P3384 【模板】树链剖分

题面

https://www.luogu.org/problem/P3384

题解

#include<iostream>
#include<cstdio>
#include<vector>
#include<algorithm>

using namespace std;

struct node{
  long long lb,rb,add,val;
} tree[405000];

long long n,m,r,p,a[105000],dfsxu[105000],cnt,le[105000],re[105000],sum;
long long d[105000],fa[105000],top[105000],siz[105000],fatson[105000];
vector <long long> to[105000];

void dfs1(long long x,long long da,long long deep){
  long long i,l=to[x].size(),fs=-1,maxd=0;
  fa[x]=da;
  d[x]=deep;
  siz[x]=1;
  for (i=0;i<l;i++) if (to[x][i]!=da) {
    dfs1(to[x][i],x,deep+1);
    siz[x]+=siz[to[x][i]];
    if (siz[to[x][i]]>maxd) maxd=siz[to[x][i]],fs=to[x][i];
  }
  fatson[x]=fs;
}

void dfs2(long long x,bool is){
  long long i,l=to[x].size();
  dfsxu[++cnt]=x;
  le[x]=cnt;
  if (is) top[x]=top[fa[x]]; else top[x]=x;
  if (fatson[x]!=-1) dfs2(fatson[x],1);
  for (i=0;i<l;i++) if (to[x][i]!=fa[x] && to[x][i]!=fatson[x]) dfs2(to[x][i],0);
  re[x]=cnt;
}

void makesegmenttree(long long x,long long l,long long r){
  tree[x].lb=l; tree[x].rb=r;
  if (l==r) {
    tree[x].val=a[dfsxu[l]];
    return;
  }
  long long mid=(l+r)/2;
  makesegmenttree(2*x,l,mid);
  makesegmenttree(2*x+1,mid+1,r);
  tree[x].val=(tree[2*x].val+tree[2*x+1].val)%p;
}

void pushdown(long long x){
  long long kk=tree[x].add;
  tree[x].add=0;
  tree[2*x].val+=(tree[2*x].rb-tree[2*x].lb+1)*kk; tree[2*x].val%=p;
  tree[2*x].add+=kk; tree[2*x].add%=p;
  tree[2*x+1].val+=(tree[2*x+1].rb-tree[2*x+1].lb+1)*kk; tree[2*x+1].val%=p;
  tree[2*x+1].add+=kk; tree[2*x+1].add%=p;
}

void cha(long long x,long long l,long long r){
  if (l>tree[x].rb || r<tree[x].lb) return;
  if (l<=tree[x].lb && tree[x].rb<=r) {
    sum+=tree[x].val;
    sum%=p;
    return;
  }
  if (tree[x].add!=0) pushdown(x);
  cha(2*x,l,r); cha(2*x+1,l,r);
}

void jia(long long x,long long l,long long r,long long kk){
  if (l>tree[x].rb || r<tree[x].lb) return;
  if (l<=tree[x].lb && tree[x].rb<=r) {
    tree[x].val+=kk*(tree[x].rb-tree[x].lb+1);
    tree[x].val%=p;
    tree[x].add+=kk;
    tree[x].add%=p;
    return;
  }
  if (tree[x].add!=0) pushdown(x);
  jia(2*x,l,r,kk); jia(2*x+1,l,r,kk);
  tree[x].val=(tree[2*x].val+tree[2*x+1].val)%p;
}

void jialian(long long u,long long v,long long kk){
  while (top[u]!=top[v]) {
    if (d[top[u]]<d[top[v]]) swap(u,v);
    jia(1,le[top[u]],le[u],kk);
    u=fa[top[u]];
  }
  if (d[u]<d[v]) swap(u,v);
  jia(1,le[v],le[u],kk);
}

void chalian(long long u,long long v){
  while (top[u]!=top[v]) {
    if (d[top[u]]<d[top[v]]) swap(u,v);
    cha(1,le[top[u]],le[u]);
    u=fa[top[u]];
  }
  if (d[u]<d[v]) swap(u,v);
  cha(1,le[v],le[u]);
}

int main() {
  //freopen("dd.cpp","r",stdin);
  long long i,u,v,opt,k;
  scanf("%lld %lld %lld %lld",&n,&m,&r,&p);
  for (i=1;i<=n;i++) {
    scanf("%lld",&a[i]);
    a[i]%=p;
  }
  for (i=1;i<n;i++) {
    scanf("%lld %lld",&u,&v);
    to[u].push_back(v);
    to[v].push_back(u);
  }
  cnt=0;
  dfs1(r,-1,1);
  dfs2(r,0);
  /*
  cout<<"ylq::";
  for (i=1;i<=n;i++) cout<<dfsxu[i]<<" ";
  puts("");
  for (i=1;i<=n;i++) cout<<"ylq"<<le[i]<<" "<<re[i]<<endl;
  */
  makesegmenttree(1,1,n);
  for (i=1;i<=m;i++) {
    scanf("%lld",&opt);
    if (opt==4) {
      scanf("%lld",&u);
      sum=0;
      //printf("ylq::%lld %d\n",le[u],re[u]);
      cha(1,le[u],re[u]);
      printf("%lld\n",sum);
    }
    if (opt==3) {
      scanf("%lld %lld",&u,&k);
      //printf("ylq::%lld %lld %d\n",le[u],re[u],k);
      jia(1,le[u],re[u],k);
    }
    if (opt==1) {
      scanf("%lld %lld %lld",&u,&v,&k);
      jialian(u,v,k);
    }
    if (opt==2) {
      scanf("%lld %lld",&u,&v);
      sum=0;
      chalian(u,v);
      printf("%lld\n",sum);
    }
  }
}