Update Permutation and Combination cheatsheets. (#963)
@ -5,14 +5,14 @@ When the order doesn't matter, it is a **Combination**.
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When the order **does** matter it is a **Permutation**.
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When the order **does** matter it is a **Permutation**.
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**"My fruit salad is a combination of apples, grapes and bananas"**
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**"My fruit salad is a combination of apples, grapes and bananas"**
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We don't care what order the fruits are in, they could also be
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We don't care what order the fruits are in, they could also be
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"bananas, grapes and apples" or "grapes, apples and bananas",
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"bananas, grapes and apples" or "grapes, apples and bananas",
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its the same fruit salad.
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its the same fruit salad.
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## Combinations without repetitions
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## Combinations without repetitions
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This is how lotteries work. The numbers are drawn one at a
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This is how lotteries work. The numbers are drawn one at a
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time, and if we have the lucky numbers (no matter what order)
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time, and if we have the lucky numbers (no matter what order)
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we win!
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we win!
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No Repetition: such as lottery numbers `(2,14,15,27,30,33)`
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No Repetition: such as lottery numbers `(2,14,15,27,30,33)`
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@ -30,12 +30,12 @@ It is often called "n choose r" (such as "16 choose 3"). And is also known as th
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Repetition is Allowed: such as coins in your pocket `(5,5,5,10,10)`
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Repetition is Allowed: such as coins in your pocket `(5,5,5,10,10)`
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Or let us say there are five flavours of ice cream:
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Or let us say there are five flavours of ice cream:
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`banana`, `chocolate`, `lemon`, `strawberry` and `vanilla`.
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`banana`, `chocolate`, `lemon`, `strawberry` and `vanilla`.
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We can have three scoops. How many variations will there be?
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We can have three scoops. How many variations will there be?
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Let's use letters for the flavours: `{b, c, l, s, v}`.
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Let's use letters for the flavours: `{b, c, l, s, v}`.
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Example selections include:
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Example selections include:
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- `{c, c, c}` (3 scoops of chocolate)
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- `{c, c, c}` (3 scoops of chocolate)
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@ -46,23 +46,21 @@ Example selections include:
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![Formula](https://www.mathsisfun.com/combinatorics/images/combinations-repeat.gif)
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![Formula](https://www.mathsisfun.com/combinatorics/images/combinations-repeat.gif)
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Where `n` is the number of things to choose from, and we
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Where `n` is the number of things to choose from, and we
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choose `r` of them. Repetition allowed,
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choose `r` of them. Repetition allowed,
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order doesn't matter.
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order doesn't matter.
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## Cheat Sheets
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## Cheatsheet
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Permutations cheat sheet
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![Permutations and Combinations Overview](./images/overview.png)
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![Permutations Cheat Sheet](https://cdn-images-1.medium.com/max/2000/1*JNK-n0Pt0Vbxk0lxVpgT5A.png)
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![Combinations overview](./images/combinations-overview.jpg)
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Combinations cheat sheet
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| --- | --- |
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|![Combinations with repetition](./images/combinations-with-repetitions.jpg) | ![Combinations without repetition](./images/combinations-without-repetitions.jpg) |
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![Combinations Cheat Sheet](https://cdn-images-1.medium.com/max/2000/1*7cFRn8jW4g_91YgDAbmxRQ.png)
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*Made with [okso.app](https://okso.app)*
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Permutations/combinations algorithm ideas.
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![Algorithms Idea](https://cdn-images-1.medium.com/max/2000/1*vLsSsZMnesCFPCYTYMbxrQ.png)
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## References
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## References
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After Width: | Height: | Size: 345 KiB |
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After Width: | Height: | Size: 302 KiB |
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src/algorithms/sets/combinations/images/overview.png
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@ -4,13 +4,13 @@ When the order doesn't matter, it is a **Combination**.
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When the order **does** matter it is a **Permutation**.
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When the order **does** matter it is a **Permutation**.
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**"The combination to the safe is 472"**. We do care about the order. `724` won't work, nor will `247`.
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**"The combination to the safe is 472"**. We do care about the order. `724` won't work, nor will `247`.
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It has to be exactly `4-7-2`.
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It has to be exactly `4-7-2`.
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## Permutations without repetitions
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## Permutations without repetitions
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A permutation, also called an “arrangement number” or “order”, is a rearrangement of
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A permutation, also called an “arrangement number” or “order”, is a rearrangement of
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the elements of an ordered list `S` into a one-to-one correspondence with `S` itself.
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the elements of an ordered list `S` into a one-to-one correspondence with `S` itself.
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Below are the permutations of string `ABC`.
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Below are the permutations of string `ABC`.
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@ -37,19 +37,17 @@ For example the the lock below: it could be `333`.
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n * n * n ... (r times) = n^r
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n * n * n ... (r times) = n^r
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```
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```
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## Cheat Sheets
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## Cheatsheet
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Permutations cheat sheet
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![Permutations and Combinations Overview](./images/overview.png)
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![Permutations Cheat Sheet](https://cdn-images-1.medium.com/max/2000/1*JNK-n0Pt0Vbxk0lxVpgT5A.png)
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![Permutations overview](./images/permutations-overview.jpeg)
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Combinations cheat sheet
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| --- | --- |
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|![Permutations with repetition](./images/permutations-with-repetitions.jpg) | ![Permutations without repetition](./images/permutations-without-repetitions.jpg) |
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![Combinations Cheat Sheet](https://cdn-images-1.medium.com/max/2000/1*7cFRn8jW4g_91YgDAbmxRQ.png)
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*Made with [okso.app](https://okso.app)*
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Permutations/combinations algorithm ideas.
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![Algorithms Idea](https://cdn-images-1.medium.com/max/2000/1*vLsSsZMnesCFPCYTYMbxrQ.png)
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## References
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## References
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BIN
src/algorithms/sets/permutations/images/overview.png
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After Width: | Height: | Size: 142 KiB |
After Width: | Height: | Size: 307 KiB |
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After Width: | Height: | Size: 364 KiB |