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Permutations/Combinations
Algorithms Cheat Sheets
Oleksii Trekhleb · Follow
Published in ITNEXT · 3 min read · Jun 29, 2018
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3
TL;DR
This article briefly describes the difference between mathematical
permutations and combinations, explains the main idea behind permutations
and combinations algorithms and contains links to algorithms
implementation in JavaScript.
JavaScript code examples may be found in JavaScript Algorithms and Data
Structures repository. Read more for further details.
What are Combinations and Permutations
Let’s say we have a collection or set of something (collection of numbers,
letters, fruits, coins etc.) and we need to pick items from a collection to form
another collection. For example imagine that you’re picking lottery numbers
from the collection of available numbers ({0, 1, 2, 3, 4, 5, 6, 7, 8, 9} → {4, 5, 9}).
Or you’re picking the fruits from collections of available fruits to make a fruit
salad ({orange, apple, banana, grape} → {apple, banana}). Or you’re trying to
guess the lock password and you’re choosing 3 numbers out of {0, 1, 2, 3, 4, 5,
6, 7, 8, 9} set to guess the correct password ({1, 1, 2}, {1, 1, 3}, {1, 1, 4}, …). In
all these cases you’re creating one collection out from the other one by
following some rules. And these rules define whether your new collection is
a permutation or a combination.
If the order of the elements in your new collection matters then you’re
dealing with permutations (for example in case of lock password the set of
{1, 1, 2} is not the same as set of {2, 1, 1}). Otherwise if the order doesn’t
matter then you’re making a combination (combination of fruits {apple,
Open in app
banana} to make a salad — it doesn’t
matter if you’ll pick apple or banana
Search
first).
Your new collection may or may not contain duplicates (or repetitions). For
example in lock password you’re allowed to use duplicate numbers but when
you’re dealing with collection of race winners ({Black, Smith, Brown}) you’re
not allowed to make duplicates because it doesn’t make sense to have the
same person to be on two winning positions.
To illustrate all these differences I’ve created small cheat sheets to make it
more easy to remember them.
Permutations Concept Cheat Sheet
Write
Permutations concept cheat sheet
Combinations Concept Cheat Sheet
Combinations concept cheat sheet
Permutations/Combinations Algorithms Cheat Sheet
If you would want to implement permutation and combination algorithms
you might find the following permutation/combination algorithms cheat
sheet useful.
Permutation/combination algorithms cheat sheet
Combinations and Permutations in JavaScript
If you want to see exact implementations of these algorithms in JavaScript
you may find follow these links:
Combinations in JavaScript
Permutations in JavaScript
I hope you’ll find these cheat sheets helpful and they will help you to write
combinations/permutations algorithms smoothly.
Happy coding!
Oleksii Trekhleb (@Trekhleb) | Twitter
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Written by Oleksii Trekhleb
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