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

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+# 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:
+```expander
+tag:#math
+```
+ 
+ 
+
+##### 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
+```