树链剖分

https://www.luogu.org/problemnew/show/P3384

知识点 ：1.先切割重边，还记得求出top

　　　　 2.线段树维护dfs序下的val数组，一条链上的数在dfs序中是连续的

　　　　3.求值时就在树上跑，优化在于一条链上的信息可以直接求，顾跳top即可

There is a false in the code : False 1 

#include <bits/stdc++.h>
#define M 200002
using namespace std;
long long n,m,rt,mod;
long long tot = 0;
long long val[M];
long long head[M * 4],cnt = 0;
struct edge
{
    long long to;
    long long nxt;
}e[M * 4];
void add(long long x,long long y)
{
    e[++cnt].nxt = head[x];
    e[cnt].to = y;
    head[x] = cnt;
} 
long long siz[M];
long long son[M],rk[M],tp[M],fa[M],dep[M],top[M];
long long tre[M * 4],lazy[M * 4];
void build(long long t,long long l,long long r)
{
    if(l == r)
    {
        tre[t] = tp[l];
        return;
    }
    long long mid = (l + r) / 2;
    build(t *  2,l,mid);
    build(t * 2 + 1,mid + 1,r);
    tre[t] = (tre[t * 2] + tre[t * 2 + 1]) %  mod; 
}
void up(long long t,long long l,long long r,long long x)
{
    lazy[t] += x;
    lazy[t] %= mod;
    tre[t] += (r - l + 1) * x;
    tre[t] %= mod;
}
void pushdown(long long l,long long r,long long t)
{
    long long mid = (l + r) / 2;
    up(t * 2,l,mid,lazy[t]);
    up(t * 2 + 1,mid + 1,r,lazy[t]);
    lazy[t] = 0;
}
long long query(long long t,long long l,long long r,long long b,long long e)
{
    if(b <= l && r <= e)
    {
        return tre[t] % mod;
    }
    long long mid = (l + r) / 2;
    pushdown(l,r,t);
    long long ans = 0;
    if(b <= mid)ans += query(t * 2,l,mid,b,e);
    ans = ans % mod;
    if(mid < e)ans += query(t * 2 + 1,mid + 1,r,b,e);
    return ans % mod;
}
void updata(long long t,long long l,long long r,long long b,long long e,long long k)
{
    if(b <= l && r <= e)
    {
        tre[t] += (r - l + 1) * k;
        tre[t] %= mod;
        lazy[t] += k;
        lazy[t] %= mod;
        return;
    }
    long long mid = (l + r) / 2;
    pushdown(l,r,t);
    if(b <= mid)updata(t * 2,l,mid,b,e,k);
    if(mid < e)updata(t * 2 + 1,mid + 1,r,b,e,k);
    tre[t] = (tre[t * 2] + tre[t * 2 + 1]) % mod;
}
void dfs1(long long x,long long depth,long long fat)
{
    fa[x] = fat;
    dep[x] = depth;
    siz[x] = 1;
    long long maxn = -1;
    for(long long i = head[x];i;i = e[i].nxt)
    {
        if(e[i].to != fat)
        {
            dfs1(e[i].to,depth + 1,x);
            siz[x] += siz[e[i].to];
            if(maxn < siz[e[i].to] || maxn == -1)
            {
                son[x] = e[i].to;
                maxn = siz[e[i].to];
            }
        }
    }
}
void qupdata(long long l,long long r,long long k)
{
    k %= mod;
    long long fx = l,fy = r;    
    while(top[fx] != top[fy])
    {
        if(dep[top[fx]] < dep[top[fy]])swap(fx,fy);//False 1 : 这里应该是dep[top[fx]] < dep[top[fy]]而并非dep[fx] < dep[fy] 
        updata(1,1,n,rk[top[fx]],rk[fx],k);
        fx = fa[top[fx]];
    }
    if(dep[fx] > dep[fy])swap(fx,fy);
    updata(1,1,n,rk[fx],rk[fy],k);
} 
long long qquery(long long l,long long r)
{
    long long ans = 0;
    long long fx = l ,fy = r;
    while(top[fx] != top[fy])
    {
        if(dep[top[fx]] < dep[top[fy]])swap(fx,fy);
        ans += query(1,1,n,rk[top[fx]],rk[fx]);
        ans %= mod;
        fx = fa[top[fx]];
    }
    if(dep[fx] > dep[fy])swap(fx,fy);
    ans += query(1,1,n,rk[fx],rk[fy]);
    ans %= mod;
    return ans;
}
void rupdata(long long x,long long k)
{
    k %= mod;
    updata(1,1,n,rk[x],rk[x] + siz[x] - 1,k);
}
long long rquery(long long x)
{
    return query(1,1,n,rk[x],rk[x] + siz[x] - 1) % mod;
}
void dfs2(long long x,long long t)
{
    rk[x] = ++tot;
    tp[tot] = val[x];
    top[x] = t;
    if(!son[x])return;
    dfs2(son[x],t);
    for(long long i = head[x];i;i = e[i].nxt)
    {
        long long y = e[i].to;
        if(y != son[x] && y != fa[x])
            dfs2(y,y);
    }
}
int main()
{
    scanf("%lld%lld%lld%lld",&n,&m,&rt,&mod);
    for(long long i = 1;i <= n;i++)scanf("%lld",&val[i]);
    long long x,y,z,a;
    for(long long i = 1;i < n;i++)
    {
        scanf("%lld%lld",&x,&y);
        add(x,y);
        add(y,x);
    }
    dfs1(rt,1,0);
    dfs2(rt,rt);
    build(1,1,n);
    while(m--)
    {
        scanf("%lld",&a);
        if(a == 1)
        {
            scanf("%lld%lld%lld",&x,&y,&z);
            qupdata(x,y,z);    
        }
        else if(a == 2)
        {
            scanf("%lld%lld",&x,&y);
            printf("%lld
",qquery(x,y) % mod);            
        }
        else if(a == 3)
        {
            scanf("%lld%lld",&x,&y);
            rupdata(x,y);    
        }
        else if(a == 4)
        {
            scanf("%lld",&x);
            printf("%lld
",rquery(x) % mod);
        }
    }
    return 0;
}