<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:
        n = len(points)
        lines = {}
        for i in range(n):
            for j in range(i + 1, n):
                if points[i][0] == points[j][0]:
                    idx = f"1,0,{-points[i][0]}"
                elif points[i][1] == points[j][1]:
                    idx =  f"0,1,{-points[i][1]}"
                else:
                    x1, y1 = points[i]
                    x2, y2 = points[j]
                    idx = f"{(y2 - y1) / (x2 - x1)},-1,{(y1 * x2 - y2 * x1) / (x2 - x1)}"
                if idx in lines:
                    lines[idx].add(i)
                    lines[idx].add(j)
                else:
                    lines[idx] = set([i, j])
        ans = 1
        for k, v in lines.items():
            ans = max(ans, len(v))
        return ans
33026