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‎book/chapters/algorithms-analysis.adoc‎

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Not all algorithms are created equal. There are "good" and "bad" algorithms. The good ones are fast; the bad ones are slow. Slow algorithms cost more money to run. Inefficient algorithms could make some calculations impossible in our lifespan!
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To give you a clearer picture of how different algorithms perform as the input size grows, take a look at the following problems and how their relative execution time changes as the input size increases.
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(((table)))
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.Relationship between algorithm input size and time taken to complete
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[cols=",,,,,",options="header",]
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TIP: Asymptotic analysis describes the behavior of functions as their inputs approach to infinity.
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In the previous example, we analyzed `getMin` with an array of size 3; what happen size is 10 or 10k or a million?
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(((table)))
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.Operations performed by an algorithm with a time complexity of 3n+3
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.Operations performed by an algorithm with a time complexity of `3n + 3`
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[cols=",,",options="header",]
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|===========================
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|n (size) |Operations |total

‎book/chapters/array.adoc‎

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== Array Complexity
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To sum up, the time complexity on an array is:
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(((table)))
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// tag::table[]
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.Time/Space complexity for the array operations
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|===
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.2+.^s| Data Structure 2+^s| Searching By 3+^s| Inserting at the 3+^s| Deleting from .2+.^s| Space
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(((Constant)))
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(((Runtime, Constant)))
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Array Operations
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.Array Operations timex complexity
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|===
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| Operation | Time Complexity | Usage
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| push ^| O(1) | Insert element to the right side.
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| shift ^| O(n) | Remove leftmost element.
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| splice ^| O(n) | Insert and remove from anywhere.
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|===
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//end::table

‎book/chapters/big-o-examples.adoc‎

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== Summary
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We went through 8 of the most common time complexities and provided examples for each of them. Hopefully, this will give you a toolbox to analyze algorithms.
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(((table)))
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// tag::table[]
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.Most common algorithmic running times and their examples
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[cols="2,2,5",options="header"]
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|===
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|<<Factorial>>
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|<<factorial-example>>
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|===
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// end::table[]

‎book/chapters/cheatsheet.adoc‎

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== Runtimes
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.Most common algorithmic running times and their examples
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[cols="2,2,5",options="header"]
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|===
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|Big O Notation
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|Name
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|Example(s)
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|O(1)
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|<<Constant>>
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|#<<constant-example>>, #<<linked-list-inserting-beginning>>
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|O(log n)
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|<<Logarithmic>>
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|<<logarithmic-example>>
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|O(n)
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|<<Linear>>
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|<<linear-example>>
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|O(n log n)
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|<<Linearithmic>>
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|<<linearithmic-example>>
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|O(n^2^)
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|<<Quadratic>>
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|<<quadratic-example>>
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|O(n^3^)
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|<<Cubic>>
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|<<cubic-example>>
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|O(2^n^)
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|<<Exponential>>
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|<<exponential-example>>
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|O(n!)
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|<<Factorial>>
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|<<factorial-example>>
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|===
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include::big-o-examples.adoc[tag=table]
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.How long an algorithm takes to run based on their time complexity and input size
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[cols=",,,,,,",options="header",]

‎book/chapters/graph.adoc‎

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== Graph Complexity
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(((table)))
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// tag::table[]
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.Time complexity for a Graph data structure
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|===
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.2+.^s| Data Structure 2+^s| Vertices 2+^s| Edges .2+^.^s| Space Complexity
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| Graph (adj. list w/array) ^| O(1) ^| O(\|V\| + \|E\|)) ^|O(1) ^|O(\|V\| + \|E\|) ^|O(\|V\| + \|E\|)
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| Graph (adj. list w/HashSet) ^| O(1) ^| O(\|V\|)) ^|O(1) ^|O(\|V\|) ^|O(\|V\| + \|E\|)
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|===
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// end::table[]
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As you can see using a `HashSet` on for the adjacency list make a performance improvement.

‎book/chapters/linear-data-structures-outro.adoc‎

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.Use a Stack when:
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* You need to access your data as last-in, first-out (LIFO).
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* You need to implement a <<Depth-First Search for Binary Tree, Depth-First Search>>
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// tag::table[]
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.Time/Space Complexity of Linear Data Structures (Array, LinkedList, Stack & Queues)
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|===
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| Queue (w/array) ^|- ^|- ^|- ^|- ^|*O(n)* ^|- ^|- ^|O(1) ^|O(n)
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| <<Queue>> (w/list) ^|- ^|- ^|- ^|- ^|O(1) ^|- ^|- ^|O(1) ^|O(n)
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|===
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// end::table[]

‎book/chapters/linked-list.adoc‎

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== Linked List Complexity vs. Array Complexity
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So far, we have seen two liner data structures with different use cases. Here’s a summary:
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.Big O cheat sheet for Linked List and Array
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|===
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| Linked List (singly) ^|O(n) ^|O(n) ^|O(1) ^|O(n) ^|O(1) ^|O(1) ^|O(n) ^|*O(n)* ^|O(n)
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| Linked List (doubly) ^|O(n) ^|O(n) ^|O(1) ^|O(n) ^|O(1) ^|O(1) ^|O(n) ^|*O(1)* ^|O(n)
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|===
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// end::table[]
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(((Linear)))
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(((Runtime, Linear)))
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‎book/chapters/map-hashmap-vs-treemap.adoc‎

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== TreeMap Time complexity vs HashMap
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As we discussed so far, there is a trade-off between the implementations.
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// tag::table[]
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.Time complexity for different Maps implementations
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| Tree Map (Red-Black Tree) ^|O(log n) ^|O(n) ^|O(log n) ^|O(log n) ^|O(log n)
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|===
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{empty}* = Amortized run time. E.g. rehashing might affect run time to *O(n)*.
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// end::table[]
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(((Linear)))
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‎book/chapters/map-hashmap.adoc‎

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== HashMap time complexity
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Hash Map it’s very optimal for searching values by key in constant time *O(1)*. However, searching by value is not any better than an array since we have to visit every value *O(n)*.
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// tag::table[]
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.Time complexity for a Hash Map
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| Hash Map (optimized) ^|O(1)* ^|O(n) ^|O(1)* ^|O(1)* ^|O(1)*
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// end::table[]
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indexterm:[Runtime, Linear]
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As you can notice we have amortized times since, in the unfortunate case of a rehash, it will take O(n) while it resizes. After that, it will be *O(1)*.

‎book/chapters/preface.adoc‎

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This book is for software developers familiar with JavaScript looking to improve their problem-solving skills or preparing for a job interview.
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NOTE: You can apply the concepts in this book to any programming language. However, instead of doing examples on pseudo-code we are going to use JavaScript to implement the code examples.
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NOTE: You can apply the concepts in this book to any programming language. However, instead of doing examples in pseudo-code we are going to use JavaScript to implement the code examples.
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== What you need for this book
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