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L12cs2110fa08-6up

L12cs2110fa08-6up - Announcements Prelim 1 Thursday October...

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Searching, Sorting, and Asymptotic Complexity Lecture 12 CS2110 – Fall 2008 2 Announcements ! Prelim 1 " Thursday, October 16, 7:30 - 9pm, Uris Auditorium " Topics # all material up to (but not including) searching and sorting (this week’s topics) # including interfaces & inheritance ! Exam conflicts " Email Kelly Patwell ASAP ! A3 due Friday, October 10, 11:59pm ! Prelim 1 review sessions " Wednesday 10/15, 7:30-9pm & 9-10:30pm, Upson B17 (sessions are identical) " See Exams on course website for more information " Individual appointments are available if you cannot attend the review sessions (email one TA to arrange appointment) ! Old exams are available for review on the course website 3 What Makes a Good Algorithm? ! Suppose you have two possible algorithms or data structures that basically do the same thing; which is better ? ! Well… what do we mean by better ? " Faster? " Less space? " Easier to code? " Easier to maintain? " Required for homework? ! How do we measure time and space for an algorithm? 4 Sample Problem: Searching static boolean find(int[] a, int item) { for (int i = 0; i < a.length; i++) { if (a[i] == item) return true; } return false; } ! Determine if a sorted array of integers contains a given integer ! First solution: Linear Search (check each element) static boolean find(int[] a, int item) { for ( int x : a ) { if (x == item) return true; } return false; } 5 Sample Problem: Searching static boolean find (int[] a, int item) { int low = 0; int high = a.length - 1; while (low <= high) { int mid = (low + high)/2; if (a[mid] < item) low = mid + 1; else if (a[mid] > item) high = mid - 1; else return true; } return false; Second solution: Binary Search 6 Linear Search vs Binary Search ! Which one is better? " Linear Search is easier to program " But Binary Search is faster… isn’t it? ! How do we measure to show that one is faster than the other " Experiment? " Proof? " Which inputs do we use? ! Simplifying assumption #1: Use the size of the input rather than the input itself " For our sample search problem, the input size is n+1 where n is the array size ! Simplifying assumption #2: Count the number of “ basic steps ” rather than computing exact times
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7 One Basic Step = One Time Unit ! Basic step: " input or output of a scalar value "
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