Lecture 1: Algorithms and Computation Brief

Computation problem - binary relation from problem inputs to correct outputs.

Algorithm - a set of steps to be followed to perform a particular task.

Induction - making a generalization based on observed patterns.

Asymptotic Notation - mathematical notations used to describe the running time of an algorithm when the input tends towards a particular value or a limiting value .

The 3 main asymptotic notations:

1. Upper bound (O) - Big-O notation (Worst case)
2. Lower bound (Ω) - Omega notation (Best case)
3. Tight bound (Θ) - Theta notation (Average case)

How to Solve Algorithms Problem

• Reduce to a problem that you already know - using a data structure or algorithm:
  • Search Problem(Data Structure)
  • Sort Algorithms
  • Shortest Path Algorithms
• Design your own (recursive) algorithm.
  • Brute Force
  • Divide and Conquer
  • Dynamic Programming