<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>

class Solution:
    def maxPoints(self, points: List[List[int]]) -> int:
        l, cache = len(points), {}

        if l == 1:
            return 1

        def countPoints(p1, p2):
            count = 0

            x1, y1 = p1
            x2, y2 = p2

            if x1 != x2:
                k = y1 - y2 
                c = x1 - x2
                b = x1 * y2 - x2 * y1
                if (k, b) in cache:
                    return cache[(k, b)]
                for point in points:
                    x, y = point
                    if c * y == k * x + b:
                        count += 1
            else:
                k = float('inf')
                b = x1
                if (k, b) in cache:
                    return cache[(k, b)]
                for point in points:
                    x, y = point
                    if x == x1:
                        count += 1
            
            cache[(k, b)] = count

            return count

        max_num = float('-inf')
        for i in range(l):
            for j in range(i + 1, l):
                max_num = max(max_num, countPoints(points[i], points[j]))
        
        return max_num
                
24999