if(E.yes == false) E = edge[pos<<1|1];
	E.dis = val;
	updata(p[E.to], val, 1);
}
ll n, m;
void init(){
	memset(head, -1, sizeof(head)), edgenum = 0;
	memset(son, -1, sizeof(son));
	tree_id = 1;
}
int main(){
	ll i, j, u, v, d;
	while(~scanf("%I64d %I64d",&n,&m))
	{
		init();
		for(i = 1; i < n; i++) {
			scanf("%I64d %I64d %I64d",&u,&v,&d);
			addedge(u,v,d);
			addedge(v,u,d);
		}
		dfs(1,1,0);
		getpos(1,1);
		build(1,n,1); //建立虛擬根節點1
		updata(p[1],0,1);
		for(i = 2; i <= n; i++)	updata(p[i],dis[i],1);
		while(m--)
		{
			scanf("%I64d %I64d %I64d",&d,&u,&v);
			if(d == 0)change(u-1,v);
			else printf("%I64d\n",Query(u,v));
		}
	}
	return 0;
}
/*
7 99
7 1 1
1 2 2
1 3 3
2 6 4
2 4 5
3 5 6

1 6 3
1 2 5
1 4 5
1 1 5
1 7 5

0 1 100
1 7 5
0 6 100
1 3 5
1 5 3
1 5 4

*/