# Algorithms

### From charlesreid1

## Contents

# Overview of Categories

Algorithms can be divided into categories:

- Data structures - algorithmic analysis of data structures
- Strings - algorithms for operations on strings
- Search - search algorithms for searching and search-related data structures
- Sort - basic and advanced algorithms for sorting data
- Graphs - graph structures, algorithms on graph structures. Design graph structures, not algorithms!
- Optimization - solving minimization/maximization problems under constraints, counting problems, etc.

Programming practice and writeups:

- Competitive programming
- Project Euler
- Research and Teaching Blog - https://charlesreid1.github.io

List from Princeton ALGS DS07:

- https://www.cs.princeton.edu/~rs/AlgsDS07/
- Overview
- Union-Find Algorithms
- Stacks and Queues
- Sorting Algorithms
- Advanced Topics in Sorting
- Priority Queues
- Symbol Tables
- Binary Search Trees
- Balanced Trees
- Hashing
- Undirected Graphs
- Directed Graphs
- Minimum Spanning Trees
- Shortest Paths
- Geometric Algorithms
- Search and Intersection
- Radix Sorts
- Tries
- Data Compression
- Pattern Matching
- Linear Programming
- Reductions
- Combinatorial Search

## Search

- search trees
- hash tables

## Sort

- kinds of sort
- sort algorithms
- memory
- scaling
- mathematical analysis
- priority queues

## Data Structures

Algorithmic analysis of data structures, such as binary search trees. Mathematical modeling and probability tools for quantitative analysis of code.

## Strings

Algorithms for strings. What are some fast String algorithms, and how can we utilize them in other contexts? (e.g., comparing extremely large subtrees.)

- sorts
- tries
- search
- regular expressions
- compression

## Graphs

## Optimization

Some of the basic algorithms of optimization, types of constraints, types of solvers and solutions.

Don't waste all your time implementing solutions from scratch if there are better tools available. And in this case, there are: Google OR tools.

- Combinatorics
- Recursion
- backtracking
- Heuristics
- parallel algorithms
- caching, dynamic programming

## Practice and Writeups

Project Euler - number theory and mathematical programming

https://charlesreid1.github.io/ - research and teaching blog

# Flags

AlgorithmsSeries on Algorithms
Algorithms/Sort Three solid O(n log n) search algorithms: Merge Sort Algorithm Analysis/Merge Sort
Algorithms/Search
Algorithms/Combinatorics
Algorithms/Strings
Algorithm complexity Amortization Algorithm Analysis/Matrix Multiplication
Estimation
Project Euler
· Template:AlgorithmsFlag · e |

# References

Awesome algorithms: https://github.com/tayllan/awesome-algorithms

Awesome math: https://github.com/rossant/awesome-math

Stony Brook Algorithm Repository: http://www3.cs.stonybrook.edu/~algorith/implement/graphbase/implement.shtml

Programming Challenges (Skiena's non-red book): https://www.amazon.com/exec/obidos/ASIN/0387001638/thealgorithmrepo

Introduction to the Analysis of Algorithms: http://aofa.cs.princeton.edu/home/