<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 {
public:
    int maxPoints(vector<vector<int>>& points) {
        int N = points.size();
        if(N <= 2) return N;

        int result = 0;
        for(int i = 0; i < N-1; i++) {
            unordered_map<string, int> slopeMap;
            for(int j = i+1; j < N; j++) {
                string key;
                if(points[j][0] - points[i][0] == 0) {
                    key = "infinite," + to_string(points[i][0]); 
                } else if(points[j][1] - points[i][1] == 0) {
                    key = "0," + to_string(points[i][1]); 
                } else {
                    float slope = (points[j][1] - points[i][1]) / (float)(points[j][0] - points[i][0]);
                    float b = points[i][1] - points[i][0]*slope;
                    key = to_string(slope) + "," + to_string(b);
                }
                
                if(slopeMap.find(key) == slopeMap.end()) {
                    slopeMap.insert({ key, 2 });
                } else {
                    slopeMap[key]++;
                }

                // cout << key << "-->" << slopeMap[key] << endl;
                if(result < slopeMap[key])
                    result = slopeMap[key];
            }
        }

        return result;
    }
};
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