@dxzmpk/js-algorithms-data-structures
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Algorithms and data-structures implemented on JavaScript
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# Combinations
When the order doesn't matter, it is a **Combination**.
When the order **does** matter it is a **Permutation**.
**"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
"bananas, grapes and apples" or "grapes, apples and bananas",
its the same fruit salad.
## Combinations without repetitions
This is how lotteries work. The numbers are drawn one at a
time, and if we have the lucky numbers (no matter what order)
we win!
No Repetition: such as lottery numbers `(2,14,15,27,30,33)`
**Number of combinations**
where `n` is the number of things to choose from, and we choose `r` of them,
no repetition, order doesn't matter.
It is often called "n choose r" (such as "16 choose 3"). And is also known as the Binomial Coefficient.
## Combinations with repetitions
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:
`banana`, `chocolate`, `lemon`, `strawberry` and `vanilla`.
We can have three scoops. How many variations will there be?
Let's use letters for the flavours: `{b, c, l, s, v}`.
Example selections include:
- `{c, c, c}` (3 scoops of chocolate)
- `{b, l, v}` (one each of banana, lemon and vanilla)
- `{b, v, v}` (one of banana, two of vanilla)
**Number of combinations**
Where `n` is the number of things to choose from, and we
choose `r` of them. Repetition allowed,
order doesn't matter.
## Cheat Sheets
Permutations cheat sheet
Combinations cheat sheet
Permutations/combinations algorithm ideas.
## References
- [Math Is Fun](https://www.mathsisfun.com/combinatorics/combinations-permutations.html)
- [Permutations/combinations cheat sheets](https://medium.com/@trekhleb/permutations-combinations-algorithms-cheat-sheet-68c14879aba5)