BZOJ1036: [ZJOI2008]树的统计Count

题目链接

单点修改，区间最大值，区间和。
树链剖分裸的不能再裸了。
LCT也可以完成。

1.树链剖分

#include <cstdio>
#include <iostream>
#include <queue>
#include <vector>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <stack>
#define N 30005 
#define M 200005
#define INF 1e9
#define mod 1000000
using namespace std;
typedef long long ll;
typedef pair<ll,ll> pa;

int read()
{
    int x=0,f=1;char ch=getchar();
    while(!isdigit(ch)){if(ch=='-') f=-1;ch=getchar();}
    while(isdigit(ch)){x=(x<<1)+(x<<3)+ch-'0';ch=getchar();}
    return x*f;
}

int n,m,cnt,ind,T;
int b[N<<1],p[N],nextedge[N<<1];
int deep[N],fa[N],son[N],sz[N],pos[N],ftree[N],top[N],a[N];

class Seg_Tree{
    public:
        int l,r,mx,sum;
}e[N<<2];

void Add(int x,int y)
{
    cnt++;
    b[cnt]=y;
    nextedge[cnt]=p[x];
    p[x]=cnt;
}

void Anode(int x,int y){
    Add(x,y);Add(y,x);
}

void Input_Init()
{
    n=read();
    for(int i=1;i<n;i++)
    {
        static int x,y;
        x=read(),y=read();
        Anode(x,y);
    }
    for(int i=1;i<=n;i++) a[i]=read();
}

void Dfs(int x)
{
    sz[x]=1;
    for(int i=p[x];i;i=nextedge[i])
    {
        int v=b[i];
        if(v==fa[x]) continue;
        deep[v]=deep[x]+1;fa[v]=x;
        Dfs(v);sz[x]+=sz[v];
        son[x]=sz[son[x]]>sz[v]?son[x]:v;
    }
}

void dfs(int x,int root)
{
    pos[x]=++ind;ftree[pos[x]]=x;
    top[x]=root;
    if(!son[x]) return;
    dfs(son[x],root);
    for(int i=p[x];i;i=nextedge[i])
    {
        int v=b[i];
        if(v!=fa[x]&&v!=son[x]) dfs(v,v);
    }
}

void pushup(int p){
    e[p].mx=max(e[p<<1].mx,e[p<<1|1].mx);
    e[p].sum=e[p<<1].sum+e[p<<1|1].sum;
}

void Build(int p,int l,int r)
{
    e[p].l=l,e[p].r=r;
    if(l==r)
    {
        e[p].mx=e[p].sum=a[ftree[l]];
        return;
    }
    int mid=l+r>>1;
    Build(p<<1,l,mid);Build(p<<1|1,mid+1,r);
    pushup(p);
}

void Solve_Change(int p,int x,int y)
{
    int l=e[p].l,r=e[p].r,mid=l+r>>1;
    if(l==x&&r==x)
    {
        e[p].mx=e[p].sum=y;
        return;
    }
    if(x<=mid) Solve_Change(p<<1,x,y);
    else Solve_Change(p<<1|1,x,y);
    pushup(p);
}

int Query_Max(int p,int x,int y)
{
    int l=e[p].l,r=e[p].r,mid=l+r>>1;
    if(l==x&&y==r)
        return e[p].mx;
    if(y<=mid) return Query_Max(p<<1,x,y);
    if(x>mid) return Query_Max(p<<1|1,x,y);
    return max(Query_Max(p<<1,x,mid),Query_Max(p<<1|1,mid+1,y));
}

void Solve_Max(int x,int y)
{
    int fx=top[x],fy=top[y];
    int rtn=-INF;
    while(fx!=fy)
    {
        if(deep[fx]<deep[fy]) swap(x,y),swap(fx,fy);
        rtn=max(rtn,Query_Max(1,pos[fx],pos[x]));
        x=fa[fx],fx=top[x];
    }
    if(deep[x]<deep[y]) swap(x,y);
    rtn=max(rtn,Query_Max(1,pos[y],pos[x]));
    printf("%d\n",rtn);
}

int Query_Sum(int p,int x,int y)
{
    int l=e[p].l,r=e[p].r,mid=l+r>>1;
    if(l==x&&y==r)
        return e[p].sum;
    if(y<=mid) return Query_Sum(p<<1,x,y);
    if(x>mid) return Query_Sum(p<<1|1,x,y);
    return Query_Sum(p<<1,x,mid)+Query_Sum(p<<1|1,mid+1,y);
}

void Solve_Sum(int x,int y)
{
    int fx=top[x],fy=top[y];
    int rtn=0;
    while(fx!=fy)
    {
        if(deep[fx]<deep[fy]) swap(x,y),swap(fx,fy);
        rtn+=Query_Sum(1,pos[fx],pos[x]);
        x=fa[fx],fx=top[x];
    }
    if(deep[x]<deep[y]) swap(x,y);
    rtn+=Query_Sum(1,pos[y],pos[x]);
    printf("%d\n",rtn);
}

void Solve()
{
    m=read();
    char ch[10];static int x,y;
    while(m--)
    {
        scanf("%s",ch);x=read(),y=read();
        if(ch[1]=='M') Solve_Max(x,y);
        else if(ch[1]=='S') Solve_Sum(x,y);
        else Solve_Change(1,pos[x],y);
    }
}

int main()
{
    Input_Init(); 
    Dfs(1);dfs(1,1);Build(1,1,n);
    Solve();
    return 0;
}

刚学LCT。。拿来练习一下。（但是比树链剖分慢很多╮(╯▽╰)╭）
2.LCT

#include <cstdio>
#include <iostream>
#include <queue>
#include <vector>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <stack>
#define N 30005 
#define M 2001005
#define INF 1e9
using namespace std;
typedef long long ll;
typedef pair<ll,ll> pa;

int read()
{
    int x=0,f=1;char ch=getchar();
    while(!isdigit(ch)){if(ch=='-') f=-1;ch=getchar();}
    while(isdigit(ch)){x=(x<<1)+(x<<3)+ch-'0';ch=getchar();}
    return x*f;
}

int n,m,top,cnt;
int b[N<<1],p[N],nextedge[N<<1];
int mx[N],tag[N],a[N],son[N][2],st[N],fa[N],sum[N];
bool rev[N];

void Add(int x,int y)
{
    cnt++;
    b[cnt]=y;
    nextedge[cnt]=p[x];
    p[x]=cnt;
}

void Anode(int x,int y){
    Add(x,y);Add(y,x);
}

void dfs(int x)
{
    for(int i=p[x];i;i=nextedge[i])
    {
        int v=b[i];
        if(v==fa[x]) continue;
        fa[v]=x;dfs(v);
    }
}

void Input_Init()
{
    n=read();mx[0]=-INF;
    for(int i=1;i<n;i++)
    {
        static int x,y;
        x=read(),y=read();
        Anode(x,y);
    }
    for(int i=1;i<=n;i++) sum[i]=a[i]=mx[i]=read();
    dfs(1);
}

bool isroot(int x){
    return son[fa[x]][0]!=x&&son[fa[x]][1]!=x;
}

void pushup(int k)
{
    int l=son[k][0],r=son[k][1];
    mx[k]=max(max(mx[l],mx[r]),a[k]);
    sum[k]=sum[l]+sum[r]+a[k];
}

void pushdown(int k)
{
    int l=son[k][0],r=son[k][1];
    if(rev[k])
    {
        rev[k]=0;rev[l]^=1;rev[r]^=1;
        swap(son[k][0],son[k][1]);
    }
}

void Rotate(int x)
{
    int y=fa[x],z=fa[y],l,r;
    l=son[y][1]==x;r=l^1;
    if(!isroot(y)) son[z][son[z][1]==y]=x;
    fa[x]=z;fa[y]=x;fa[son[x][r]]=y;
    son[y][l]=son[x][r];son[x][r]=y;
    pushup(y);pushup(x);
}

void Splay(int x)
{
    top=0;st[++top]=x;
    for(int i=x;!isroot(i);i=fa[i]) st[++top]=fa[i];
    while(top) pushdown(st[top--]);
    while(!isroot(x))
    {
        int y=fa[x],z=fa[y];
        if(!isroot(y)) {
            if(son[z][0]==y^son[y][0]==x) Rotate(x);
            else Rotate(y);
        }
        Rotate(x);
    }
}

void Access(int x)
{
    for(int t=0;x;t=x,x=fa[x])
        Splay(x),son[x][1]=t,pushup(x);
}

void Make_Root(int x){
    Access(x);Splay(x);rev[x]^=1;
}

void Solve_Change(int x,int y){
    Splay(x);mx[x]=sum[x]=a[x]=y;
    pushup(x);
}

void Solve_Max(int x,int y)
{
    Make_Root(x);Access(y);Splay(y);
    printf("%d\n",mx[y]);
}

void Solve_Sum(int x,int y)
{
    Make_Root(x);Access(y);Splay(y);
    printf("%d\n",sum[y]);
}

void Solve()
{
    m=read();
    while(m--)
    {
        char ch[10];static int x,y;
        scanf("%s",ch);x=read(),y=read();
        if(ch[0]=='C') Solve_Change(x,y);
        else if(ch[1]=='M') Solve_Max(x,y);
        else Solve_Sum(x,y);
    }
}

int main()
{
    Input_Init();
    Solve(); 
    return 0;
}