Introduction to Algorithms Lecture Notes

Course Overview

• Offered by Treehouse, in collaboration with Free Code Camp.
• Focus on algorithms, particularly sorting and searching.
• Designed to dispel fear around algorithms and provide a foundational understanding.

What is an Algorithm?

• A set of steps or instructions for completing a task.
• Examples:
  • Recipes
  • Morning routines
  • Driving directions
• In computer science, refers to the steps a program takes to finish a task.

Importance of Algorithms

• Knowing about algorithms is crucial for:
  • Evaluating their performance.
  • Understanding efficiency and complexity.
  • Preparing for technical interviews in the industry.

Key Concepts

• Algorithmic Thinking:
  • Breaking down a problem into distinct steps.
  • Identifying the right data structures and algorithms for a task.
• Complexity and Efficiency:
  • Understanding how code performs in different situations is critical.
  • Algorithms are often evaluated for their time and space complexity.

Types of Algorithms Covered

Searching Algorithms

• Linear Search:
  • Iterates through each element until the target is found.
  • Time complexity: O(n)
• Binary Search:
  • Requires sorted data.
  • Cuts search space in half with each comparison.
  • Time complexity: O(log n)

Sorting Algorithms

• Selection Sort:
  • Simple but inefficient.
  • Time complexity: O(n²)
• Merge Sort:
  • A more efficient sorting algorithm.
  • Time complexity: O(n log n)

Recursion

• A technique where a function calls itself.
• Essential for many algorithms, including sorting (e.g., merge sort).
• Base cases are needed to terminate the recursive calls.

Recursion Example: Sum Function

• Demonstrated through a function that sums a list of numbers.
• Base case: when the list is empty.

Implementation Examples

Bogosort

• Inefficient sorting algorithm; randomizes list until sorted.
• Time complexity is highly unpredictable and inefficient.

Selection Sort

• Compares each value to find the minimum.
• Moves that minimum to the sorted list.
• Time complexity: O(n²).

Quicksort

• Picks a pivot and partitions the list into smaller lists based on that pivot.
• Utilizes recursion to sort these smaller lists.
• Time complexity: Average case O(n log n), worst case O(n²).

Key Differences Between Sorting Algorithms

• Efficiency:
  • Quick sort is faster than selection sort and merges sort for larger datasets.
• Big O Notation:
  • Useful for evaluating algorithm performance as data size increases.

Conclusion

• Understanding and implementing algorithms are critical for effective programming.
• Algorithmic thinking will aid in solving complex problems.
• Preparation for technical interviews can benefit from strong knowledge of algorithms.

Next Steps

• Explore additional algorithms and data structures.
• Practical application of the concepts learned in real-world programming scenarios.