> For the complete documentation index, see [llms.txt](https://leetcodebook-1.gitbook.io/top-interview-150/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://leetcodebook-1.gitbook.io/top-interview-150/math/max-points-on-a-line.md).

# 直线上最多的点数

题目链接: <https://leetcode.cn/problems/max-points-on-a-line>

## 解题思路：

枚举每一对点，计算它们构成的直线的斜率，然后将斜率相同的点分为一组，统计每组中点的个数，最后取所有组中点的个数的最大值作为答案

使用了哈希表来存储每个斜率对应的点的个数。由于斜率可能是一个分数，我们需要使用字符串来表示斜率。在计算斜率时，我们使用了欧几里得算法来计算两个点之间的最大公约数，以避免精度误差

**具体实现：**

1. 遍历每一对点，计算它们构成的直线的斜率
2. 将斜率相同的点分为一组，统计每组中点的个数
3. 取所有组中点的个数的最大值作为答案

```go
func maxPoints(points [][]int) int {
	n := len(points)
	if n <= 2 {
		return n
	}

	res := 0
	for i := 0; i < n; i++ {
		m := make(map[string]int) // 用于存储每个斜率对应的点的个数
		dup := 1                  // 用于记录与当前点重合的点的个数

		for j := i + 1; j < n; j++ {
			x, y := points[j][0], points[j][1]
			if x == points[i][0] && y == points[i][1] { // 如果当前点与当前枚举的点重合，则将 dup 加 1
				dup++
				continue
			}

			g := gcd(x-points[i][0], y-points[i][1])         // 计算两个点之间的最大公约数
			dx, dy := (x-points[i][0])/g, (y-points[i][1])/g // 计算斜率
			m[itoa(dx, dy)]++                                // 将斜率相同的点分为一组，统计每组中点的个数
		}

		// 更新最大值
		res = max(res, dup)
		for _, v := range m {
			res = max(res, v+dup)
		}
	}

	return res
}

func itoa(a, b int) string {
	if a == 0 {
		return "0"
	}

	if b == 0 {
		return "1"
	}

	if a < 0 {
		a, b = -a, -b
	}

	return strconv.Itoa(a) + "/" + strconv.Itoa(b)
}

func gcd(a, b int) int {
	for a != 0 {
		a, b = b%a, a
	}

	return b
}

func max(a, b int) int {
	if a > b {
		return a
	}

	return b
}
```

## 复杂度分析

* **时间复杂度：** 时间复杂度是 $$O(n^2)$$，其中 $$n$$ 是点的个数
* **空间复杂度：** 空间复杂度是 $$O(n)$$，算法使用了哈希表来存储每个斜率对应的点的个数


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://leetcodebook-1.gitbook.io/top-interview-150/math/max-points-on-a-line.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.