87 lines
1.5 KiB
Markdown
87 lines
1.5 KiB
Markdown
# Leetcode Check-If-It-Is-a-Straight-Line
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#### 2022-07-27 11:38
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> ##### Algorithms:
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>
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> #algorithm #math
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>
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> ##### Difficulty:
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>
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> #coding_problem #difficulty-easy
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>
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> ##### Additional tags:
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>
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> #leetcode
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>
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> ##### Revisions:
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>
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> N/A
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##### Related topics:
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##### Links:
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- [Link to problem](https://leetcode.com/problems/check-if-it-is-a-straight-line/)
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---
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### Problem
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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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#### Examples
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**Example 1:**
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```
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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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```
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**Example 2:**
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****
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```
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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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```
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#### Constraints
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### Thoughts
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> [!summary]
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> This is a #math problem.
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Many math problems can be simplified by:
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- work out the expression
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- Simplify it.
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This is also true in this problem.
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We want to calculate the k for every consecutive points, if they are the same, they are on one straight line.
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By starting from the first, using them as the base k:
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```
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k = (dx0 - dx1) / (dy0 - dy1) = (dx - dx') / (dy - dy')
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v
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dx*yi - dy*xi = dx*y0 - dy*x0
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```
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Which is the cross product of these two points.
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### Solution
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==#TODO: Fill this out==
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```cpp
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WIP
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```
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