Setup

APTs

1. Birthday

Natural Prestidigitation

So, what are the populations of every town in North Carolina and the number of posts by various authors to a Duke sports bulletin board hiding from you?

Assignment Overview

We provide you with a suggested decomposition of the problem into functions that you can implement. However, you can ignore the framework below and create whatever methods you like as long as you produce the same output in the end.

Note: throughout this problem, you may assume that the numbers processed are non-negative or you can use the absolute value function Math.abs to help you handle negative numbers in a reasonable way.

Assignment Details

1. Write a method nthDigit. nthDigit(n,num) finds the n^th highest order digit of num, i.e., the n^th digit from the left. We take the leftmost digit to be the 0^th. nthDigit should evaluate to 0 for digits beyond the "end" of the number. For example:

   When computing

   • nthDigit(0,678) ⇒ 6
   • nthDigit(1,678) ⇒ 7
   • nthDigit(2,678) ⇒ 8
   • nthDigit(3,678) ⇒ 0
   • nthDigit(0,0) ⇒ 0
   • nthDigit(3,18023) ⇒ 2

2. Write a method nthDigitTally, using nthDigit. nthDigitTally(n, nums) returns a tally of frequencies of 0–9 as the n^th digits of all the numbers in nums.

   Here's a sample test case. These are enrollments in Research Triangle Park colleges and universities in Fall 2000 (thanks to the "Research Triangle Regional Partnership" website: http://www.researchtriangle.org/data/enrollment.html).

   Institution	Enrollment
   Duke University	12176
   North Carolina Central University	5476
   Louisburg College (Junior College)	543
   Campbell University	3490
   University of North Carolina at Chapel Hill	24892
   North Carolina State University	28619
   Meredith College	2595
   Peace College	603
   Shaw University	2527
   St. Augustine's College	1465
   Southeastern Baptist Theological Seminary	1858

   Assume the variable enrollments contains the enrollment numbers from that table. Then:

   nthDigitTally(0, enrollments) ⇒ [0,3,4,1,0,2,1,0,0,0]

3. Write a method readNumbers that reads whitespace-separated integers from a Scanner and returns a list of the numbers suitable as input to nthDigitTally. Here's the university enrollment data from above:

   12176
   5476
   543
   3490
   24892
   28619
   2595
   603
   2527
   1465
   1858
   

   From this, readNumbers should produce the list [12176, 5476, 543, 3490, 24892, 28619, 2595, 603, 2527, 1465, 1858].

4. Finally, compose your main method to prompt the user for the number n and to choose a file for the data set. The program should tally the n^th digits of the numbers in the data set and print out a table of the results. For example, given that n=0 and the following file: 12176 5476 543 3490 24892 28619 2595 603 2527 1465 1858 Your program should print: 0s: 0 (0%) 1s: 3 (27%) 2s: 4 (36%) 3s: 1 (9%) 4s: 0 (0%) 5s: 2 (18%) 6s: 1 (9%) 7s: 0 (0%) 8s: 0 (0%) 9s: 0 (0%)

5. In your README, you should describe the distribution of digits for each of the data files and how they conform or differ from what you would expect from a random list of numbers.

Extra Credit

1. To be human-readable, the data files should also allow labels for the data. We'll accomplish this by allowing commenting in the input file. Change readNumbers to ignore anything between (* and *). (You may assume that the (* and *) symbols will be surround by whitespace and that nested comments — comments inside other comments — are not allowed.) Now, the unversity data set can look like:

   (* Duke University *)                             12176
   (* North Carolina Central University *)           5476
   (* Louisburg College (Junior College) *)          543
   (* Campbell University *)                         3490
   (* University of North Carolina at Chapel Hill *) 24892
   (* North Carolina State University *)             28619
   (* Meredith College *)                            2595
   (* Peace College *)                               603
   (* Shaw University *)                             2527
   (* St. Augustine's College *)                     1465
   (* Southeastern Baptist Theological Seminary *)   1858
   

2. If you want to find the patterns hidden in the numbers around you, try the following three-part bonus problem:
   1. Find a data source on the web that no one else has used (see next part) and transform it into a format suitable for input to readNumbers. The data must all be separate measurements of a single type of phenomenon. For example: measurements of university/college enrollments across different institutions (like above) or at the same institution across different years; measurements of the flow rates of all the major rivers in British Columbia; measurements of the height of 10000 randomly chosen Vancouver residents; measurements of the number of hits per day on the UBC computer science website over three years; measurements of the length in characters of each article in the Wikipedia; measurements of the population of the 1000 largest cities and townships in Canada; etc. Furthermore, there must be at least 250 measurements in the list (but more would be better!).

   2. Post all of the following items to the course discussion forum with a title describing your data: the URL for your data source, a description of the data source, one attachment with bare data suitable for readNumbers, and one attachment with labelled data (using the (* *) style above).

   3. Submit with your assignment the URL of your data, a description of the data source, and digit tallies for digit 1 and digit 2 of your data (using nthDigitTally). Are there any oddities in the tallies? What about in other students' data?

Hints:

• To calculate the number of digits in a number, use repeated division by 10 or use the Math.log10 method.
• To calculate a particular digit of a number, use repeated division by 10 again, followed by the modulo operator to pick out just the rightmost digit or use the Math.pow method to avoid repeated division.
• You can check to see if two strings are equal using the .equals method. For example, if some String token is equal to (*, then token.equals("(*") will evaluate to true.

Submitting