poj-2318 TOYS （叉积）

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.

Input

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.

Output

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.

Sample Input

5 6 0 10 60 03 14 36 810 1015 301 52 12 85 540 107 94 10 0 10 100 020 2040 4060 6080 80 5 1015 1025 1035 1045 1055 1065 1075 1085 1095 100

Sample Output

0: 21: 12: 13: 14: 05: 10: 21: 22: 23: 24: 2

Hint

As the example illustrates, toys that fall on the boundary of the box are "in" the box.

题目大意：将一个箱子用n块隔板分开，一个小孩向里面仍m个玩具，告诉你箱子左上和右下，和隔板两端的坐标，还有玩具落点的坐标，求每块区间内有多少个玩具。（玩具不会落在隔板上和箱子的边缘）。

分析：利用向量的叉乘判断玩具的落点是在隔板的右边还是左边，再用二分来查找隔板，单独判断最右边和最左边的空间。

#include<cstdio>#include<iostream>#include<cstring>using namespace std;struct point{int x,y;}p0,pn;//箱子端点坐标int cross(point a,point b){//叉乘return a.x*b.y-a.y*b.x; }int judge(point t,point a){//点在线段的左1，右0；point s1,s2;s1.x=t.x-a.x;s1.y=t.y-p0.y;s2.x=t.x-a.y;s2.y=t.y-pn.y; if(cross(s2,s1)>0)return 1;return 0;} int main(){int n,m,ans[5050];point a[5050],t;while(scanf("%d",&n)&&n){memset(ans,0,sizeof(ans));scanf("%d%d%d%d%d",&m,&p0.x,&p0.y,&pn.x,&pn.y);for(int i=0;i<n;i++)scanf("%d%d",&a[i].x,&a[i].y);for(int i=0;i<m;i++){scanf("%d%d",&t.x,&t.y);if(t.x>pn.x||t.x<p0.x||t.y>p0.y||t.y<pn.y)continue;if(judge(t,a[0])){ans[0]++;continue;}if(!judge(t,a[n-1])){ans[n]++;continue;}int low=0,high=n-1;int mid;while(low<=high){mid=(high+low)/2;if(judge(t,a[mid])&&!judge(t,a[mid-1])){ans[mid]++;break;}else if(judge(t,a[mid]))high=mid-1;elselow=mid+1;}}for(int i=0;i<=n;i++)printf("%d: %d\n",i,ans[i]);putchar('\n');}return 0;}