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Commit fee24f8

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‎book/book.adoc‎

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include::chapters/divide-and-conquer--intro.adoc[]
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‎book/chapters/algorithms-intro.adoc‎

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IMPORTANT: There's not a single approach to solve all problems but knowing well-known techniques can help you build your own faster.
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.We are going to discuss the following approaches for solving algorithms problems:
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- <<Greedy Algorithms>>: makes choices at each step trying to find the optimal solution.
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- <<Dynamic Programming>>: use memoization for repated subproblems.
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- <<Greedy Algorithms>>: makes greedy choices using heuristics to find the best solution without looking back.
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- <<Dynamic Programming>>: technique for solving problems with *overlapping subproblems*. It uses *memoization* to avoid duplicated work.
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- <<Divide and conquer>>: *divide* problems into smaller pieces, *conquer* each subproblem and then *join* the results.
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- <<Backtracking>>: search all possible combinations until it finds the solution.
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- <<Divide and conquer>>: break problems into smaller pieces and then join the results.

‎book/chapters/backtracking.adoc‎

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‎book/chapters/cheatsheet.adoc‎

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| Selection sort | O(n^2^) | O(1) | Yes | Yes | Yes | Yes |
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| Bubble sort | O(n^2^) | O(1) | Yes | Yes | Yes | Yes |
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| Merge sort | O(n log n) | O(n) | Yes | No | No | No |
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| Quick sort | O(n log n) | O(log n) | Yes | No | No | No |
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| Quicksort | O(n log n) | O(log n) | Yes | No | No | No |
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// | Tim sort | O(n log n) | O(log n) | Yes | No | No | Yes | Hybrid of merge and insertion sort
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|===
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Divide and conquer is another strategy for solving algorithmic problems.
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It splits the input into manageble parts recursively and finally join solved pieces to form the end result.
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.Examples of divide and conquer algorithms:
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- <<Merge Sort>>: *divides* the input into pairs, sort them and them *join* all the pieces in ascending order.
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- <<Quicksort>>: *splits* the data by a random number called "pivot", then move everything smaller than the pivot to the left and anything bigger to the right. Repeat the process on the left and right side. Note: since this works in place doesn't need a join part.
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- <<logarithmic-example, Binary Search>>: find a value in a sorted collection by *spliting* the data in half until it finds the value.
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- <<Getting all permutations of a word, Permutations>>: *Take out* the first element from the input and solve permutation for the reminder of the data recursively, then *join* results and append the elements that were take out.
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We can solve algorithms using D&C algorithms using the following steps.
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.Divide and conquer algorithms steps:
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1. *Divide* data into subproblems.
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2. *Conquer* each subproblem.
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3. *Combine* solutions.

‎book/chapters/divide-and-conquer.adoc‎

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‎book/chapters/dynamic-programming--intro.adoc‎

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Dynamic programming (dp) is a way to solve algorithmic problems by finding the base case and building a solution from the ground-up. We also keep track of previous answers to avoid re-computing the same operations.
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Dynamic programming (dp) is a way to solve algorithmic problems with *overlapping subproblems*. Algorithms using dp find the base case and building a solution from the ground-up. They also _keep track_ of previous answers to avoid re-computing the same operations.
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// https://twitter.com/amejiarosario/status/1103050924933726208
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// https://www.quora.com/How-should-I-explain-dynamic-programming-to-a-4-year-old/answer/Jonathan-Paulson

‎book/chapters/greedy-algorithms.adoc‎

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

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.Use a Queue when:
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* You need to access your data in a first-come, first served basis (FIFO).
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* You need to implement a <<BreadthFirst Search>>
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* You need to implement a <<Breadth-First Search for Binary Tree, Breadth-First Search>>
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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 <<DepthFirst Search>>
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* You need to implement a <<Depth-First Search for Binary Tree, Depth-First Search>>
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.Time Complexity of Linear Data Structures (Array, LinkedList, Stack & Queues)
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|===

‎book/chapters/output.adoc‎

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times (the input can only be halved O(log(n)) times). n items iterated
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log(n) times gives O(n log(n)).
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== Quick Sort
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== Quicksort
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