POJ TOYS（叉积的妙用+二分答案）

TOYS

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 16042		Accepted: 7688

Description

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 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

Sample Output

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

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这道题是我为数不多的能想出思路来的题，

它给的隔板都是排好序的

所以我们可以二分一个答案，

然后判断这个点在中点的哪个地方，

注意在这个地方有一个小技巧，

我们可以把点看成向量的相对向量，，，

大概就是这个意思，不是特别严谨，

 #include<iostream>
 #include<cstdio>
 #include<cstring>
 using namespace std;
 const int MAXN=;
 inline void read(int &n)
 {
     char c=getchar();bool flag=;n=;
     while(c<''||c>'')    c=='-'?flag=,c=getchar():c=getchar();
     while(c>=''&&c<='')    n=n*+(c-),c=getchar();if(flag==)n=-n;
 }
 int n,m,x1,yy1,x2,y2;
 struct node
 {
     int x,y;
 }point[MAXN];
 struct Line
 {
     node a,b;
 }line[MAXN];
 int cross(node a,node b,node c)
 {
     return (c.x-a.x)*(c.y-b.y)-(c.x-b.x)*(c.y-a.y);
 }
 int ans[MAXN];
 void calc(int num)
 {
     int l=,r=n-;
     while(l<r)
     {
         int mid=(l+r)>>;
         if(cross(point[num],line[mid].a,line[mid].b)>) l=mid+;
         else r=mid;
     }
     if(cross(point[num],line[l].a,line[l].b)<)
         ans[l]++;
     else ans[l+]++;

 }
 int main()
 {
     while(scanf("%d",&n)&&n)
     {
         scanf("%d%d%d%d%d",&m,&x1,&yy1,&x2,&y2);
         for(int i=;i<n;i++)
         {
             int p,q;read(p);read(q);
             line[i].a.x=p;
             line[i].a.y=yy1;
             line[i].b.x=q;
             line[i].b.y=y2;
         }
         memset(ans,,sizeof(ans));
         for(int i=;i<m;i++)
         {
             int p,q;read(p);read(q);
             point[i].x=p;
             point[i].y=q;
         }
         for(int i=;i<m;i++)
             calc(i);

         for(int i=;i<=n;i++)
             printf("%d: %d\n",i,ans[i]);
         printf("\n");
     }
     return ;
 }