Luogu4899 IOI2018 Werewolf 主席树Kruskal重构树

Posted 2021-02-02 itst

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IOI强行交互可还行，我Luogu的代码要改很多才能交到UOJ去……

发现问题是对边权做限制的连通块类问题，考虑(Kruskal)重构树进行解决。

对于图上的边((u,v)(u<v))，我们建两棵(Kruskal)重构树，一棵按照(u)从大到小加边表示人形时的活动区域，一棵按照(v)从小到大加边表示狼形时的活动区域。

那么我们的每组询问就变为了：给出两段区间，询问是否存在一个点同时覆盖这两个区间（即人形转换为狼形的地点）。这个是经典的二维数点问题，使用主席树计算即可。

话说感觉一堆namespace的码风看起来好舒服啊~

#include<bits/stdc++.h>
//This code is written by Itst
using namespace std;

inline int read(){
    int a = 0;
    char c = getchar();
    bool f = 0;
    while(!isdigit(c)){
        if(c == ‘-‘)
            f = 1;
        c = getchar();
    }
    while(isdigit(c)){
        a = (a << 3) + (a << 1) + (c ^ ‘0‘);
        c = getchar();
    }
    return f ? -a : a;
}

const int MAXN = 2e5 + 10;
int N , M , Q;
namespace ST{
#define mid ((l + r) >> 1)
    struct node{
        int l , r , sum;
    }Tree[MAXN * 50];
    int root[MAXN] , cnt;

    void insert(int& x , int p , int l , int r , int tar){
        x = ++cnt;
        Tree[x] = Tree[p];
        ++Tree[x].sum;
        if(l == r)
            return;
        if(mid >= tar)
            insert(Tree[x].l , Tree[p].l , l , mid , tar);
        else
            insert(Tree[x].r , Tree[p].r , mid + 1 , r , tar);
    }

    bool query(int x , int y , int l , int r , int L , int R){
        if(Tree[x].sum == Tree[y].sum)
            return 0;
        if(l >= L && r <= R)
            return 1;
        bool f = 0;
        if(mid >= L)
            f |= query(Tree[x].l , Tree[y].l , l , mid , L , R);
        if(!f && mid < R)
            f |= query(Tree[x].r , Tree[y].r , mid + 1 , r , L , R);
        return f;
    }
}

namespace Itst{
#define P pair < int , int >
    int fa[2][MAXN << 1] , ch[2][MAXN << 1][2] , jump[2][MAXN << 1][21] , que[2][MAXN << 1] , dfn[2][MAXN] , cnt[2] , ts[2] , rg[2][MAXN << 1][2];

    void init(){
        cnt[0] = cnt[1] = N;
        for(int i = 1 ; i <= N ; ++i)
            fa[0][i] = fa[1][i] = i;
    }

    int find(int ind , int x){
        return fa[ind][x] == x ? x : (fa[ind][x] = find(ind , fa[ind][x]));
    }
    
    inline void link(int ind , int x , int y){
        x = find(ind , x);
        y = find(ind , y);
        if(x == y)
            return;
        ++cnt[ind];
        fa[ind][x] = fa[ind][y] = fa[ind][cnt[ind]] = cnt[ind];
        ch[ind][cnt[ind]][0] = x;
        ch[ind][cnt[ind]][1] = y;
    }

    void dfs(int ind , int x , int p){
        jump[ind][x][0] = p;
        for(int i = 1 ; jump[ind][x][i - 1] ; ++i)
            jump[ind][x][i] = jump[ind][jump[ind][x][i - 1]][i - 1];
        if(x <= N){
            rg[ind][x][0] = rg[ind][x][1] = dfn[ind][x] = ++ts[ind];
            que[ind][x] = x;
            return;
        }
        dfs(ind , ch[ind][x][0] , x);
        dfs(ind , ch[ind][x][1] , x);
        que[ind][x] = ind ? min(que[ind][ch[ind][x][0]] , que[ind][ch[ind][x][1]]) : max(que[ind][ch[ind][x][0]] , que[ind][ch[ind][x][1]]);
        rg[ind][x][0] = rg[ind][ch[ind][x][0]][0];
        rg[ind][x][1] = rg[ind][ch[ind][x][1]][1];
    }

    int up(int ind , int x , int l , int r){
        for(int i = 19 ; i >= 0 ; --i)
            if(jump[ind][x][i] && que[ind][jump[ind][x][i]] >= l && que[ind][jump[ind][x][i]] <= r)
                x = jump[ind][x][i];
        return x;
    }
    
    void work(){
        dfs(0 , cnt[0] , 0);
        dfs(1 , cnt[1] , 0);
        vector < P > p;
        for(int i = 1 ; i <= N ; ++i)
            p.push_back(P(dfn[0][i] , dfn[1][i]));
        sort(p.begin() , p.end());
        for(int i = 1 ; i <= N ; ++i)
            ST::insert(ST::root[i] , ST::root[i - 1] , 1 , N , p[i - 1].second);

        while(Q--){
            int S = read() + 1 , E = read() + 1 , L = read() + 1 , R = read() + 1;
            E = up(0 , E , 1 , R);
            S = up(1 , S , L , N);
            puts(ST::query(ST::root[rg[0][E][1]] , ST::root[rg[0][E][0] - 1] , 1 , N , rg[1][S][0] , rg[1][S][1]) ? "1" : "0");
        }
    }
}

namespace init{
    struct Edge{
        int a , b;
    }Ed[MAXN << 1];

    bool cmp1(Edge a , Edge b){
        return a.b < b.b;
    }

    bool cmp2(Edge a , Edge b){
        return a.a > b.a;
    }
    
    void main(){
        N = read();
        M = read();
        Q = read();
        Itst::init();
        for(int i = 1 ; i <= M ; ++i){
            Ed[i].a = read() + 1;
            Ed[i].b = read() + 1;
            if(Ed[i].a > Ed[i].b)
                swap(Ed[i].a , Ed[i].b);    
        }
        sort(Ed + 1 , Ed + M + 1 , cmp1);
        for(int i = 1 ; i <= M ; ++i)
            Itst::link(0 , Ed[i].a , Ed[i].b);
        sort(Ed + 1 , Ed + M + 1 , cmp2);
        for(int i = 1 ; i <= M ; ++i)
            Itst::link(1 , Ed[i].a , Ed[i].b);
        Itst::work();
    }
}

int main(){
#ifndef ONLINE_JUDGE
    freopen("in" , "r" , stdin);
    //freopen("out" , "w" , stdout);
#endif
    init::main();
    return 0;
}