NOIP 模拟 $80\; \rm 光线追踪$

题解 \(by\;zj\varphi\)

一个矩形,它的贡献只能在它的左边界或它的下边界,意思就是,一条射线和它的第一个交点一定在它的左边界或它的下边界

而一个矩形能截到的直线的斜率在 \([\frac{y}{x_1},\frac{y_1}{x}]\) ,所以对于左边界的斜率范围,和下边界的斜率范围,分别建一棵线段树。

有小数范围,不能直接建在值域上,所以要离散化,为了防止暴精度,分数比大小用对角线乘法。

Code
#include<bits/stdc++.h>
#define ri signed
#define pd(i) ++i
#define bq(i) --i
#define func(x) std::function<x>
namespace IO{
    char buf[1<<21],*p1=buf,*p2=buf;
    #define gc() p1==p2&&(p2=(p1=buf)+fread(buf,1,1<<21,stdin),p1==p2)?(-1):*p1++
    #define debug1(x) std::cerr << #x"=" << x << ' '
    #define debug2(x) std::cerr << #x"=" << x << std::endl
    #define Debug(x) assert(x)
    struct nanfeng_stream{
        template<typename T>inline nanfeng_stream &operator>>(T &x) {
            bool f=false;x=0;char ch=gc();
            while(!isdigit(ch)) f|=ch=='-',ch=gc();
            while(isdigit(ch)) x=(x<<1)+(x<<3)+(ch^48),ch=gc();
            return x=f?-x:x,*this;
        }
    }cin;
}
using IO::cin;
namespace nanfeng{
    #define FI FILE *IN
    #define FO FILE *OUT
    template<typename T>inline T cmax(T x,T y) {return x>y?x:y;}
    template<typename T>inline T cmin(T x,T y) {return x>y?y:x;}
    using LL=long long;
    static const int N=1e5+7,INF=1061109567;
    int ll[N],ml[N],rl[N],id[N],q,cnt;
    struct Que{int opt,x,y,xx,yy;}que[N];
    struct node{int w,id;};
    struct Node{int x,y;}pnt[N<<2];
    inline bool operator<(const Node &n1,const Node &n2) {return 1ll*n1.y*n2.x<1ll*n2.y*n1.x;}
    inline bool operator==(const Node &n1,const Node &n2) {return 1ll*n1.y*n2.x==1ll*n2.y*n1.x;}
    struct Seg{
        #define ls(x) (x<<1)
        #define rs(x) (x<<1|1)
        struct segmenttree{node id;bool lz;}T[N<<4];
        func(void(int)) down=[&](int x) {
            if (!T[x].lz) return;
            if (!T[ls(x)].id.id) T[ls(x)].id=T[x].id,T[ls(x)].lz=true;
            else if (T[x].id.w<=T[ls(x)].id.w) T[ls(x)].id=T[x].id,T[ls(x)].lz=true;
            if (!T[rs(x)].id.id) T[rs(x)].id=T[x].id,T[rs(x)].lz=true;
            else if (T[x].id.w<=T[rs(x)].id.w) T[rs(x)].id=T[x].id,T[rs(x)].lz=true;
            T[x].lz=false;
        };
        func(void(int,int,int)) build=[&](int x,int l,int r) {
            T[x].id={INF,0};
            if (l==r) return;
            int mid=(l+r)>>1;
            build(ls(x),l,mid);
            build(rs(x),mid+1,r);
        };
        func(void(int,node,int,int,int,int)) update=[&](int x,node k,int l,int r,int lt,int rt) {
            if (l<=lt&&rt<=r) {
                if (T[x].id.w>=k.w) T[x].id=k,T[x].lz=true;
                return;
            }
            int mid=(lt+rt)>>1;
            down(x);
            if (l<=mid) update(ls(x),k,l,r,lt,mid);
            if (r>mid) update(rs(x),k,l,r,mid+1,rt);
        };
        func(node(int,int,int,int)) query=[&](int x,int p,int l,int r) {
            if (l==r) return T[x].id;
            int mid=(l+r)>>1;
            down(x);
            if (p<=mid) return query(ls(x),p,l,mid);
            else return query(rs(x),p,mid+1,r);
        };
    }T,S;
    inline int main() {
        FI=freopen("raytracing.in","r",stdin);
        FO=freopen("raytracing.out","w",stdout);
        cin >> q;
        for (ri i(1);i<=q;pd(i)) {
            cin >> que[i].opt;
            if (que[i].opt==1) {
                cin >> que[i].x >> que[i].y >> que[i].xx >> que[i].yy;
                pnt[++cnt]={que[i].x,que[i].y};
                pnt[++cnt]={que[i].x,que[i].yy};
                pnt[++cnt]={que[i].xx,que[i].y};
            } else {
                cin >> que[i].x >> que[i].y;
                pnt[++cnt]={que[i].x,que[i].y};
            }
        }
        std::sort(pnt+1,pnt+cnt+1);
        int k=std::unique(pnt+1,pnt+cnt+1)-pnt;
        cnt=k-1;
        T.build(1,1,cnt),S.build(1,1,cnt);
        for (ri i(1);i<=q;pd(i))
            if (que[i].opt==1) {
                ll[i]=std::lower_bound(pnt+1,pnt+k,(Node){que[i].xx,que[i].y})-pnt;
                ml[i]=std::lower_bound(pnt+1,pnt+k,(Node){que[i].x,que[i].y})-pnt;
                rl[i]=std::lower_bound(pnt+1,pnt+k,(Node){que[i].x,que[i].yy})-pnt;
            } else id[i]=std::lower_bound(pnt+1,pnt+k,(Node){que[i].x,que[i].y})-pnt;
        for (ri i(1);i<=q;pd(i))
            if (que[i].opt==1) {
                T.update(1,{que[i].x,i},ml[i],rl[i],1,cnt);
                S.update(1,{que[i].y,i},ll[i],ml[i],1,cnt);
            } else {
                node ansx=T.query(1,id[i],1,cnt);
                node ansy=S.query(1,id[i],1,cnt);
                if (!ansx.id||!ansy.id) printf("%d\n",ansx.id|ansy.id);
                else {
                    if (!que[i].y) printf("%d\n",que[ansy.id].x<ansx.w?ansy.id:ansx.id);
                    else if (!que[i].x) printf("%d\n",que[ansx.id].y<ansy.w?ansx.id:ansy.id);
                    else {
                        LL k1=1ll*ansx.w*que[i].y,k2=1ll*que[i].x*ansy.w;
                        if (k1==k2) printf("%d\n",cmax(ansx.id,ansy.id));
                        else printf("%d\n",k1<k2?ansx.id:ansy.id);
                    }
                }
            }
        return 0;
    }
}
int main() {return nanfeng::main();}
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