CMSC 351 - Programming Homework #1 - Due by 11:59pm on March 26th

This will be worth 15 points in the HW/Quiz/Programming pool of points.
Due 11:59pm, Monday March 26th (though I encourage doing it earlier, I am allowing the use of Spring Break to work on it if you so desire).

We define an algorithm as follows:

it takes a four-digit number as input (value)

it sorts the digits in descending order to get n1

it sorts the digits in ascending order to get n2

it calculates n1 - n2 to get newValue which is also a four-digit number (pad with leading "0" values to get to a four-digit number if needed)

if the number in newValue is one that we've seen before, we stop at that point

otherwise, if we haven't gone through all 10,000 possible four-digit numbers, make value=newValue and repeat the above

the output is the number of "iterations" it had to go through to get to the the first duplicate and the value that was the duplicate (returning an object or structure that contains the two is likely the easiest approach)

Example iteration 1
value:    3546
n1:       6543
n2:       3456
newValue: 3087

Example iteration 2
value:    3087
n1:       8730
n2:       0378
newValue: 8352

Example iteration 3
value:    8352
n1:       8532
n2:       2358
newValue: 6174

Example iteration 4
value:    6174
n1:       7641
n2:       1467
newValue: 6174

For this programming homework assignment (individual like the other homework assignments, and "no searching for solutions" like other closed programming projects), you will need to implement a program in Java or C that allows you to programmatically determine (don't look for math tricks, just brute force the algorithm as stated above) the following:

the smallest number of iterations taken

the largest number of iterations taken

the most popular repeat four-digit number (so if 253 of the inputs lead to 1357 being the first value to appear twice, and no other four-digit number appeared more often as the "repeated" number, then it would be the most popular repeat)

This means that your code should (a) implement the algorithm, and then (b) run the algorithm on all inputs from 0000 to 9999 to determine the answers about smallest/largest number of iterations and the most-repeated "stopping" value.

You will submit a PDF file on ELMS with:

the smallest iterations, the largest iterations, the most popular digit set

your opinion on whether your program could reasonably be used to determine the answer if the input were 5-digits long and if the input was 6-digits wrong (and write a sentence or two explaining your opinion)

your source code

Web Accessibility