牛客 - 小V和gcd树

传送门：牛客 - 小V和gcd树

思路分析

将每个点的贡献设为他与他父亲的边权
对于修改操作，只修改其重儿子的边权
对于查询操作，先跳到顶端处，加上这个点和他父亲的边权，再跳到他的父亲

样例输入

6 5 
3 6 4 9 9 9 
2 1
3 2
4 2
5 4
6 5 
2 4 2 2 
2 1 3 5 
1 3 4 
2 3 6 3 
2 2 3 4

样例输出

0 
2 
2 
1

AC代码

#include <bits/stdc++.h>
#define ls x<<1
#define rs x<<1|1
#define fi first
#define se second
#define ll long long
#define pb push_back
#define mp make_pair
#define fun function
#define sz(x) (x).size()
#define lowbit(x) (x)&(-x)
#define all(x) (x).begin(),(x).end()
#define mem(a,b) memset(a,b,sizeof(a))

namespace FastIO {
#define BUF_SIZE 100000
#define OUT_SIZE 100000
    bool IOerror=0;
    inline char nc() {
        static char buf[BUF_SIZE],*p1=buf+BUF_SIZE,*pend=buf+BUF_SIZE;
        if(p1==pend) {
            p1=buf;
            pend=buf+fread(buf,1,BUF_SIZE,stdin);
            if(pend==p1) {
                IOerror=1;
                return -1;
            }
        }
        return *p1++;
    }
    inline bool blank(char ch) {
        return ch==' '||ch=='\n'||ch=='\r'||ch=='\t';
    }
    template<class T> inline bool read(T &x) {
        bool sign=0;
        char ch=nc();
        x=0;
        for(; blank(ch); ch=nc());
        if(IOerror)return false;
        if(ch=='-')sign=1,ch=nc();
        for(; ch>='0'&&ch<='9'; ch=nc())x=x*10+ch-'0';
        if(sign)x=-x;
        return true;
    }
    template<class T,class... U>bool read(T& h,U&... t) {
        return read(h)&&read(t...);
    }
#undef OUT_SIZE
#undef BUF_SIZE
};
using namespace std;
using namespace FastIO;

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

const int INF = 0x3f3f3f3f;
const int N = 1e5+10;

int a[N],w[N];
vector<int>e[N];
int siz[N],son[N],fa[N],top[N],dep[N],dfn[N],cnt;

void dfs1(int u,int f){
    fa[u]=f;
    dep[u]=dep[f]+1;
    siz[u]=1;
    for(auto v:e[u]){
        if(v==f) continue;
        dfs1(v,u);
        siz[u]+=siz[v];
        if(siz[v]>siz[son[u]]) son[u]=v;
    }
}

void dfs2(int u,int t){
    top[u]=t;
    dfn[u]=++cnt;
    w[cnt]=__gcd(a[u],a[fa[u]]);
    if(!son[u]) return ;
    dfs2(son[u],t);
    for(auto v:e[u]){
        if(v==son[u]|v==fa[u]) continue;
        dfs2(v,v);
    }
}

int getsum(int l,int r,int k){
    int ans=0;
    for(int i=l;i<=r;i++) ans+=(w[i]<=k);
    return ans;
}

int query(int x,int y,int k){
    int ans=0;
    while(top[x]!=top[y]){
        if(dep[top[x]]<dep[top[y]]) swap(x,y);
        ans+=getsum(dfn[top[x]]+1,dfn[x],k);
        x=top[x];
        ans+=(__gcd(a[x],a[fa[x]])<=k);
        x=fa[x];
    }
    if(dep[x]>dep[y]) swap(x,y); 
    ans+=getsum(dfn[x]+1,dfn[y],k);
    return ans;
}

int main() {

#ifdef xiaofan
    freopen("1.in","r",stdin);
    freopen("1.out","w",stdout);
#endif

    int n,q;
    read(n,q);
    for(int i=1;i<=n;i++) read(a[i]);
    for(int i=1;i<n;i++){
        int u,v;
        read(u,v);
        e[u].pb(v);
        e[v].pb(u);
    }
    dfs1(1,1);
    dfs2(1,1);
    while(q--){
        int op,u,v,k;
        read(op,u,v);
        if(op==1){
            a[u]=v;
            w[dfn[u]]=__gcd(a[u],a[fa[u]]);
            if(son[u]) w[dfn[son[u]]]=__gcd(a[son[u]],a[u]);
            
        }else{
            read(k);
            printf("%d\n",query(u,v,k));
        }
    }
    




    return 0;
}