Summary: In this assignment, you will implement a version of the standard binary search algorithm.
Assigned: Tuesday, 21 January 2003.
Due: noon, Wednesday, 22 January 2003.
Citation: Much of the problem statement is based on Column 4 of the second edition Jon Bentley's Programming Pearls.
Bentley, Jon (2000). Programming Pearls, 2nd Edition. Reading, MA: Addison-Wesley.
Collaboration: You may certainly discuss the assignment with other students. However, each student should turn in his or her own solution. Once you've started to write code, you may not show your code to others.
Reuse: Please do not reuse code you've written previously
(except for homework 0)
or that you've found on the Web. The goal of this assignment is to see how
you do implementing binary search
Submitting Your Work: Submit your source code with the ECA. If you can't get it to work, email me your source code.
Implement (in Scheme or Java) the following version of Binary search.
If you use Scheme, substitute
array in the
Reflect on the errors discussed in class and then perform enough analysis and testing that you are confident that your binary search is correct. I'd appreciate it if you showed me your testing steps.
Note that the standard way to
keep track of a range within an array
is with two integer values, one of which gives the lower bound of the
range and the other of which gives the upper bound (both inclusive). You
can use l and u, lb and ub, lower and
upper, lower_index and upper_index, or any other
reasonable pair of names for those two values.
n, an integer
x, a sorted array of integers indexed from 0 to n-1
t, an integer
|Purpose||Determine if t appears in x.|
|Produces||p, an integer|
|Preconditions||x is sorted in increasing order. That is,
x[i] <= x[i+1] for all reasonable
n >= 0.
|Postconditions||If t appears in x, x[p] = t.
If t does not appear in x, p = -1.
|Process||Keep track of the range within the array that holds t (if t is anywhere in the array). Initially, the range is the entire array. The range is shrunk by comparing its middle element to t and discarding half the range. The process continues until t is found or until the range in which it must lie is known to be empty. (Bentley 2000, p. 34)|
I usually create these pages
on the fly, which means that I rarely
proofread them and they may contain bad grammar and incorrect details.
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