solution.md

# 直线上最多的点数

<p>给你一个数组 <code>points</code> ，其中 <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> 表示 <strong>X-Y</strong> 平面上的一个点。求最多有多少个点在同一条直线上。</p>

<p> </p>

<p><strong>示例 1：</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/25/plane1.jpg" style="width: 300px; height: 294px;" />
<pre>
<strong>输入：</strong>points = [[1,1],[2,2],[3,3]]
<strong>输出：</strong>3
</pre>

<p><strong>示例 2：</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/25/plane2.jpg" style="width: 300px; height: 294px;" />
<pre>
<strong>输入：</strong>points = [[1,1],[3,2],[5,3],[4,1],[2,3],[1,4]]
<strong>输出：</strong>4
</pre>

<p> </p>

<p><strong>提示：</strong></p>

<ul>
	<li><code>1 <= points.length <= 300</code></li>
	<li><code>points[i].length == 2</code></li>
	<li><code>-10<sup>4</sup> <= x<sub>i</sub>, y<sub>i</sub> <= 10<sup>4</sup></code></li>
	<li><code>points</code> 中的所有点 <strong>互不相同</strong></li>
</ul>


## template

```cpp
#include <bits/stdc++.h>
using namespace std;

struct Point
{
    int x;
    int y;
    Point() : x(0), y(0) {}
    Point(int a, int b) : x(a), y(b) {}
};

class Solution
{
public:
    int maxPoints(vector<Point> &points)
    {
        int ans = 0;
        for (int i = 0; i < points.size(); ++i)
        {
            map<pair<int, int>, int> m;
            int p = 1;
            for (int j = i + 1; j < points.size(); ++j)
            {
                if (points[i].x == points[j].x && (points[i].y == points[j].y))
                {
                    ++p;
                    continue;
                }
                int dx = points[j].x - points[i].x;
                int dy = points[j].y - points[i].y;
                int d = gcd(dx, dy);
                ++m[{dx / d, dy / d}];
            }
            ans = max(ans, p);
            for (auto it = m.begin(); it != m.end(); ++it)
            {
                ans = max(ans, it->second + p);
            }
        }
        return ans;
    }
    int gcd(int a, int b)
    {
        return (b == 0) ? a : gcd(b, a % b);
    }
};


```

## 答案

```cpp

```

## 选项

### A

```cpp

```

### B

```cpp

```

### C

```cpp

```