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72 lines
2.0 KiB
Markdown
Executable File
72 lines
2.0 KiB
Markdown
Executable File
# [1232. Check If It Is a Straight Line](https://leetcode.com/problems/check-if-it-is-a-straight-line/)
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## 题目
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You are given an array `coordinates`, `coordinates[i] = [x, y]`, where `[x, y]` represents the coordinate of a point. Check if these points make a straight line in the XY plane.
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**Example 1**:
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Input: coordinates = [[1,2],[2,3],[3,4],[4,5],[5,6],[6,7]]
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Output: true
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**Example 2**:
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Input: coordinates = [[1,1],[2,2],[3,4],[4,5],[5,6],[7,7]]
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Output: false
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**Constraints**:
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- `2 <= coordinates.length <= 1000`
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- `coordinates[i].length == 2`
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- `-10^4 <= coordinates[i][0], coordinates[i][1] <= 10^4`
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- `coordinates` contains no duplicate point.
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## 题目大意
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在一个 XY 坐标系中有一些点，我们用数组 coordinates 来分别记录它们的坐标，其中 coordinates[i] = [x, y] 表示横坐标为 x、纵坐标为 y 的点。
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请你来判断，这些点是否在该坐标系中属于同一条直线上，是则返回 true，否则请返回 false。
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提示：
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- 2 <= coordinates.length <= 1000
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- coordinates[i].length == 2
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- -10^4 <= coordinates[i][0], coordinates[i][1] <= 10^4
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- coordinates 中不含重复的点
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## 解题思路
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- 给出一组坐标点，要求判断这些点是否在同一直线上。
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- 按照几何原理，依次计算这些点的斜率是否相等即可。斜率需要做除法，这里采用一个技巧是换成乘法。例如 `a/b = c/d` 换成乘法是 `a*d = c*d` 。
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## 代码
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```go
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package leetcode
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func checkStraightLine(coordinates [][]int) bool {
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dx0 := coordinates[1][0] - coordinates[0][0]
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dy0 := coordinates[1][1] - coordinates[0][1]
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for i := 1; i < len(coordinates)-1; i++ {
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dx := coordinates[i+1][0] - coordinates[i][0]
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dy := coordinates[i+1][1] - coordinates[i][1]
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if dy*dx0 != dy0*dx { // check cross product
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return false
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}
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}
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return true
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}
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``` |