Update Permutation and Combination cheatsheets. (#963)

This commit is contained in:
Oleksii Trekhleb 2022-11-28 16:43:30 +01:00 committed by GitHub
parent 565256088a
commit 025b9a390b
No known key found for this signature in database
GPG Key ID: 4AEE18F83AFDEB23
10 changed files with 25 additions and 29 deletions

View File

@ -5,14 +5,14 @@ When the order doesn't matter, it is a **Combination**.
When the order **does** matter it is a **Permutation**. When the order **does** matter it is a **Permutation**.
**"My fruit salad is a combination of apples, grapes and bananas"** **"My fruit salad is a combination of apples, grapes and bananas"**
We don't care what order the fruits are in, they could also be We don't care what order the fruits are in, they could also be
"bananas, grapes and apples" or "grapes, apples and bananas", "bananas, grapes and apples" or "grapes, apples and bananas",
its the same fruit salad. its the same fruit salad.
## Combinations without repetitions ## Combinations without repetitions
This is how lotteries work. The numbers are drawn one at a This is how lotteries work. The numbers are drawn one at a
time, and if we have the lucky numbers (no matter what order) time, and if we have the lucky numbers (no matter what order)
we win! we win!
No Repetition: such as lottery numbers `(2,14,15,27,30,33)` No Repetition: such as lottery numbers `(2,14,15,27,30,33)`
@ -30,12 +30,12 @@ It is often called "n choose r" (such as "16 choose 3"). And is also known as th
Repetition is Allowed: such as coins in your pocket `(5,5,5,10,10)` Repetition is Allowed: such as coins in your pocket `(5,5,5,10,10)`
Or let us say there are five flavours of ice cream: Or let us say there are five flavours of ice cream:
`banana`, `chocolate`, `lemon`, `strawberry` and `vanilla`. `banana`, `chocolate`, `lemon`, `strawberry` and `vanilla`.
We can have three scoops. How many variations will there be? We can have three scoops. How many variations will there be?
Let's use letters for the flavours: `{b, c, l, s, v}`. Let's use letters for the flavours: `{b, c, l, s, v}`.
Example selections include: Example selections include:
- `{c, c, c}` (3 scoops of chocolate) - `{c, c, c}` (3 scoops of chocolate)
@ -46,23 +46,21 @@ Example selections include:
![Formula](https://www.mathsisfun.com/combinatorics/images/combinations-repeat.gif) ![Formula](https://www.mathsisfun.com/combinatorics/images/combinations-repeat.gif)
Where `n` is the number of things to choose from, and we Where `n` is the number of things to choose from, and we
choose `r` of them. Repetition allowed, choose `r` of them. Repetition allowed,
order doesn't matter. order doesn't matter.
## Cheat Sheets ## Cheatsheet
Permutations cheat sheet ![Permutations and Combinations Overview](./images/overview.png)
![Permutations Cheat Sheet](https://cdn-images-1.medium.com/max/2000/1*JNK-n0Pt0Vbxk0lxVpgT5A.png) ![Combinations overview](./images/combinations-overview.jpg)
Combinations cheat sheet | | |
| --- | --- |
|![Combinations with repetition](./images/combinations-with-repetitions.jpg) | ![Combinations without repetition](./images/combinations-without-repetitions.jpg) |
![Combinations Cheat Sheet](https://cdn-images-1.medium.com/max/2000/1*7cFRn8jW4g_91YgDAbmxRQ.png) *Made with [okso.app](https://okso.app)*
Permutations/combinations algorithm ideas.
![Algorithms Idea](https://cdn-images-1.medium.com/max/2000/1*vLsSsZMnesCFPCYTYMbxrQ.png)
## References ## References

Binary file not shown.

After

Width:  |  Height:  |  Size: 345 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 324 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 302 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 142 KiB

View File

@ -4,13 +4,13 @@ When the order doesn't matter, it is a **Combination**.
When the order **does** matter it is a **Permutation**. When the order **does** matter it is a **Permutation**.
**"The combination to the safe is 472"**. We do care about the order. `724` won't work, nor will `247`. **"The combination to the safe is 472"**. We do care about the order. `724` won't work, nor will `247`.
It has to be exactly `4-7-2`. It has to be exactly `4-7-2`.
## Permutations without repetitions ## Permutations without repetitions
A permutation, also called an “arrangement number” or “order”, is a rearrangement of A permutation, also called an “arrangement number” or “order”, is a rearrangement of
the elements of an ordered list `S` into a one-to-one correspondence with `S` itself. the elements of an ordered list `S` into a one-to-one correspondence with `S` itself.
Below are the permutations of string `ABC`. Below are the permutations of string `ABC`.
@ -37,19 +37,17 @@ For example the the lock below: it could be `333`.
n * n * n ... (r times) = n^r n * n * n ... (r times) = n^r
``` ```
## Cheat Sheets ## Cheatsheet
Permutations cheat sheet ![Permutations and Combinations Overview](./images/overview.png)
![Permutations Cheat Sheet](https://cdn-images-1.medium.com/max/2000/1*JNK-n0Pt0Vbxk0lxVpgT5A.png) ![Permutations overview](./images/permutations-overview.jpeg)
Combinations cheat sheet | | |
| --- | --- |
|![Permutations with repetition](./images/permutations-with-repetitions.jpg) | ![Permutations without repetition](./images/permutations-without-repetitions.jpg) |
![Combinations Cheat Sheet](https://cdn-images-1.medium.com/max/2000/1*7cFRn8jW4g_91YgDAbmxRQ.png) *Made with [okso.app](https://okso.app)*
Permutations/combinations algorithm ideas.
![Algorithms Idea](https://cdn-images-1.medium.com/max/2000/1*vLsSsZMnesCFPCYTYMbxrQ.png)
## References ## References

Binary file not shown.

After

Width:  |  Height:  |  Size: 142 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 307 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 301 KiB

Binary file not shown.

After

Width:  |  Height:  |  Size: 364 KiB