149、Max Points on a Line (Hard)

Given n points
on a 2D plane, find the maximum number of points that lie on the same straight line.

题目就是在二维平面里给一堆点的x坐标和y坐标，求一条能穿过点的直线的上面的点的最大数目。

题意很明确，难点在于一是用何种数据结构解决，二是如何区分直线。因为每个直线有k和b两个属性，而两点共线说明y1=kx1+b,y2=kx2+b，所以可以用k=(y2-y1)/(x2-x1)这个数字来唯一区分直线，注意这里把b消除了，其实加上b也没事，因为用k和b区分和只用k区分是一样的。那么考虑到直线的唯一性问题，用HashMap实现就显而易见了（这个题自己思路正确了，但是由于程序的实现没有考虑到两个点完全重合的情况，所以修改实现流程的逻辑判断花了很长时间）。

import java.util.HashMap;
import java.util.Map;
import java.util.Map.Entry;
import java.util.Scanner;
import java.util.Set;

public class Test {
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
int number = in.nextInt();
Point[] p = new Point[number];
for (int i = 0; i < number; i++) {
int a = in.nextInt();
int b = in.nextInt();
p[i] = new Point(a, b);
}
System.out.println(maxPoints(p));
}

public static int maxPoints(Point[] points) {
if (points.length < 3) {
return points.length;
}

HashMap<Integer, Integer> xmap = new HashMap<Integer, Integer>();
HashMap<String, Integer> xymap = new HashMap<String, Integer>();
int x = 0;
int y = 0;
int x1 = 0;
int y1 = 0;
int xcount = 1;
int xycount = 1;
for (int i = 0; i < points.length; i++) {
x = points[i].x;
y = points[i].y;
String s = x + "," + y;
if (xmap.get(x) != null) {
xcount = xmap.get(x) + 1;
}
xmap.put(x, xcount);
}

int result = 0;

for (int i = 0; i < points.length-1; i++) {
xymap.clear();
x = points[i].x;
y = points[i].y;
int flag = 0;
int max = 0;
for (int j = i + 1; j < points.length; j++) {
xycount = 1;
x1 = points[j].x;
y1 = points[j].y;
if (x1 - x == 0) {
if (y1 - y == 0) {
flag++;
continue;
}

}
int gcd = getMaxGCD(x1 - x, y1 - y);
System.out.println("gcd:"+gcd);
String s = ((y1 - y) / gcd) + "/" + ((x1 - x) / gcd);
if (xymap.get(s) != null) {
xycount = xymap.get(s) + 1;
}
xymap.put(s, xycount);
max = Math.max(max,xycount);
}
result = Math.max(result, max+flag+1);
}
Set<Entry<Integer, Integer>> entrySetx = xmap.entrySet();
xcount = 1;
for (Entry<Integer, Integer> entry : entrySetx) {
if (entry.getValue() > xcount) {
xcount = entry.getValue();
}
}
System.out.println("xcount"+xcount);
System.out.println("result"+result);
return xcount > result ? xcount : result;

}

public static int getMaxGCD(int x, int y) {
if (y == 0) {
return x;
} else {
return getMaxGCD(y, x % y);
}
}

public static int getNumber(int x) {
int number = (int) Math.sqrt(x);
if (number * number > x) {
for (int i = number; i >= 0; i--) {
if (i * (i - 1) / 2 == x) {
return i;
}
}
} else {
for (int i = number; i <= x; i++) {
if (i * (i - 1) / 2 == x) {
return i;
}
}
}
return 0;
}

/*
if (points==null) return 0;
if (points.length<=2)
8f6b
return points.length;

Map<Integer,Map<Integer,Integer>> map = new HashMap<Integer,Map<Integer,Integer>>();
int result=0;
for (int i=0;i<points.length;i++){
map.clear();
int overlap=0,max=0;
for (int j=i+1;j<points.length;j++){
int x=points[j].x-points[i].x;
int y=points[j].y-points[i].y;
System.out.println("i:"+i+" x:"+x+" y:"+y);
if (x==0&&y==0){
overlap++;
continue;
}
int gcd=generateGCD(x,y);
System.out.println("gcd:"+gcd);
if (gcd!=0){
x/=gcd;
y/=gcd;
}

if (map.containsKey(x)){
if (map.get(x).containsKey(y)){
map.get(x).put(y, map.get(x).get(y)+1);
}else{
map.get(x).put(y, 1);
}
}else{
Map<Integer,Integer> m = new HashMap<Integer,Integer>();
m.put(y, 1);
map.put(x, m);
}
max=Math.max(max, map.get(x).get(y));
}
result=Math.max(result, max+overlap+1);
}
return result;

}

public static int generateGCD(int x, int y) {
if (y == 0) {
return x;
} else {
return generateGCD(y, x % y);
}
}
*/
}

class Point {
int x;
int y;

Point() {
x = 0;
y = 0;
}

Point(int a, int b) {
x = a;
y = b;
}
}