Introduction to Algorithms and Data Structures

Course Overview

• Presented by Treehouse, available on FreeCodeCamp's YouTube channel.
• Target audience includes high school/college students, developers, or anyone learning to code.
• Focus on algorithms: understanding their performance, comparison, and utility.
• Less about specific algorithms, more about foundational tools and concepts.
• Programming language used: Python.

What is an Algorithm?

• An algorithm is a set of steps or instructions to complete a task.
• Examples:
  • Recipe
  • Morning routine
  • Driving directions
• In computer science, an algorithm is a set of steps a program follows to complete a task.
• Understanding algorithms involves knowing established solutions and when to apply them.
• Algorithmic thinking: Break problems into steps and identify the right algorithm or data structure.

Why Learn Algorithms?

• Essential for understanding complexity and efficiency in programming.
• Important for technical interviews, especially in big tech companies.

Sample Game Demonstration

• Objective: Guess a number between 1 and 10.
• **Key Strategies: Ensuring bounds are established accurately.
• Game example:
  • John’s approach: Sequential guesses (took more tries)
  • Brittany’s approach: Binary search-like guesses (took fewer tries)
• Different strategies perform better based on the situation.

Core Concepts of Algorithms

• Algorithm Definition must have:
  • Clearly Defined Problem Statement
  • Specific set of instructions and order
  • Each step must be clear and distinct
  • Must produce a result
  • Should complete in finite time
• Ensuring an algorithm’s correctness involves consistent output for the same input.

Evaluating Algorithms

• Focus on both correctness and efficiency.
• Efficiency: Two measures of efficiency (time complexity and space complexity).
• Time Complexity: Measure of how long an algorithm takes to run as input size grows.
• Space Complexity: Measure of the memory an algorithm uses as input size grows.

Example: Linear Search vs Binary Search

• Linear Search:
  • Time complexity: O(n)
  • Implementation: Sequentially checking each element until the target is found.
• Binary Search:
  • Requires sorted input.
  • Time complexity: O(log n)
  • Implementation: Dividing the search interval in half repeatedly.
  • Example: Implementing binary search in Python with midpoints calculated and comparisons made.

Recursion

• Definition: Recursive function calls itself within its definition.
• Requires a base case to prevent infinite looping.
• Used in several algorithms for efficiency in breaking problems into smaller parts.

Sorting Algorithms

Bubble Sort

• Simple sorting algorithm, compares adjacent elements and swaps them if out of order.
• Time complexity: O(n^2)

Selection Sort

• Selects the smallest element repeatedly and builds a sorted list.
• Uses two arrays (unsorted and sorted).
• Time complexity: O(n^2)

Quick Sort

• Uses a pivot to partition the array into elements less than and greater than the pivot.
• Recursively sorts partitions.
• Best case time complexity: O(n log n)
• Worst case time complexity: O(n^2) if poor pivot selection.

Merge Sort

• Divides array into halves, recursively sorts them, and then merges the sorted halves.
• Time complexity: O(n log n)
• Example implementation with Python, emphasizing splitting the list and merging sorted lists.

Searching in Sorted Lists

Binary Search

• Efficient searching method on sorted lists.
• Divides search interval repeatedly.
• Time complexity: O(log n)
• Detailed Python implementation illustrated in the course.

Summary

• Algorithmic thinking: Develops through practice, helps break down complex problems.
• Big O Notation: Essential for comparing algorithm performance, especially for large datasets.
• Choosing Algorithms: Based on problem context, data structure, and specific use cases.

Homework/Exercises

• Implement various searches and sorts in Python or your preferred language.
• Experiment with algorithm performance on different data sets.
• Read additional resources on advanced sorting and searching algorithms.