LCT - hdu5002 Tree

题目：

http://acm.hdu.edu.cn/showproblem.php?pid=5002

题意：

给一棵树树，提供四种操作

1：删除(x,y)边，添加(a,b)边，保证操作前后都是合法的树

2：修改a--b路径上所有点的权值为x

3：a--b路径上所有点的权值增加d

4：输出a--b路径上的第二大值及出现的次数，这里的第二大指的为严格第二大，即1 1 2 2 3 3 3 的第二大值为2

思路：

算是LCT的模板题，利用LCT的各种操作实现以上功能，这里讲一下怎么删除(x,y)边，因为LCT的基础cut操作只能删除x与x的父结点的连边

changeRoot(x);//调整x为树的根节点
cut(y);//因为x--y边一定存在，x为根，则y的父结点定为x

这题比较麻烦的是维护第二大值，嗯思路是对伸展树每个结点维护第一大数及出现的次数，再维护第二大数及出现的次数，则伸展树的每个结点的第二大值为自身的权值，左儿子的第一，第二大值，右儿子的第一，第二大值这五个数中的严格第二大

代码：

#include 
#include 
#include 
#include 
using namespace std;

const int MAXSIZE = 100010;
const int INF = 0x1FFFFFFF;

struct Node{
    int sz;
    Node *ch[2], *pnt;
    bool rt;
    bool rev;

    bool ischange;
    int add;
    int wei;
    int fir, firnum, sec, secnum;
};

Node nodes[MAXSIZE];
Node *null = &nodes[0];
int ncnt;

int sortarr[6][2];
void push_up(Node *x){
    x->sz = 1 + x->ch[0]->sz + x->ch[1]->sz;

    if (x->ischange){
        x->fir = x->wei;
        x->firnum = x->sz;
        x->sec = 0;
    }
    else{
        sortarr[0][0] = x->wei, sortarr[0][1] = 1;
        if (x->ch[0] != null)
            if (x->ch[0]->ischange)
                sortarr[1][0] = x->ch[0]->wei + x->ch[0]->add, sortarr[1][1] = x->ch[0]->sz, sortarr[2][1] = 0;
            else
                sortarr[1][0] = x->ch[0]->fir + x->ch[0]->add, sortarr[1][1] = x->ch[0]->firnum,
                sortarr[2][0] = x->ch[0]->sec + x->ch[0]->add, sortarr[2][1] = x->ch[0]->secnum;
        else sortarr[1][1] = sortarr[2][1] = 0;
        if (x->ch[1] != null)
            if (x->ch[1]->ischange)
                sortarr[3][0] = x->ch[1]->wei + x->ch[1]->add, sortarr[3][1] = x->ch[1]->sz, sortarr[4][1] = 0;
            else
                sortarr[3][0] = x->ch[1]->fir + x->ch[1]->add, sortarr[3][1] = x->ch[1]->firnum,
                sortarr[4][0] = x->ch[1]->sec + x->ch[1]->add, sortarr[4][1] = x->ch[1]->secnum;
        else sortarr[3][1] = sortarr[4][1] = 0;
        int maximum=0;
        for (int i=1;i<5;++i)
            if (sortarr[i][1]!=0 && sortarr[i][0] > sortarr[maximum][0])
                maximum = i;
        x->fir = sortarr[maximum][0];
        x->firnum = 0;
        for (int i=0;i<5;++i)
            if (sortarr[i][0] == sortarr[maximum][0])
                x->firnum += sortarr[i][1], sortarr[i][1] = 0;
        maximum = 0;
        for (int i=1;i<5;++i)
            if (sortarr[maximum][1] == 0 || (sortarr[i][1]!=0 && sortarr[i][0] > sortarr[maximum][0]))
                maximum = i;
        if (sortarr[maximum][1] != 0){
            x->sec = sortarr[maximum][0];
            x->secnum = 0;
            for (int i=0;i<5;++i)
                if (sortarr[i][0] == sortarr[maximum][0])
                    x->secnum += sortarr[i][1];
        }
        else x->secnum = 0;
    }
}

void update_change(Node *x, int wei){
    x->add = 0;
    x->wei = wei;
    x->ischange = true;
    x->fir = wei;
    x->firnum = x->sz;
    x->secnum = 0;
}

void push_down(Node *x){
    if (x->ischange){
        if (x->ch[0] != null) update_change(x->ch[0], x->wei);
        if (x->ch[1] != null) update_change(x->ch[1], x->wei);
        x->ischange = false;
    }
    if (x->add != 0){
        if (x->ch[0] != null) x->ch[0]->add += x->add;
        if (x->ch[1] != null) x->ch[1]->add += x->add;
        x->wei += x->add;
        x->add = 0;
    }
    if (x->rev){
        swap(x->ch[0],x->ch[1]);
        x->ch[0]->rev = !x->ch[0]->rev;
        x->ch[1]->rev = !x->ch[1]->rev;
        x->rev = false;
    }
}

void debug(){
    for (int j=1;j<=7;++j){
        Node *t = nodes+j;
        cout<wei<<" "
            <<"add: "<add<<" "
            <<"ischange: "<ischange<<" "
            <<"fir: "<fir<<" "
            <<"firnum: "<firnum<<" "
            <<"sec: "<sec<<" "
            <<"secnum: "<secnum<<" "
            <pnt - null<<" "
            <<"leftchild: "<ch[0] - null<<" "
            <<"rightchild: "<ch[1] - null <<" "
            <<"isrev: "<rev<<" "
            <<"isroot: "<rt<sz = 1;
    t->pnt = t->ch[0] = t->ch[1] = null;
    t->rt = true;
    t->wei = wei;
    t->add = 0;
    t->ischange = false;
    t->fir = wei;t->firnum = 1;
    t->sec = -INF;t->secnum = 0;
    t->rev = false;
    return t;
}

void init(){
    ncnt = 1;
    null->sz = 0;
    null->pnt = null->ch[0] = null->ch[1] = null;
}

void srotate(Node *x, bool d){
    Node *y = x->pnt;
    y->ch[!d] = x->ch[d];
    if (x->ch[d] != null)
        x->ch[d]->pnt = y;
    x->pnt = y->pnt;
    if (!y->rt){
        if (y == y->pnt->ch[d])
            y->pnt->ch[d] = x;
        else
            y->pnt->ch[!d] = x;
    }
    x->ch[d] = y;
    y->pnt = x;
    if (y->rt){
        y->rt = false;
        x->rt = true;
    }
    push_up(y);
}

void pushdownAll(Node *x){
    if (!x->rt) pushdownAll(x->pnt);
    push_down(x);
}

void splay(Node *x){
    Node *y;
    pushdownAll(x);
    while (!x->rt){
        y = x->pnt;
        if (x == y->ch[0]){
            if (!y->rt && y == y->pnt->ch[0]){
                srotate(y, true);
                //push_up(y);
            }
            srotate(x, true);
        }
        else{
            if (!y->rt && y == y->pnt->ch[1]){
                srotate(y, false);
                //push_up(y);
            }
            srotate(x, false);
        }
    }
    push_up(x);
}

void access(Node* u){
    Node *v = null;
    while (u != null){
        splay(u);
        u->ch[1]->rt = true;
        (u->ch[1] = v)->rt = false;
        push_up(u);
        v = u;
        u = u->pnt;
    }
}

void cut(Node* v) {
    access(v);
    splay(v);
    v->ch[0]->rt = true;
    v->ch[0]->pnt = null;
    v->ch[0] = null;
    push_up(v);
}

void changeRoot(Node *x){
    access(x);
    splay(x);
    x->rev = !x->rev;
}

void link(Node *v, Node *u){
    changeRoot(v);
    v->pnt = u;
}

int arr[MAXSIZE];

int main(){
    int total;
    int n,m;
    int i,j,k;
    int a,b,c,d;
    scanf("%d",&total);
    for (i=1;i<=total;++i){
        init();
        printf("Case #%d:\n",i);
        scanf("%d %d",&n,&m);
        for (j=1;j<=n;++j){
            scanf("%d",arr+j);
            newNode(arr[j]);
        }
        for (j=1;j ischange = true;
                    x -> wei = c;
                    x -> add = 0;
                    break;
                case 3:
                    scanf("%d %d %d",&a,&b,&c);
                    x = nodes + a, y = nodes + b;
                    changeRoot(x);
                    access(y);
                    splay(x);
                    x -> add += c;
                    break;
                case 4:
                    scanf("%d %d",&a,&b);
                    x = nodes + a, y = nodes + b;
                    changeRoot(x);
                    //debug();
                    access(y);
                    splay(x);
                    if (x->secnum == 0) printf("ALL SAME\n");
                        else printf("%d %d\n", x->sec, x->secnum);
                    break;
            }
            //debug();
        }
    }
    return 0;
}