I think there are several questions buried in this topic: How do you implement buildHeap so it runs in O(n) time? How do you show that buildHeap runs in O(n) time when implemented correctly? Why doesn’t that same logic work to make heap sort run in O(n) time rather than O(n log n)? How do … Read more
I’ll do my best to explain it here on simple terms, but be warned that this topic takes my students a couple of months to finally grasp. You can find more information on the Chapter 2 of the Data Structures and Algorithms in Java book. There is no mechanical procedure that can be used to … Read more
How to find time complexity of an algorithm You add up how many machine instructions it will execute as a function of the size of its input, and then simplify the expression to the largest (when N is very large) term and can include any simplifying constant factor. For example, lets see how we simplify … Read more
I assume that you are looking for intuitive definitions, since the technical definitions require quite some time to understand. First of all, let’s remember a preliminary needed concept to understand those definitions. Decision problem: A problem with a yes or no answer. Now, let us define those complexity classes. P P is a complexity class … Read more