Lecture Notes: Introduction to Algorithms by Treehouse

Course Overview

• Provider: Treehouse (available on Free Code Camp's YouTube channel)
• Instructor: Pasan (Treehouse instructor)
• Target Audience: High school/college students, developers, coding learners
• Course Goal: Alleviate fears around algorithms and build foundational knowledge
• Topics: Evaluating algorithms, performance, comparisons, utility in context
• Programming Language: Python (familiarity with programming expected)

What Is an Algorithm?

• Definition: A set of steps/instructions to complete a task
• Examples: Recipes, morning routines, driving directions
• In Computer Science: Steps a program takes to finish a task
• Importance: Efficiency and correctness in solving problems using known solutions
• Algorithmic Thinking: Breaking down problems and identifying appropriate algorithms/data structures

Game Example to Explain Algorithmic Thinking

• Game: Guess a number between 1 and 10
• Goal: Illustrate different strategies for searching for a value
  • John's Linear Approach: Sequentially guesses each number
  • Brittany's Binary Search Approach: Narrows down range based on feedback
• Takeaway: Some strategies work better depending on the context/problem
• Worst-case Scenario: Always evaluate to understand performance bounds

Key Components and Characteristics of Algorithms

• Clear Problem Statement: Defined input and expected output
• Order of Steps: Specific and distinct steps in a defined sequence
• Efficiency: How well the steps are optimized
• Termination: Algorithm must complete in finite time and produce a result

Linear vs Binary Search

• Linear Search: Sequentially checks each element until the target is found
  • Complexity: O(n)
• Binary Search: Divides range and eliminates half the possibilities each time
  • Complexity: O(log n)
  • Precondition: List must be sorted

Implementing Algorithms in Code

• Linear Search (Python):

  def linear_search(list, target):
      for i in range(len(list)):
          if list[i] == target:
              return i
      return None
  

• Binary Search (Python):

  def binary_search(list, target):
      first = 0
      last = len(list) - 1
      while first <= last:
          midpoint = (first + last) // 2
          if list[midpoint] == target:
              return midpoint
          elif list[midpoint] < target:
              first = midpoint + 1
          else:
              last = midpoint - 1
      return None
  

Understanding Algorithm Efficiency

• Time Complexity: Measure of how long it takes for algorithm to run
  • Common Notations: O(1), O(log n), O(n), O(n log n), O(n^2), O(2^n), O(n!)
• Space Complexity: Measure of memory usage of algorithm
• Trade-offs: Between time and space, balance needs based on context

Example: Measuring Complexity of Algorithms using Games Simulation

• Linear Search Time Complexity: Linear, O(n)
• Binary Search Time Complexity: Logarithmic, O(log n)
• Worst-Case Analysis: Ensures no surprises in performance

Recursive Binary Search

• Concept: Function calls itself to half the list until the target is found or list is empty
• Code Implementation:

  def recursive_binary_search(list, target):
      if len(list) == 0:
          return False
      else:
          midpoint = len(list) // 2
          if list[midpoint] == target:
              return True
          elif list[midpoint] < target:
              return recursive_binary_search(list[midpoint+1:], target)
          else:
              return recursive_binary_search(list[:midpoint], target)
  

• Pros: Intuitive and often easier to implement
• Cons: Higher space complexity due to function call stack

Conclusion

• Algorithmic Thinking Skills: Break down problems, define inputs/outputs, choose appropriate algorithms
• Practice: Implement different algorithms, evaluate efficiency, balance between runtime and space complexity
• Advanced Topics: Continued learning of additional algorithms and data structures