<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();
        vector<vector<bool>> pairs(n, vector<bool>(n, false));
        int res = 1;
        for (int i = 0; i < n; i++) {
            for (int j = i+1; j < n; j++) {
                if (!pairs[i][j]) {
                    int temp = 2;
                    pairs[i][j] = true;
                    vector<int> nodes = {i, j};
                    if (points[i][0] == points[j][0]) {
                        for (int k = 0; k < n; k++) {
                            if (k == i || k == j) continue;
                            if (points[k][0] == points[i][0]) {
                                for (int l : nodes) {
                                    pairs[l][k] = true;
                                    pairs[k][l] = true;
                                }
                                nodes.push_back(k);
                                temp++;
                            }
                        }
                    }
                    else {
                        int x = points[i][0], y = points[i][1];
                        int diffX = x - points[j][0];
                        int diffY = y - points[j][1];

                        for (int k = 0; k < n; k++) {
                            if (k == i || k == j) continue;
                            int candX = x - points[k][0];
                            int candY = y - points[k][1];
                            if (diffX * candY  == diffY * candX) {
                                for (int l : nodes) {
                                    pairs[l][k] = true;
                                    pairs[k][l] = true;
                                }
                                nodes.push_back(k);
                                temp++;
                            }
                        }
                    }
                        
                    res = max(res, temp);
                }
            }
        }
        return res;
    }
};
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