ural 1052. Rabbit Hunt hash

1052. Rabbit Hunt

Time limit: 1.0 second
Memory limit: 64 MB

A good hunter kills two rabbits with one shot. Of course, it can be easily done since for any two points we can always draw a line containing the both. But killing three or more rabbits in one shot is much more difficult task. To be the best hunter in the world one should be able to kill the maximal possible number of rabbits. Assume that rabbit is a point on the plane with integer x and ycoordinates. Having a set of rabbits you are to find the largest number of rabbits that can be killed with single shot, i.e. maximum number of points lying exactly on the same line. No two rabbits sit at one point.

Input

An input contains an integer N (3 ≤ N ≤ 200) specifying the number of rabbits. Each of the next N lines in the input contains the x coordinate and the y coordinate (in this order) separated by a space (−2000 ≤ x, y ≤ 2000).

Output

The output contains the maximal number of rabbits situated in one line.

Sample

inputoutput

67 1228 1399 15610 17311 190-100 1

5

Problem Author: Stanislav Vasilyev 
Problem Source: Ural State University collegiate programming contest (25.03.2000)

import java.io.BufferedReader;import java.io.InputStream;import java.io.InputStreamReader;import java.io.PrintWriter;import java.math.BigInteger;import java.util.HashMap;import java.util.StringTokenizer;public class Main {public static void main(String[] args) {new Task().solve();}}class Task {InputReader in = new InputReader(System.in);PrintWriter out = new PrintWriter(System.out);class Node{int x , y ;Node(int x , int y){if(x != 0){int g = gcd(Math.abs(x) , Math.abs(y)) ;    x /= g ;    y /= g ;    if(x < 0 && y < 0){    x = -x ;    y = -y ;    }}else{y = 10000 ;}this.x = x ;this.y = y ;}int gcd(int x , int y){return y == 0 ? x : gcd(y , x%y) ;}@Overridepublic int hashCode() {final int prime = 31;int result = 1;result = prime * result + getOuterType().hashCode();result = prime * result + x;result = prime * result + y;return result;}@Overridepublic boolean equals(Object obj) {if (this == obj)return true;if (obj == null)return false;if (getClass() != obj.getClass())return false;Node other = (Node) obj;if (!getOuterType().equals(other.getOuterType()))return false;if (x != other.x)return false;if (y != other.y)return false;return true;}private Task getOuterType() {return Task.this;}        }void put(HashMap<Node , Integer> hash , Node node){Integer cnt = hash.get(node) ;hash.put(node, cnt == null ? 1 : cnt+1) ;}void solve() {HashMap<Node , Integer> hash = new HashMap<Node, Integer>() ;int n = in.nextInt() ;int[][] p = new int[n][2] ;for(int i = 0 ; i < n ; i++){p[i][0] = in.nextInt() ;p[i][1] = in.nextInt() ;}int res = 0 ;for(int o = 0 ; o < n ; o++){hash.clear() ;int cnt = 1 ;for(int i = 0 ; i < n ; i++){if(i == o){continue ;}put(hash, new Node(p[i][0] - p[o][0] , p[i][1] - p[o][1])) ;}for(int c : hash.values()){cnt = Math.max(c , cnt) ;}res = Math.max(res , cnt+1) ;}out.println(res) ;out.flush() ;}}class InputReader {public BufferedReader reader;public StringTokenizer tokenizer;public InputReader(InputStream stream) {reader = new BufferedReader(new InputStreamReader(stream), 32768);tokenizer = new StringTokenizer("");}private void eat(String s) {tokenizer = new StringTokenizer(s);}public String nextLine() {try {return reader.readLine();} catch (Exception e) {return null;}}public boolean hasNext() {while (!tokenizer.hasMoreTokens()) {String s = nextLine();if (s == null)return false;eat(s);}return true;}public String next() {hasNext();return tokenizer.nextToken();}public int nextInt() {return Integer.parseInt(next());}public int[] nextInts(int n) {int[] nums = new int[n];for (int i = 0; i < n; i++) {nums[i] = nextInt();}return nums;}public long nextLong() {return Long.parseLong(next());}public double nextDouble() {return Double.parseDouble(next());}public BigInteger nextBigInteger() {return new BigInteger(next());}}