Algorithms

Internal

• Programming

Overview

A data structure is an arrangement of data in computer's memory or external storage. Data structures include arrays, linked lists, stacks, binary trees, hash tables, etc.

Algorithms manipulate the data in these structures in various ways. One of the most important characteristics of an algorithm is its efficiency, which can be analyzed through formal methods. A special notation, called asymptotic notation is used to express the time efficiency of algorithms, by bounding algorithms running time from above and from below. All these notions are expanded upon in Algorithm Complexity.

• Arrays.
• Lists (single linked and double linked)
• Stack
• Queue. Difference between list and queue.
• Sorting
  • Comparison Sort. Comparison sort algorithm class. Know that comparison sort cannot do better than n ln n. Proof in a separate article.
  • Non-comparison Sort
  • Sorting algorithms characteristics (in-place, stability)
• Algorithm complexity, Bounds. Understand and document O, Omega and Theta notations. Perform complexity analysis on all the algorithms I examine. Expected running time, worst-case running time. Average case running time.
• Iteration and recursion – fundamentally different approaches.
• Set
• Map
• Hash Map
• Distributed Hash Map. Insist on this as is key to systems that scale.
• Collision resistant hash function.
• Trees
  • Binary Trees. Binary tree height.
    • Sorting trees. Difference between a binary search tree and a red-black tree.
  • BTrees
• Tree walking algorithms. Difference between depth first and breadth first.
• Graphs
• Graph algorithms
• Dynamic programming and memoization.
• Greedy algorithms.
• Matrix multiplication (NOKB and code).
• lg and ln notation. Link from the Mathematics main page.
• Random variable analysis. Indicator random variable.

Probability Distribution.

• Consider starting upside down, with the bottom (math) sections, and NOKB concepts from them first.
• Mathematics: Understand and document induction.
• Need to understand aggregate analysis Section 17.1

Organizatorium

• Array
• Directed Acyclic Graph
• Associative Array
• Map
• Tree
  • Red-Black Tree
• Consistent Hashing
• https://en.wikipedia.org/wiki/Big_O_notation
• https://probablydance.com/2018/06/16/fibonacci-hashing-the-optimization-that-the-world-forgot-or-a-better-alternative-to-integer-modulo
• http://infotechgems.blogspot.com/2011/11/java-collections-performance-time.html