Joe's CSUMB Computer Science Blog

 This week, I continued to learn about the divide and conquer approach to solving problems. The class lessons used merge sorting as example to demonstrate how divide and conquer algorithms can be implemented. An unsorted array is repeatedly split in half into sub arrays until the sub arrays are one element in size. At this point, the sub arrays are considered to be sorted and can be merged back together in a sorted order. This is repeated until all the sorted sub arrays are merged in order. Using the master theorem, I was shown how this sorting method results in n*log n order of growth. In community college, I had to show how many operations had to occur for sorting an array of n size by counting operations at each step of the algorithm. Learning how to apply the master theorem to merge sorting has made understanding time complexities much simpler.

 My studies this week revolved around different search algorithms. The exhaustive search algorithm for graphs is fairly straightforward as it involves finding solutions by testing all possible combinations of paths. Although simple in concept, this approach can be extremely inefficient since the number of possible paths grows rapidly as the number of nodes in a graph increases. I also learned how to perform a DFS to traverse a graph, which finds the furthest unvisited node before back tracking. This strategy adds nodes to a stack and ensures the deepest nodes are visited first. The material this week also covered performing BFS, which involves exploring the nodes adjacent to the current node first. This strategy uses a queue to ensure the closest nodes are visited first. 

 During this week of class, I spent much of my time learning about the different ways to describe the growth rate of functions. I found the informal definition in the text book was helpful to me in understanding this topic. Recognizing notations such as big oh, big omega and big theta, as the set of all functions with a smaller, larger, or the same order of growth made this material a little easier to digest. Additionally, I began to read about recursion and how to analyze the time complexity of recursive algorithms. I used a recursive merge sort algorithm in hw2-2 to finish the assignment. The merge sort function divides a large array into 2 halves over and over until it reaches its base case. It then merges the sub arrays into sorted sub arrays over and over until it returns 1 sorted array.

This week’s reading material provided an introduction to the design and analysis of algorithms. I have taken classes on data structures and algorithms before, so nothing this week seemed entirely new to me. One example problem covered this week that I believe highlights the importance of this class is finding the greatest common divisor between 2 non negative integers. The reading materials from this week covered several ways to accomplish this. The intuitive way to solve this problem involves starting at the smaller of the 2 numbers and checking each descending integer until a greatest common divisor is found. Another way to do this would be to use Euclid's algorithm, which uses recursion to solve this problem. Comparing each approach and how many operations are required to solve this problem highlights the importance of analyzing the time complexity of algorithms.