POJ原址链接：POJ2318 TOYS 牛客上的链接：TOYS
Calculate the number of toys that land in each bin of a partitioned toy box. Mom and dad have a problem - their child John never puts his toys away when he is finished playing with them. They gave John a rectangular box to put his toys in, but John is rebellious and obeys his parents by simply throwing his toys into the box. All the toys get mixed up, and it is impossible for John to find his favorite toys.
John’s parents came up with the following idea. They put cardboard partitions into the box. Even if John keeps throwing his toys into the box, at least toys that get thrown into different bins stay separated. The following diagram shows a top view of an example toy box.
For this problem, you are asked to determine how many toys fall into each partition as John throws them into the toy box.
The input file contains one or more problems. The first line of a problem consists of six integers, n m x1 y1 x2 y2. The number of cardboard partitions is n (0 < n <= 5000) and the number of toys is m (0 < m <= 5000). The coordinates of the upper-left corner and the lower-right corner of the box are (x1,y1) and (x2,y2), respectively. The following n lines contain two integers per line, Ui Li, indicating that the ends of the i-th cardboard partition is at the coordinates (Ui,y1) and (Li,y2). You may assume that the cardboard partitions do not intersect each other and that they are specified in sorted order from left to right. The next m lines contain two integers per line, Xj Yj specifying where the j-th toy has landed in the box. The order of the toy locations is random. You may assume that no toy will land exactly on a cardboard partition or outside the boundary of the box. The input is terminated by a line consisting of a single 0.
The output for each problem will be one line for each separate bin in the toy box. For each bin, print its bin number, followed by a colon and one space, followed by the number of toys thrown into that bin. Bins are numbered from 0 (the leftmost bin) to n (the rightmost bin). Separate the output of different problems by a single blank line.
5 6 0 10 60 0 3 1 4 3 6 8 10 10 15 30 1 5 2 1 2 8 5 5 40 10 7 9 4 10 0 10 100 0 20 20 40 40 60 60 80 80 5 10 15 10 25 10 35 10 45 10 55 10 65 10 75 10 85 10 95 10 0
0: 2 1: 1 2: 1 3: 1 4: 0 5: 1
0: 2 1: 2 2: 2 3: 2 4: 2 Hint
As the example illustrates, toys that fall on the boundary of the box are “in” the box. Source
Rocky Mountain 2003
一个矩形左上角为(x1,y1)，右下角为(x2,y2)，被划分成n+1个区域；n次输出每个区域边界连线上顶点的横坐标 U i U_i Ui和下顶点的横坐标 L i L_i Li ；m次输入一个玩具的坐标；最终输出每个区域内的玩具的个数。
设该点为p(x,y)，求p与各个边界连接的向量做叉积（由叉积的政府可判断向量的相对顺逆时针方向），如为负，则证明p与上顶点的向量位于p与下顶点的向量的逆时针方向，符合在该区间中，二分不断缩小直到符合的唯一区间。
//#pragma GCC optimize(2) //#include<bits/stdc++.h> #include <iostream> #include <stdio.h> #include <algorithm> #include <vector> using namespace std; #define ll long long #define endl "\n" const int MAX=1e6+7; struct Point{ int x,y; Point(){}; Point(int tx,int ty):x(tx),y(ty){}; Point operator-(Point b){ return Point(x-b.x,y-b.y); } }p; double Cross(Point a,Point b){ return a.x*b.y-a.y*b.x; } struct Line{ Point a,b; Line(){}; Line(Point ta,Point tb):a(ta),b(tb){}; }; int n,m,x1,y1,x2,y2,Ui,Li; int tx,ty,l,r,tmp,mid,f; int main(){ ios_base::sync_with_stdio(0);cin.tie(0); while(cin>>n){ if(n==0)break; vector<Line>line(n+1); vector<ll>ans(n+1); cin>>m>>x1>>y1>>x2>>y2; for(int i=0;i<n;i++){ cin>>Ui>>Li; line[i]=Line(Point(Ui,y1),Point(Li,y2)); } line[n]=Line(Point(x2,y1),Point(x2,y2)); while(m--){ cin>>tx>>ty; p=Point(tx,ty); l=0,r=n; while(l<=r){ mid=(l+r)/2; if(Cross(p-line[mid].a,p-line[mid].b)<0){ tmp=mid; r=mid-1; } else l=mid+1; } ans[tmp]++; } for(int i=0;i<=n;i++)cout<<i<<": "<<ans[i]<<endl; cout<<endl; } return 0; }