<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:
        # max_points = 0
        # for point1 in points:
        #     for point2 in points:
        #         count = 0
        #         if point1[0] != point2[0]: # line is not vertical
        #             yslope = (point2[1] - point1[1])
        #             xslope = (point2[0] - point1[0])
        #             for point in points:
        #                 if xslope * (point[1] - point1[1]) == yslope * (point[0] - point1[0]):
        #                     count += 1
        #         else: # vertical
        #             for point in points:
        #                 if point[0] == point1[0]:
        #                     count += 1
        #         print(count)
        #         max_points = max(max_points, count)
        # return max_points

        slopes = {}
        for i, point1 in enumerate(points):
            for j, point2 in enumerate(points[:i]):
                if point1[0] == point2[0]: # vertical
                    slopeStr = "inf"
                else:
                    slopeStr = str((point2[1] - point1[1]) / (point2[0] - point1[0]))
                
                if slopeStr in slopes: 
                    slopes[slopeStr].append((j,i))
                else: 
                    slopes[slopeStr] = [(j,i)]
        
        maxLength = 1
        for slopeStr in slopes:
            components = []
            for pair in slopes[slopeStr]:
                s = set(pair)
                flag = True
                #print(s)
                for st in components:
                    if len(st.intersection(s)) > 0:
                        #print("JOIN")
                        components.remove(st)
                        st = st.union(s)
                        components.append(st)
                        flag = False
                        #print(components)
                if flag:
                    components.append(s)
            if max([len(c) for c in components]) > maxLength:
                maxLength = max([len(c) for c in components])
        
        return maxLength
        
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