# 149 Max Points on a Line

### Problem

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

### Solutions

``````public class Solution {
public int maxPoints(Point[] points) {
int res = 0;
for (int i = 0; i < points.length; ++i) {
HashMap<Integer, HashMap<Integer, Integer>> lines = new HashMap<>();
int duplicate = 1;
for (int j = i + 1; j < points.length; ++j) {
if (points[i].x == points[j].x && points[i].y == points[j].y) {
duplicate++;
continue;
}
int dx = points[j].x - points[i].x;
int dy = points[j].y - points[i].y;
int d = gcd(dx, dy);
if (!lines.containsKey(dx/d)) {
lines.put(dx/d, new HashMap<Integer, Integer>());
}
if (!lines.get(dx/d).containsKey(dy/d)) {
lines.get(dx/d).put(dy/d, 0);
}
lines.get(dx/d).put(dy/d, lines.get(dx/d).get(dy/d) + 1);
}
res = Math.max(res, duplicate);
for (Integer a:lines.keySet()) {
for (Integer b:lines.get(a).keySet()) {
res = Math.max(res, lines.get(a).get(b) + duplicate);
}
}
}
return res;
}
// greatest common divisor
public int gcd(int a, int b) {
return (b == 0) ? a : gcd(b, a % b);
}
}
``````