<p>Given an array of <code>points</code> where <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> represents a point on the <strong>X-Y</strong> plane, return <em>the maximum number of points that lie on the same straight line</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/25/plane1.jpg" style="width: 300px; height: 294px;" />
<pre>
<strong>Input:</strong> points = [[1,1],[2,2],[3,3]]
<strong>Output:</strong> 3
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/25/plane2.jpg" style="width: 300px; height: 294px;" />
<pre>
<strong>Input:</strong> points = [[1,1],[3,2],[5,3],[4,1],[2,3],[1,4]]
<strong>Output:</strong> 4
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= points.length &lt;= 300</code></li>
	<li><code>points[i].length == 2</code></li>
	<li><code>-10<sup>4</sup> &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 10<sup>4</sup></code></li>
	<li>All the <code>points</code> are <strong>unique</strong>.</li>
</ul>

import numpy as np
import math
class Solution:
    def maxPoints(self, points: List[List[int]]) -> int:
        record = {}
        best = 0
        directions = [[1, 0], [0, 1], [-1, 0], [0, -1], [1, 1], [-1,-1], [-1, 1], [1, -1]]

        for i in range(len(points)):
            record[tuple(points[i])] = {}
            current = points[i]
            #print("Current is: ", current)
            for j in range(i+1, len(points)):
                other = points[j]
                difference = [current[0]-other[0], current[1]-other[1]]
                # here I'll have to convert the difference to a normalised direction vector
                current_gcd = math.gcd(difference[0], difference[1])
                difference[0] = int(difference[0]/current_gcd)
                difference[1] = int(difference[1]/current_gcd)
                if difference[0]<=0 and difference[1]<=0:
                    difference[0] = difference[0]*(-1)
                    difference[1] = difference[1]*(-1)
                #print("         Difference is: ", difference)
                if difference[0]>0 and difference[1]<0:
                    difference[0] = difference[0]*(-1)
                    difference[1] = difference[1]*(-1)
                #print(difference, current, other)
                if tuple(difference) in record[tuple(current)].keys():
                    #print("heya")
                    record[tuple(current)][tuple(difference)].append(tuple(other))
                    best = max(best, len(record[tuple(current)][tuple(difference)]))
                else :
                    record[tuple(current)][tuple(difference)] = [tuple(other)]
                    best = max(1, best)
                #print('\t\t\t', record)
        return best+1



        
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