树链剖分

luo 树剖模板题 https://www.luogu.org/problemnew/show/P3384

代码：

#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;

const int maxn=100000+10;

struct my{
    int v,Next;
};

typedef long long ll;

my edge[maxn*2];
ll p;
int adj[maxn],tot;
ll w[maxn];
int dep[maxn],son[maxn],siz[maxn],fa[maxn],top[maxn];
ll tree[maxn<<2],add[maxn<<2];
int id[maxn],cnt;
ll nw[maxn];
int n;

void dfs1(int x,int f,int deep){
    dep[x]=deep;//记录深度
    siz[x]=1;//记录子树大小
    fa[x]=f;//记录父亲节点
    int maxx=-1;
    for (int i=adj[x];i;i=edge[i].Next){
        int v=edge[i].v;
        if(v==f) continue;
        dfs1(v,x,deep+1);
        siz[x]+=siz[v];
        if(maxx<siz[v]) son[x]=v,maxx=siz[v];//更新最大子树，即找重儿子
    }
}

void dfs2(int x,int f,int topf){
    id[x]=++cnt;//给节点重新编号，因为每个子树节点以及每条重链编号都是有序的，所以可以线段树维护
    nw[cnt]=w[x];
    top[x]=topf;//记录链的顶端
    if(!son[x]) return ;
    dfs2(son[x],x,topf);
    for (int i=adj[x];i;i=edge[i].Next){
        int v=edge[i].v;
        if(v==f||v==son[x]) continue;
        dfs2(v,x,v);//v,v是因为每个轻儿子是一条链的顶部
    }
}

void myinsert(int u,int v){
    edge[++tot].v=v;
    edge[tot].Next=adj[u];
    adj[u]=tot;
}

void pushdown(int x,int ln,int rn){
     if(add[x]){
        add[x<<1]=(add[x<<1]+add[x])%p;
        add[x<<1|1]=(add[x<<1|1]+add[x])%p;
        tree[x<<1]=(tree[x<<1]+add[x]*ln%p)%p;
        tree[x<<1|1]=(tree[x<<1|1]+add[x]*rn%p)%p;
        add[x]=0;
     }
}

void pushup(int x){
    tree[x]=(tree[x<<1]+tree[x<<1|1])%p;
}

void build(int l,int r,int rt){
     if(l==r){
        tree[rt]=nw[l];
        return ;
     }
     int mid=(l+r)>>1;
     build(l,mid,rt<<1);
     build(mid+1,r,rt<<1|1);
     pushup(rt);
}

void change(int l,int r,int rt,int L,int R,ll c){
    if(l>=L&&r<=R){
        add[rt]=(add[rt]+c)%p;
        tree[rt]=(tree[rt]+(r-l+1)*c%p)%p;
        return ;
    }
    int mid=(l+r)>>1;
    pushdown(rt,mid-l+1,r-mid);
    if(L<=mid) change(l,mid,rt<<1,L,R,c);
    if(R>mid) change(mid+1,r,rt<<1|1,L,R,c);
    pushup(rt);
}

ll getans(int l,int r,int rt,int L,int R){
    if(l>=L&&r<=R){
        return tree[rt];
    }
    int  mid=(l+r)>>1;
    pushdown(rt,mid-l+1,r-mid);
    ll ans=0;
    if(L<=mid) ans=(ans+getans(l,mid,rt<<1,L,R))%p;
    if(R>mid) ans=(ans+getans(mid+1,r,rt<<1|1,L,R))%p;
    return ans%p;
}

ll getans1(int x,int y){
    ll ans=0;
    while(top[x]!=top[y]){
        if(dep[top[x]]<dep[top[y]]) swap(x,y);
        ans=(ans+getans(1,n,1,id[top[x]],id[x]))%p;
        x=fa[top[x]];
    }
    if(dep[x]>dep[y]) swap(x,y);
    ans=(ans+getans(1,n,1,id[x],id[y]))%p;
    return ans%p;
}

void change1(int x,int y,ll z){
    while(top[x]!=top[y]){
         if(dep[top[x]]<dep[top[y]]) swap(x,y);//相当于一直往上跳到两个点在同一条链为止，可画图模拟一波
         change(1,n,1,id[top[x]],id[x],z);
         x=fa[top[x]];
    }
   if(dep[x]>dep[y]) swap(x,y);
   change(1,n,1,id[x],id[y],z);
}

ll getans2(int x){
   return getans(1,n,1,id[x],id[x]+siz[x]-1)%p;//因为节点是有序的，所以求子树大小就可以直接加了
}

void change2(int x,ll z){
    change(1,n,1,id[x],id[x]+siz[x]-1,z);
}

int main(){
    freopen("read.in","r",stdin);
    int m,root;
    scanf("%d%d%d%lld",&n,&m,&root,&p);
    for (int i=1;i<=n;i++){
        scanf("%lld",&w[i]);
    }
    for (int i=1;i<n;i++){
        int u,v;
        scanf("%d%d",&u,&v);
        myinsert(u,v);
        myinsert(v,u);
    }
    dfs1(root,root,1);
    dfs2(root,root,root);
    build(1,n,1);
    int opt,x,y;
    ll z;
    while(m--){
        scanf("%d",&opt);
        if(opt==1){
            scanf("%d%d%lld",&x,&y,&z);
            change1(x,y,z);
        }
        if(opt==2){
            scanf("%d%d",&x,&y);
            printf("%lld
",getans1(x,y));
        }
        if(opt==3){
           scanf("%d%lld",&x,&z);
           change2(x,z);
        }
        if(opt==4){
            scanf("%d",&x);
            printf("%lld
",getans2(x));
        }
    }
return 0;
}

#include<cstdio>
#include<algorithm>
#include<cstring>
using namespace std;

struct my{
    int v,Next;
};

struct node{
    int l,r,max,sum;
};

const int maxn=100000+10;
int adj[maxn],tot,n;
char ch[50];
int w[maxn],c[maxn],dep[maxn],fa[maxn],son[maxn],siz[maxn];
int top[maxn],cnt,len,mp[maxn],id[maxn];
int root[maxn];
my edge[maxn<<1];
node tree[maxn*25];

void myinsert(int u,int v){
    edge[++tot].v=v;
    edge[tot].Next=adj[u];
    adj[u]=tot;
}

void dfs1(int x,int f,int deep){
    siz[x]=1;
    dep[x]=deep;
    fa[x]=f;
    int maxx=-1;
    for (int i=adj[x];i;i=edge[i].Next){
        int v=edge[i].v;
        if(v==f) continue;
        dfs1(v,x,deep+1);
        siz[x]+=siz[v];
        if(siz[v]>maxx) maxx=siz[v],son[x]=v;
    }
}

void dfs2(int x,int f,int topf){
    id[x]=++cnt;
    mp[cnt]=x;
    top[x]=topf;
    if(!son[x]) return ;
    dfs2(son[x],x,topf);
    for (int i=adj[x];i;i=edge[i].Next){
        int v=edge[i].v;
        if(v==f||v==son[x]) continue;
        dfs2(v,x,v);
    }
}

void pushup(int x){
    tree[x].max=max(tree[tree[x].l].max,tree[tree[x].r].max);
    tree[x].sum=tree[tree[x].l].sum+tree[tree[x].r].sum;
}

void update(int &rt,int l,int r,int pos,int C){
    if(!rt) rt=++len;
    if(l==r){
        tree[rt].max=C;
        tree[rt].sum=C;
    return ;
    }
    int mid=(l+r)>>1;
    if(pos<=mid) update(tree[rt].l,l,mid,pos,C);
    else update(tree[rt].r,mid+1,r,pos,C);
    pushup(rt);
}

void del(int &rt,int l,int r,int pos){
    if(!rt) return ;
    if(l==r){
        tree[rt].max=tree[rt].sum=0;
    return ;
    }
    int mid=(l+r)>>1;
    if(pos<=mid) del(tree[rt].l,l,mid,pos);
    else del(tree[rt].r,mid+1,r,pos);
    pushup(rt);
}

int getmax(int &rt,int l,int r,int L,int R){
    if(!rt) return 0;
    if(l>=L&&r<=R){
        return tree[rt].max;
    }
    int ans=0;
    int mid=(l+r)>>1;
    if(L<=mid) ans=max(getmax(tree[rt].l,l,mid,L,R),ans);
    if(R>mid) ans=max(ans,getmax(tree[rt].r,mid+1,r,L,R));
    return ans;
}

int getsum(int &rt,int l,int r,int L,int R){
    if(!rt) return 0;
    if(l>=L&&r<=R){
        return tree[rt].sum;
    }
    int mid=(l+r)>>1;
    int ans=0;
    if(L<=mid) ans+=getsum(tree[rt].l,l,mid,L,R);
    if(R>mid) ans+=getsum(tree[rt].r,mid+1,r,L,R);
    return ans;
}

void change1(int x,int p){
    del(root[c[x]],1,n,id[x]);
    c[x]=p;
    update(root[c[x]],1,n,id[x],w[x]);
}  

void change2(int x,int p){
    del(root[c[x]],1,n,id[x]);
    w[x]=p;
    update(root[c[x]],1,n,id[x],w[x]);
}

int getans1(int x,int y){
    int ans=0;
    int k=c[x];
    while(top[x]!=top[y]){
        if(dep[top[x]]<dep[top[y]]) swap(x,y);
        ans+=getsum(root[k],1,n,id[top[x]],id[x]);
        x=fa[top[x]];
    }
    if(dep[x]>dep[y]) swap(x,y);
    ans+=getsum(root[k],1,n,id[x],id[y]);
    return ans;
}

int getans2(int x,int y){
    int ans=0;
    int k=c[x];
    while(top[x]!=top[y]){
        if(dep[top[x]]<dep[top[y]]) swap(x,y);
        ans=max(ans,getmax(root[k],1,n,id[top[x]],id[x]));
        x=fa[top[x]];
    }
    if(dep[x]>dep[y]) swap(x,y);
    ans=max(ans,getmax(root[k],1,n,id[x],id[y]));
    return ans;
}

int main(){
    //freopen("read.in","r",stdin);
    int u,v;
    int m;
    scanf("%d%d",&n,&m);
    for (int i=1;i<=n;i++){
        scanf("%d%d",&w[i],&c[i]);
    }
    for (int i=1;i<n;i++){
        scanf("%d%d",&u,&v);
        myinsert(u,v);
        myinsert(v,u);
    }
    dfs1(1,1,1);
    dfs2(1,1,1);
    for (int i=1;i<=n;i++){
        update(root[c[mp[i]]],1,n,i,w[mp[i]]);
    }
    int x,p;
    while(m--){
        scanf("%s",ch);
        if(ch[1]=='C'){
           scanf("%d%d",&x,&p);
           change1(x,p);
        }
        if(ch[1]=='W'){
            scanf("%d%d",&x,&p);
            change2(x,p);
        }
        if(ch[1]=='S'){
            scanf("%d%d",&x,&p);
            printf("%d
",getans1(x,p));
        }
        if(ch[1]=='M'){
            scanf("%d%d",&x,&p);
            printf("%d
",getans2(x,p));
        }
    }
return 0;
}