## Max Points on A Line

07/15/2016 Hash Table Math

## Question

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

## Solution

Result: Accepted Time: 28 ms

Here should be some explanations.

/**
* Definition for a point.
* struct Point {
*     int x;
*     int y;
*     Point() : x(0), y(0) {}
*     Point(int a, int b) : x(a), y(b) {}
* };
*/
#define HASH_VALUE (1000000007ll)
class Solution {
public:
long long gcd(long long a, long long b)
{
return !b?a:gcd(b,a%b);
}
long long get_rate(const Point & a, const Point & b)
{
long long dx = a.x - b.x, dy = a.y - b.y;
long long ans = gcd(dx,dy);
if(ans)
{
dx /= ans;
dy /= ans;
}
return dx* HASH_VALUE + dy;
}
int maxPoints(vector<Point>& points) {
const int psz = points.size();
int ans = (psz > 0);
for(int i = 0; i < psz; i++)
{
unordered_map<long long,int> table;
int duplicate = 0;
for(int j = i + 1; j < psz; j++)
if(points[i].x != points[j].x || points[i].y != points[j].y)
{
long long rate = get_rate(points[i],points[j]);
if(table.count(rate))
table[rate] ++;
else
table[rate] = 2;
}
else
duplicate ++;
if(ans <= duplicate)
ans = duplicate + 1;
for(const auto & term: table)
if(term.second + duplicate > ans)
ans = term.second + duplicate;
}
return ans;
}
};


Complexity Analytics

• Time Complexity: $O(n^2)$
• Space Complexity: $O(n)$