codeforces 593D(并查集 + LCA)

题意不在描述.

首先我们注意到改变每个点的值时，只会变的更小，每次要除的数为1e18 , 由于log2(1e18)　＜＝　６０　．那么最多只需要除以至多60次大于等于2的数变回变成0，所以我们

只以任意一点为根建立有根树，并且在每次遍历一条链时进行压缩，当该路经值为1，应该被压缩，每次走到多余六十个点直接结束。

#include <bits/stdc++.h>

#define fst first
#define snd second
#define ALL(a) a.begin(), a.end()
#define clr(a, x) memset(a, x, sizeof a)
#define rep(i,x) for(int i=0;i<(int)x;i++)
#define rep1(i,x,y) for(int i=x;i<=(int)y;i++)
#define LOGN  22
typedef long long ll;
using namespace std;

const int N = 2e5 + 10000;
vector<int> tree[N];
int fa[N][LOGN],pa[N] , realpa[N];
int depth[N];
ll val[N*2] , ided[N];
void dfs(int u, int p, int d) {
    depth[u] = d;  pa[u] = p; realpa[u] = p;
    fa[u][0] = p;
    for (int i = 0; i < tree[u].size(); ++i) {
        if (tree[u][i] != p)
            dfs(tree[u][i], u, d + 1);
    }
}

int LCA(int u, int v) {
    if (depth[u] > depth[v]) swap(u, v);
    for (int i = 0; i < LOGN; ++i) {
        if (((depth[v] - depth[u]) >> i) & 1)
            v = fa[v][i];
    }
    if (u == v) return u;
    for (int i = LOGN - 1; i >= 0; --i) {
        if (fa[u][i] != fa[v][i]) {
            u = fa[u][i];
            v = fa[v][i];
        }
    }
    return fa[u][0];
}
void predo(int n) {
    int root = 1;  pa[root] = -1;
    dfs(root, -1, 0);
    depth[0] = -1;
    for (int j = 0; j + 1 < LOGN; ++j) {
        for (int i = 1; i <= n; ++i) {
            if (fa[i][j] < 0) fa[i][j + 1] = -1;
            else fa[i][j + 1] = fa[fa[i][j]][j];
        }
    }
}
typedef pair<int,int> pii;
map<pii,int> M;
ll get_c(int u){ return val[ided[u]]; }
int n,m;
int find(int u){
   if(realpa[pa[u]] == -1 || get_c(pa[u]) > 1) return pa[u];
   else return pa[u] = find(pa[u]);
}
ll cal1(int a,int b,ll c){
   int lca = LCA(a,b);
   int u = a , v = b; ll now = c;
   vector<ll> lt,rt;
   while(u != v){
       if(depth[u] >= depth[v]){
            int fau = find(u);
            if(depth[fau] < depth[lca]) fau = lca;
            if(get_c(u) > 1) lt.push_back(get_c(u));
            u = fau;
       }
       else {
            int fav = find(v);
            if(depth[fav] < depth[lca]) fav = lca;
            if(get_c(v) > 1) rt.push_back(get_c(v));
            v = fav;
       }
       if(lt.size() + rt.size() > 60) return 0;
   }
   if(rt.size()) reverse(ALL(rt));
   rep(i,rt.size()) lt.push_back(rt[i]);
   for(int i=0;i<lt.size();i++){
       now/=lt[i];
   }
   return now;
}
void read(){
   scanf("%d %d",&n,&m);
   rep(i,n-1){
       int u,v; ll w;
       scanf("%d %d %I64d",&u,&v,&w);
       M[pii(u,v)] = M[pii(v,u)] = 1 + i;
       val[1+i] = w;
       tree[u].push_back(v);
       tree[v].push_back(u);
   }
   predo(n);
   rep1(i,2,n) ided[i] = M[pii(i,realpa[i])] ;
   rep1(i,1,m){
      ll cmd , x ,y , z;
      scanf("%I64d %I64d %I64d",&cmd,&x,&y);
      if(cmd == 1) {
          scanf("%I64d",&z);
          printf("%I64d\n",cal1(x,y,z));
      }
      else {
         val[x] = y;
      }
   }
}
int main()
{
   read();
   return 0;
}