1232. Check if It Is a Straight Line

# 1232. Check If It Is a Straight Line#

## 题目 #

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.

Example 1:

``````Input: coordinates = [[1,2],[2,3],[3,4],[4,5],[5,6],[6,7]]
Output: true
``````

Example 2:

``````Input: coordinates = [[1,1],[2,2],[3,4],[4,5],[5,6],[7,7]]
Output: false
``````

Constraints:

• `2 <= coordinates.length <= 1000`
• `coordinates[i].length == 2`
• `-10^4 <= coordinates[i][0], coordinates[i][1] <= 10^4`
• `coordinates` contains no duplicate point.

## 题目大意 #

• 2 <= coordinates.length <= 1000
• coordinates[i].length == 2
• -10^4 <= coordinates[i][0], coordinates[i][1] <= 10^4
• coordinates 中不含重复的点

## 解题思路 #

• 给出一组坐标点，要求判断这些点是否在同一直线上。
• 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`

## 代码 #

``````
package leetcode

func checkStraightLine(coordinates [][]int) bool {
dx0 := coordinates[1][0] - coordinates[0][0]
dy0 := coordinates[1][1] - coordinates[0][1]
for i := 1; i < len(coordinates)-1; i++ {
dx := coordinates[i+1][0] - coordinates[i][0]
dy := coordinates[i+1][1] - coordinates[i][1]
if dy*dx0 != dy0*dx { // check cross product
return false
}
}
return true
}

``````

Sep 6, 2020