2013
11-09

# Lining Up

“How am I ever going to solve this problem?” said the pilot.

Indeed, the pilot was not facing an easy task. She had to drop packages at specific points scattered in a dangerous area. Furthermore, the pilot could only fly over the area once in a straight line, and she had to fly over as many points as possible. All points were given by means of integer coordinates in a two-dimensional space. The pilot wanted to know the largest number of points from the given set that all lie on one line. Can you write a program that calculates this number?

Your program has to be efficient!

Input consist several case,First line of the each case is an integer N ( 1 < N < 700 ),then follow N pairs of integers. Each pair of integers is separated by one blank and ended by a new-line character. The input ended by N=0.

output one integer for each input case ,representing the largest number of points that all lie on one line.

5
1 1
2 2
3 3
9 10
10 11
0

3

//* @author: 82638882@163.com
import java.util.*;
public class Main
{
public static void main(String[] args)
{
Scanner in=new Scanner(System.in);
while(true)
{
int a=in.nextInt();
if(a==0)break;
int[] arrx=new int[a];
int[] arry=new int[a];
for(int i=0;i< a;i++)
{
arrx[i]=in.nextInt();
arry[i]=in.nextInt();
}
int max=0;
for(int i=0;i< a-2;i++)
{
for(int j=i+1;j< a-1;j++)
{
int c=0;
for(int u=j+1;u< a;u++)
{
if((arrx[i]-arrx[u])*(arry[i]-arry[j])==(arrx[i]-arrx[j])*(arry[i]-arry[u]))c++;
}
if(c>max)max=c;
}
}
System.out.println(max+2);
}
}
}

1. L（X [0 .. M-1]，Y [0 .. N-1]）= 1 + L（X [0 .. M-2]，Y [0 .. N-1]）这个地方也也有笔误
应改为L（X [0 .. M-1]，Y [0 .. N-1]）= 1 + L（X [0 .. M-2]，Y [0 .. N-2]）

2. Thanks for using the time to examine this, I truly feel strongly about it and enjoy finding out far more on this subject matter. If achievable, as you achieve knowledge

3. 换句话说，A[k/2-1]不可能大于两数组合并之后的第k小值，所以我们可以将其抛弃。
应该是，不可能小于合并后的第K小值吧