<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:
        from collections import defaultdict

        if len(points)==1:
            return 1

        counter = defaultdict(set)
        n = len(points)
    
        # Initialize a 2D list (list of lists) to store (slope, intercept) tuples
        result = [[None] * n for _ in range(n)]
        
        for i in range(n):
            for j in range(i):
                x1, y1 = points[i]
                x2, y2 = points[j]
                
                if x1 == x2:
                    slope = float('inf')  # Infinite slope
                    intercept = None  # Intercept is undefined
                    x_intercept = x1  # x-intercept is the x-coordinate of the line
                else:
                    # Calculate slope (m)
                    slope = (y2 - y1) / (x2 - x1)
                    # Calculate y-intercept (c)
                    intercept = y1 - slope * x1
                    # Calculate x-intercept (-c/m) if slope is not zero
                    x_intercept = -intercept / slope if slope != 0 else None
                
                # Store the result as a tuple (slope, y_intercept, x_intercept)
                result[i][j] = (slope, intercept, x_intercept)

        for i in range(n):
            for j in range(i):
                counter[result[i][j]].update({i,j})

        # print(counter)
        counter = max([len(v) for v in counter.values()])

        return counter
37966