Merge Sort Lecture Notes

Course Overview

• Course: Strivers A to Z, India's most in-depth DS and Algo course.
• Content:
  • Over 56 modules.
  • Solutions for 400+ problems.

Prerequisites

• Must complete Module 1.5 before attending this lecture on Merge Sort.

Purpose of Merge Sort

• Definition: Merge Sort is a sorting algorithm.
• Comparison:
  • Previous algorithms: Bubble Sort, Insertion Sort, Selection Sort (Time Complexity: O(n²)).
  • Merge Sort is more optimized with better time complexity.

Sorting Algorithm Definition

• Sorts data structures (numbers, characters, strings) according to specific order.

Lecture Flow

1. Explanation of the algorithm.
2. Pseudocode walkthrough.
3. Dry run of the recursion.

Merge Sort Algorithm

1. Divide and Merge Principle:

   • Key terms: divide and merge.
   • Example using an array of size 9.

2. Dividing the Array:

   • Odd numbers (e.g., 9) can divide into groups of 4 and 5 or vice versa.
   • Follow the same pattern for odd/even divisions.

3. Stopping Condition:

   • When divided down to a single element, recursion stops.

4. Merging Process:

   • Combine arrays while ensuring they are sorted.
   • Example:
     • Given two sorted arrays, choose the smallest element to merge.

5. Recursive Structure:

   • Keep calling the merge sort for left and right halves, then merge sorted halves.

Pseudocode Explanation

• Use indices instead of creating new arrays to sort.
• Base Case: When low index equals high index, return (single element).
• Recursive Calls:
  • Split the array by defining low, mid, and high indices.

Dry Run Example

• Use specific indices to illustrate the recursive flow and how the merge is accomplished after sorting sub-arrays.

Merge Algorithm Structure

• Merging Two Arrays:
  • Use two pointers, one for each half, comparing values and merging into a temporary array.
  • Handle leftovers after comparison until one side is exhausted.

Time Complexity

• Overall Time Complexity: O(n log n)
  • Merging happens at O(n) while splitting occurs log(n) times.

Space Complexity

• Space Complexity: O(n)
  • Due to use of a temporary array during the merging.

Conclusion

• Understanding the mechanism of Merge Sort through examples and its implementation is crucial.
• Encourage students to practice coding it out themselves for better understanding.

Call to Action

• Engagement with the material: Like, subscribe, and comment 'understood'.
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Additional Resources

• Course materials and notes available in the description.