[BZOJ 2002] [HNOI2010] Danfei sheep (Link Cut Tree)

[BZOJ 2002] [HNOI2010] Danfei sheep (Link Cut Tree)

Face questions

One day, Lostmonkey invented a super-elastic device, in order to show off in front of his friend's sheep, he was invited to play a game with little sheep. A game start, Lostmonkey put on the ground along a line of n devices, each device sets the initial elastic coefficient ki, when sheep reaches an i-th unit, it will play the next step ki, ki to reach the i th + means, if the presence of the i + ki th device, sheep Danfei. Sheep want to know when it is starting from the i-th unit, after a few shells will Danfei. To make the game more interesting, Lostmonkey can modify the elasticity coefficient of an elastic device, any time elasticity coefficients are positive integers.

analysis

First of all point number + 1, n + 1 nodes to create a virtual representation Danfei. If i + ki> n even edge (i, n + 1) or even the edge (i, i + ki).

Modification is the first cut edge plus side

Query query is actually n + x to the size of the subtrees path length .split (x, n + 1) 1 is the answer -1

Code

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm> 
#define maxn 200000
using namespace std;
struct link_cut_tree{
#define lson(x) (tree[x].ch[0])
#define rson(x) (tree[x].ch[1])
#define fa(x) (tree[x].fa)
    struct node{
        int ch[2];
        int fa;
        int sz;
        int revm;
    }tree[maxn+5];
    inline bool is_root(int x){
        return !(lson(fa(x))==x||rson(fa(x))==x);
    }
    inline int check(int x){
        return rson(fa(x))==x;
    }
    void push_up(int x){
        tree[x].sz=tree[lson(x)].sz+tree[rson(x)].sz+1;
    }
    void reverse(int x){
        swap(lson(x),rson(x));
        tree[x].revm^=1;
    }
    void push_down(int x){
        if(tree[x].revm){
            reverse(lson(x));
            reverse(rson(x));
            tree[x].revm=0;
        }
    }
    void push_down_all(int x){
        if(!is_root(x)) push_down_all(fa(x));
        push_down(x);
    }
    void rotate(int x){
        int y=fa(x),z=fa(y),k=check(x),w=tree[x].ch[k^1];
        tree[y].ch[k]=w;
        tree[w].fa=y;
        if(!is_root(y)) tree[z].ch[check(y)]=x;
        tree[x].fa=z;
        tree[x].ch[k^1]=y;
        tree[y].fa=x;
        push_up(y);
        push_up(x);
    }
    void splay(int x){
        push_down_all(x);
        while(!is_root(x)){
            int y=fa(x);
            if(!is_root(y)){
                if(check(x)==check(y)) rotate(y);
                else rotate(x);
            }
            rotate(x);
        }
        push_up(x);
    }
    void access(int x){
        for(int y=0;x;y=x,x=fa(x)){
            splay(x);
            rson(x)=y;
            push_up(x);
        }
    }
    void make_root(int x){
        access(x);
        splay(x);
        reverse(x);
    }
    void split(int x,int y){
        make_root(x);
        access(y);
        splay(y);
    }
    void link(int x,int y){
        make_root(x);
        fa(x)=y;
    }
    void cut(int x,int y){
        split(x,y);
        lson(y)=fa(x)=0;
        push_up(y);
    }
    int query(int x,int y){//查询x到y的路径长度，即split出来的子树大小-1 
        split(x,y);
        return tree[y].sz-1;
    }
}T;

int n,m;
int a[maxn+5];
//虚拟节点n+1表示被弹飞 
inline int get_nex(int x,int k){//找到被弹到的节点 
    if(x+k<=n) return x+k;
    else return n+1;
}

int main(){
    int cmd,x,k;
    scanf("%d",&n);
    for(int i=1;i<=n+1;i++) T.tree[i].sz=1;
//  T.link(4,5);
    for(int i=1;i<=n;i++){
        scanf("%d",&a[i]);
        T.link(i,get_nex(i,a[i]));
    }
    scanf("%d",&m);
    for(int i=1;i<=m;i++){
        scanf("%d",&cmd);
        if(cmd==1){
            scanf("%d",&x);
            x++;
            printf("%d\n",T.query(x,n+1));//查询x到n+1路径长度 
        }else{
            scanf("%d %d",&x,&k);
            x++;
            T.cut(x,get_nex(x,a[x]));
            a[x]=k;
            T.link(x,get_nex(x,a[x]));
        }
    }
     
}