SinaKhalili / cmpt307_Algorithms

Algorithms implemented to aid my study of algorithms class. Algorithms Sanjoy Dasgupta textbook.

CMPT307 Algorithms

Algorithms and homework to aid my study of algorithms class.

Chapter 0

• Fibonacci
• Big(O)
• Numbers of digits from base to base

Chapter 1

• Addition/Subtraction (running times)
• Multiplication/Division (running times)
• Modular Arithmetic
  • Standard : Addition, Subtraction, Multiplication
  • Fast : Exponentiation
  • Slow : Division
  • Finding modular inverse
• RSA algorithm
• Hashing <- Not covered

Chapter 2, Divide and conquer

• Fast multipilcation
• Master's Theorem
• Binary Search
• Mergesort (Recursive and iterative) (show it is optimal)
• Median Finding (Using probablity to give number of steps on average)
• Fast matrix multiplication (Strassen Algorithm)

Chapter 3, Decompositions of Graphs

• Depth First Search
  • Pre and Post ordering
• Directed Acyclic Graphs, DAGs
• Strongly Connected components

Chapter 4, Paths in graphs

• Breadth first search
  • Alarm clock algorithm (Preparation for Djikstra)
• Dijkstra's algorithm
• Proofs of correctness

Chapter 5, Greedy algorithms

• Kurskal's algorithm
• The cut property
  • Proof of the cut property
• Prim's algorithm

Chapter 6, Dynamic Programming

• Shortest path in a dag
• All dp questions are implicit dags
• Longest increasing subsequence
• Manhattan tourist problem
• Longest common subsequence
• Edit text

Class Textbook: Algorithms Sanjoy Dasgupta