[USACO5.5] 矩形周长Picture

https://www.luogu.org/problemnew/show/P1856

1.每个矩形由两条横向边和两条纵向边组成.

2.对于横向边，按纵坐标排序。设当前讨论的边为 A [s , t]

如果 A 是某个矩形的靠下的边，在树中查询[s,t]区间中被覆盖的长度为x，那么加上这条边后将增加(t-s-x);

如果 A 是某个矩形的靠上的边，先删除它的对应边，再在树中查询[s,t]区间中被覆盖的长度为x，那么加上这条边后将增加(t-s-x);

3、对于纵向边，按横坐标排序，讨论方法与横向边相同。

注意建树方式是以单位线段为叶子节点

#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>
#include <queue>
#include <cmath>

#define LL long long

using namespace std;
const int MAXN = 2e4 + ;
const int INF = 1e9;

int n,m,Ans = ;

#define Max 10001

inline void read(int &x){
    x=; int f=; register char c = getchar();
    while(c>''||c<''){ if(c=='-')f=-; c=getchar(); }
    while(c>=''&&c<=''){ x=x*+c-''; c=getchar(); } x*=f;
}

struct Seg_Ment{
    int s,t,id,p; // s、t线段端点 p是排序依据  id--排序之前的编号
    Seg_Ment(int a,int b,int c,int d):s(a),t(b),p(c),id(d){}
    Seg_Ment(){ s=t=p=id=; }
    bool operator < (const Seg_Ment a) const {
        return p < a.p;
    }
}x[MAXN],y[MAXN];

int lazy[MAXN << ],cnt[MAXN << ],l,r;

inline void Push_Down(int u){
    int ls = u <<  ,rs = u << |;
    lazy[ls] += lazy[u],cnt[ls] += lazy[u],cnt[rs] += lazy[u],lazy[rs] += lazy[u];
    lazy[u] = ;
}

void UpDate(int u,int L,int R,int Del){
    if(lazy[u]) Push_Down(u);
    if(l <= L && R <= r){
        cnt[u] += Del,lazy[u] += Del;
    }
    else if(L +  < R){
        int Mid = (L+R) >>,ls = u<<,rs = u<<|;
        if(l <= Mid && L <= r) UpDate(ls,L,Mid,Del);
        if(r >= Mid && l <= R) UpDate(rs,Mid,R,Del);
    }
}

int query(int u,int L,int R){
    if(lazy[u]) Push_Down(u);
    if(l <= L && R <= r && cnt[u] > ) return R - L;
    if(L +  < R){
        int Mid = L+R >>,a = ,b = ;
        if(l <= Mid) a = query(u<<,L,Mid);
        if(r >= Mid) b = query(u<<|,Mid,R);
        return a + b;
    }
    return ;
}

int main(int argc,char *argv[]){
    freopen("gg.out", "w", stdout);
    cin >> n;
    for(int i = ; i <= n; i ++) {
        cout << i << ":" << " " << tan(i) << endl;
    }
    return ;
    int x1,y1,xx,yy;
    read(n);
    for(int i=; i<=n; ++i){
        read(x1),read(y1),read(xx),read(yy);
        x1 += Max,xx += Max,y1 += Max, yy += Max;
        x[i] = Seg_Ment(x1,xx,y1,i),y[i] = Seg_Ment(y1,yy,x1,i);
        x[i + n] = Seg_Ment(x1,xx,yy,i + n),y[i + n] = Seg_Ment(y1,yy,xx,i + n);
    }

    return ;
    sort(x + ,x +  * n + );
    sort(y + ,y +  * n + );
    memset(lazy,,sizeof lazy ); memset(cnt,,sizeof cnt );
    for(int i=; i<=n * ; ++i){
        l = x[i].s, r = x[i].t;
        if(x[i].id <= n){
            Ans += abs(r - l - query(,,MAXN));
            UpDate(,,MAXN,);
        }
        else {
            UpDate(,,MAXN,-);
            Ans += abs(r - l - query(,,MAXN));
        }
    }
    memset(lazy,,sizeof lazy ); memset(cnt,,sizeof cnt );
    for(int i=; i<=n * ; ++i){
        l = y[i].s,r = y[i].t;
        if(y[i].id <= n){
            Ans += abs(r - l - query(,,MAXN));
            UpDate(,,MAXN,);
        }
        else{
            UpDate(,,MAXN,-);
            Ans += abs(r - l - query(,,MAXN));
        }
    }
    cout << Ans << endl;
    return ;
}