[SHOI2012]魔法树

Posted 2022-03-22 szmssf

题目传送门

省选D2T3考板子可真是不多见呢。。。。~~~

这题就是一个裸的树链剖分，对于每一个Add操作，维护从u至v的路径，对于每一个Query操作，询问以u为根的子树之和。如果不会树链剖分可以看我的往期博客，具体细节在代码之中就不多赘述了~

下面给出参考代码：

#include<iostream>
#include<cstdio>
#define N 400005
#define M 800005
#define lc k*2
#define rc k*2+1
#define mid (l+r)/2
#define int long long
using namespace std;
struct node

    int l,r,w,tag;
tree[4*N];
int n,m,r,p,x,y,z;
int v[M],head[M],nxt[M],cnt;
int dep[N],fa[N],son[N],size[N],top[N],seg[N],id;
char q;
int read()

    int x=0,f=1;char ch=getchar();
    while(ch<‘0‘||ch>‘9‘)if(ch==‘-‘)f=-1;ch=getchar();
    while(ch>=‘0‘&&ch<=‘9‘)x=x*10+ch-48;ch=getchar();
    return x*f;

void add(int a,int b)

    v[++cnt]=b;
    nxt[cnt]=head[a];
    head[a]=cnt;

void dfs1(int node,int father)

    dep[node]=dep[father]+1;
    fa[node]=father;
    size[node]=1;
    int maxson=-1;
    for(int i=head[node];i;i=nxt[i])
    
        int go=v[i];
        if(go==father)continue;
        dfs1(go,node);
        size[node]+=size[go];
        if(size[go]>maxson)maxson=size[go],son[node]=go;
    

void dfs2(int node,int topfather)

    seg[node]=++id;
    top[node]=topfather;
    if(!son[node])return;
    dfs2(son[node],topfather);
    for(int i=head[node];i;i=nxt[i])
    
        int go=v[i];
        if(go==fa[node]||go==son[node])continue;
        dfs2(go,go);
    

void build(int l,int r,int k)

    tree[k].l=l;tree[k].r=r;
    if(l==r)return;
    build(l,mid,lc);
    build(mid+1,r,rc);

void pushdown(int k)

    tree[lc].tag+=tree[k].tag;
    tree[rc].tag+=tree[k].tag;
    tree[lc].w+=(tree[lc].r-tree[lc].l+1)*tree[k].tag;
    tree[rc].w+=(tree[rc].r-tree[rc].l+1)*tree[k].tag;
    tree[k].tag=0;
    return;

void pushup(int k)

    tree[k].w=tree[lc].w+tree[rc].w;
    return;

void add(int x,int y,int k)

    int l=tree[k].l,r=tree[k].r;
    if(l>=x&&r<=y)
    
        tree[k].tag+=z;
        tree[k].w+=(r-l+1)*z;
        return;
    
    if(tree[k].tag)pushdown(k);
    if(x<=mid)add(x,y,lc);
    if(y>mid)add(x,y,rc);
    pushup(k);

int query(int x,int y,int k)

    int l=tree[k].l,r=tree[k].r;
    if(l>=x&&r<=y)
    
        return tree[k].w;
    
    if(tree[k].tag)pushdown(k);
    int res=0;
    if(x<=mid)res+=query(x,y,lc);
    if(y>mid)res+=query(x,y,rc);
    return res;

void Tadd(int x,int y)

    while(top[x]!=top[y])
    
        if(dep[top[x]]<dep[top[y]])swap(x,y);
        add(seg[top[x]],seg[x],1);
        x=fa[top[x]];
    
    if(dep[x]>dep[y])swap(x,y);
    add(seg[x],seg[y],1);

int Treequery(int x)

    return query(seg[x],seg[x]+size[x]-1,1);

signed main()

    n=read();
    for(int i=1;i<n;i++)
    
        x=read();y=read();
        x++;y++;
        add(x,y);add(y,x);
    
    dfs1(1,0);dfs2(1,1);
    build(1,n,1);
    m=read();
    while(m--)
    
        cin>>q;
        if(q==‘A‘)
        
            x=read();y=read();z=read();
            x++;y++;
            Tadd(x,y);
        
        else
        
            x=read();
            x++;
            cout<<Treequery(x)<<endl;