notes/OJ notes/pages/Leetcode Check-If-It-Is-a-Straight-Line.md

# Leetcode Check-If-It-Is-a-Straight-Line

#### 2022-07-27 11:38

> ##### Algorithms:
>
> #algorithm #math
>
> ##### Difficulty:
>
> #coding_problem #difficulty_easy
>
> ##### Additional tags:
>
> #leetcode
>
> ##### Revisions:
>
> N/A

##### Related topics:

##### Links:

- [Link to problem](https://leetcode.com/problems/check-if-it-is-a-straight-line/)

---

### Problem

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.

#### Examples

**Example 1:**

![](https://assets.leetcode.com/uploads/2019/10/15/untitled-diagram-2.jpg)

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

**Example 2:**

**![](https://assets.leetcode.com/uploads/2019/10/09/untitled-diagram-1.jpg)**

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

#### Constraints

### Thoughts

> [!summary]
> This is a #math problem.

Many math problems can be simplified by:

- work out the expression
- Simplify it.

This is also true in this problem.

We want to calculate the k for every consecutive points, if they are the same, they are on one straight line.

By starting from the first, using them as the base k:

```
k = (dx0 - dx1) / (dy0 - dy1) = (dx - dx') / (dy - dy')
|
v
dx*yi - dy*xi = dx*y0 - dy*x0
```

Which is the cross product of these two points.

### Solution

==#TODO: Fill this out==

```cpp
WIP
```