2023/7/5学习日记 树部分

学习树剖，树上差分，树剖LCA

一.P3038 [USACO11DEC] Grass Planting G

树链剖分点权转边权

#include<cstdio>
#include<algorithm>
#include<iostream>
#pragma GCC optimize(1)
#pragma GCC optimize(2)
#pragma GCC optimize(3)
#define lson pos<<1
#define rson pos<<1|1
using namespace std;
const int maxn=1e5+1;
int n,m,tot,cnt;
int a[maxn];
int head[maxn],nxt[maxn<<1],to[maxn<<1];
int deep[maxn],size[maxn],son[maxn],fa[maxn];
int top[maxn],id[maxn],w[maxn];
int tree[maxn<<2],lazy[maxn<<2];
void add(int x,int y)
{
    to[++tot]=y;
    nxt[tot]=head[x];
    head[x]=tot;
}
void dfs1(int x,int f)
{
    deep[x]=deep[f]+1;
    size[x]=1;
    fa[x]=f;
    for(int i=head[x];i;i=nxt[i])
    {
        int y=to[i];
        if(y==f)
            continue;
        dfs1(y,x);
        size[x]+=size[y];
        if(!son[x]||size[y]>size[son[x]])
            son[x]=y;
    }
}
void dfs2(int x,int t)
{
    id[x]=++cnt;
    w[cnt]=a[x];
    top[x]=t;
    if(!son[x])
        return;
    dfs2(son[x],t);
    for(int i=head[x];i;i=nxt[i])
    {
        int y=to[i];
        if(y==fa[x]||y==son[x])
            continue;
        dfs2(y,y);
    }
}
void build(int pos,int l,int r)
{
    int mid=(l+r)>>1;
    if(l==r)
    {
        tree[pos]=w[l];
        return;
    }
    build(lson,l,mid);
    build(rson,mid+1,r);
    tree[pos]=tree[lson]+tree[rson];
}
void mark(int pos,int l,int r,int k)
{
    tree[pos]+=(r-l+1)*k;
    lazy[pos]+=k;
}
void pushdown(int pos,int l,int r)
{
    int mid=(l+r)>>1;
    mark(lson,l,mid,lazy[pos]);
    mark(rson,mid+1,r,lazy[pos]);
    lazy[pos]=0;
}

void update(int pos,int l,int r,int x,int y,int k)
{
    int mid=(l+r)>>1;
    if(x<=l && r<=y)
    {
        mark(pos,l,r,k);
        return;
    }
    pushdown(pos,l,r);
    if(x<=mid)
        update(lson,l,mid,x,y,k);
    if(y>mid)
        update(rson,mid+1,r,x,y,k);
    tree[pos]=tree[lson]+tree[rson];
}

void upd_chain(int x,int y,int k)
{
    while(top[x]!=top[y])
    {
        if(deep[top[x]]<deep[top[y]])
            swap(x,y);
        update(1,1,n,id[top[x]],id[x],k);
        x=fa[top[x]];
    }
    if(deep[x]<deep[y])
        swap(x,y);
    update(1,1,n,id[y]+1,id[x],k);
}
int query(int pos,int l,int r,int x,int y)
{
    int ret=0;
    int mid=(l+r)>>1;
    if(x<=l && r<=y)
        return tree[pos];
    pushdown(pos,l,r);
    if(x<=mid)
        ret+=query(lson,l,mid,x,y);
    if(y>mid)
        ret+=query(rson,mid+1,r,x,y);
    return ret;
}
int q_chain(int x,int y)
{
    int ret=0;
    while(top[x]!=top[y])
    {
        if(deep[top[x]]<deep[top[y]])
            swap(x,y);
        ret+=query(1,1,n,id[top[x]],id[x]);
        x=fa[top[x]];
    }
    if(deep[x]<deep[y])
        swap(x,y);
    ret+=query(1,1,n,id[y]+1,id[x]);
    return ret;
}
int main()
{
    scanf("%d%d",&n,&m);
    for(int i=1;i<n;i++)
    {
        int x,y;
        scanf("%d%d",&x,&y);
        add(x,y);
        add(y,x);
    }
    dfs1(1,0);
    dfs2(1,1);
    build(1,1,n);
    while(m--)
    {
        char ch;
        cin>>ch;
        if(ch=='P')
        {
            int x,y;
            scanf("%d%d",&x,&y);
            upd_chain(x,y,1);
        }
        else
        {
            int x,y;
            scanf("%d%d",&x,&y);
            printf("%d\n",q_chain(x,y));
        }
    }
    return 0;
}