Learning Merge Sort and Graph Traversals

This week’s module focused on algorithm design and analysis, with a strong emphasis on divide-and-conquer techniques, especially Merge Sort. From the lecture video captions, I learned how Merge Sort works by repeatedly dividing an array into two halves until each subarray contains only one element. Since a single element is already sorted, the algorithm then focuses on the merge step, where two sorted arrays are combined by comparing elements one at a time. This helped me better understand why Merge Sort is efficient and reliable.

I also learned how to analyze Merge Sort using a recurrence relation and apply the Master Theorem to determine its time complexity. By identifying the values of a, b, and f(n), I was able to see why Merge Sort runs in Θ(n log n). In addition, the homework and quiz strengthened my understanding of DFS and BFS traversals, including how traversal order and marking rules affect the final result. Topics like the Traveling Salesman Problem, Knapsack Problem, and worst-case analysis helped me connect algorithm theory to practical problem-solving. Overall, this module improved my ability to analyze algorithms step by step and understand both their logic and efficiency.

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