2013
11-12

# Visible Lattice Points

A lattice point (x, y) in the first quadrant (x and y are integers greater than or equal to 0), other than the origin, is visible from the origin if the line from (0, 0) to (x, y) does not pass through any other lattice point. For example, the point (4, 2) is not visible since the line from the origin passes through (2, 1). The figure below shows the points (x, y) with 0 ≤ x, y ≤ 5 with lines from the origin to the visible points.

Write a program which, given a value for the size, N, computes the number of visible points (x, y) with 0 ≤ x, yN.

The first line of input contains a single integer C (1 ≤ C ≤ 1000) which is the number of datasets that follow.

Each dataset consists of a single line of input containing a single integer N (1 ≤ N ≤ 1000), which is the size.

For each dataset, there is to be one line of output consisting of: the dataset number starting at 1, a single space, the size, a single space and the number of visible points for that size.

4
2
4
5
231

1 2 5
2 4 13
3 5 21
4 231 32549

//* @author:
import java.util.*;
public class Main {
public static void main(String[] args){
int[] p=new int[1001];
p[1]=3;
p[2]=5;
Scanner cin=new Scanner(System.in);
int T=cin.nextInt();
for(int a=3;a<=1000;a++){
p[a]=p[a-1]+2;
for(int i=2;i<=a;i++)
p[a]+=2*c(a,i);
}
for(int t=1;t<=T;t++){
int r=cin.nextInt();
System.out.println(t+" "+r+" "+p[r]);
}
}
public static int c(int a,int b){
while(a!=0){
b=b%a;
if(a>b){
int temp=a;
a=b;
b=temp;
}
}
if(b==1)
return 1;
else
return 0;
}
}

1. 可以根据二叉排序树的定义进行严格的排序树创建和后序遍历操作。如果形成的排序树相同，其树的前、中、后序遍历是相同的，但在此处不能使用中序遍历，因为，中序遍历的结果就是排序的结果。经在九度测试，运行时间90ms，比楼主的要快。