Topics for Exam #1, Thursday 2/15

You are allowed to use one page of notes (both sides, 8.5 X 11) with anything you would like to put on it for the test.  You can also use a calculator if you wish.   Aside from those materials, no other books or notes are allowed.  The test will cover chapters 1-4, and 7-10 of the textbook.  The emphasis is on coming up with and solving recurrence relations, sorting algorithms, and heaps. 

• Math Basics
• Big-O vs Theta vs Omega and Little-O notations
• You may need to solve summations (will be one you have seen before)
  
• Solving recurrence relations
• Substitution
• Iteration
• Master Method
• Using recursion trees
  
• Heaps
• How heapify procedure works
• Mapping an array to the tree, vice versa
• Building a heap, runtime
• How to use a heap as a priority queue, runtime properties
  
• Selection Problem
• How to partition an array in linear time, no additional space
• Good, bad cases for partitioning and impact on the algorithm runtime
• Different methods for selecting the partition element
• Using the partition routine to select the ith largest element in expected linear time
  
• Sorting Algorithms
• Know how to identify, execute, and the runtime properties of
• Mergesort
• Heapsort
• Quicksort
• Insertion Sort
• Selection Sort
• Radix Sort
• Bucket Sort
• Count Sort
• Postman Sort
• Reason for the Omega(nlgn) comparison-based sorting algorithms
• Why some sorting routines can run faster than O(nlgn)