1. Wednesday, 11/25/02, Slide #1 CS 106 Intro to CS 1 Wednesday, 11/25/02  QUESTIONS??  Today:  More on sorting. Advanced sorting algorithms.  Complexity: “Big-O” notation  New files/handouts: SortDemo.exe

2. Wednesday, 11/25/02, Slide #2 “Big-O” Notation for Complexity  If an algorithm is performing a task on a list of n items, we can describe its time complexity using “Big-O” notation.  For example, if we say an algorithm “has complexity O(n 2 )”, this means that it requires approximately some constant times n 2 steps to finish. (We don’t worry about the value of the constant.)

3. Wednesday, 11/25/02, Slide #3 Complexity of elementary searching and sorting algorithms  “Elementary” searching and sorting algorithms, after each iteration, reduce the problem size by 1  Linear Search is an elementary sorting algorithm  Elementary searches generally take O(n) time  Selection Sort, Bubble Sort are elementary sorting algorithms  Elementary sorts generally take O(n 2 ) time

4. Wednesday, 11/25/02, Slide #4 Advanced Searching and Sorting Algorithms  “Advanced” searching and sorting algorithms, after each iteration, reduce the problem size by 50%  Technique is called “divide and conquer”  Binary Search is an advanced searching algorithm  Advanced searches generally take O(log n) time  Compare with O(n) for elementary search  QuickSort, MergeSort, are advanced algorithms  Advanced sorts generally take O(n log n) time  Compare with O(n 2 ) for elementary sort

5. Wednesday, 11/25/02, Slide #5 Advanced sorting algorithms  Book does not discuss any advanced sorting algorithms  QuickSort:  1. Divide list in half  2. Move small items left; big items right  3. Divide each sub-list in half  4. Do it again, etc. 35.7 -4.26 22.09 341.0 17.3 35.7 -4.26 22.09 341.0 17.3 17.3 -4.26 17.3 -4.26 22.09 341.0 35.7 17.3 -4.26 17.3 -4.26 22.09 341.0 35.7 -4.26 17.3 22.09 35.7 341.0 -4.26 17.3 22.09 35.7 341.0

6. Wednesday, 11/25/02, Slide #6 How much better are divide-and-conquer algorithms?  Searching a list with 100,000 elements:  Elementary search: 100,000 comparisons  Advanced search: 17 comparisons!  Sorting a list with 100,000 elements:  Elementary sort: 10 billion comparisons!  Advanced sort: 1.6 million comparisons