The goal of this project is to understand and implement the two great linear-time sorting algorithms, counting sort and radix sort.
Do not attempt this project until you understand counting sort and radix sort. They are not intuitive to the uninitiated, and although this project description will help you apply the concepts to this particular implementation, it will not help you understand the algorithms if you don't have a good sense of them already.
This project is found in the book as Project 2.3 on page 131.
Make a folder for this project and copy the starter code from the course folder:
cp -r ~tvandrun/Public/cs345/linear-sort/. .
Make a new project in Eclipse.
You will find two folders, sorts
for the sorting algorithms (both in the class Sorts)
and tests for the JUnit tests.
CountingSortTest and RadixSortTest are
the tests to use for parts 2 and 3, respectively;
SortTest contains code shared by the two of them.
The version of counting sort that you will implement is generic.
It can work on an array of any type.
But counting sort requires integers, right?
Not a problem; all we need is some way of converting each item
in the array into an integer that we can use for the counting
part of counting sort.
For that purpose, we define an interface ToInteger
with a method v(T) that converts generic type
T to an int.
The method countingSort(), then,
takes an array to sort and an object of type ToInteger
that indicates how to treat each item in the array as an int
Implement counting sort as five loops (each of them are single loops---no nested loops, each being a single pass over an array):
int) value of all
items in the given array, stored in maxVal.
Invariant: maxVal contains the greatest value
seen so far.
counts, an array
such that counts[j] indicates the number of
occurences of value j.
Invariant: counts[j] contains the number
of items with int value j seen so far.
nextPlace,
an array such that nextPlace[j] indicates
the location in the given array where the next occurence of
value j should go.
You will use nextPlace in part D when
putting the items in the given array in order.
In this part, populate nextPlace so that
nextPlace[j] indicates where the first
occurence of vaue j should go.
Invariant: Each position in nextPlace up to
i holds the number of array items whose int values
are less than that position.
array into another
array aux but in the right (sorted) order,
using nextPlace.
Hint: For each item in array, convert it to an
int and look up where it should go in nextPlace,
and the increment that position in nextPlace.
Invariant: Each element seen so far is in sorted position
and each position in nextPlace indicates the sorted
position of the next element, if any, whose int value is
that position.
aux back to array.
Test this using CountingSortTest.
Radix sort is essentially given to you, just with one line missing. But to fill in that one line, you will need to understand what is in the given code completely. In short, this implementation of radix sort uses your implementation of counting sort, calling it once for each digit (base r). Thus it first calculates the number of digits (that is, the maximum number of digits of any number in the array), and then calls counting sort in a loop based on the number of digits.
Each call to counting sort will sort the given array
with respect to one digit.
Thus the ToInteger object you pass to
counting sort must pick out the appropriate digit from
each number.
Your task is to finish writing the ToInteger
object (as an anonymous inner class).
Specifically you must write the body of the method
v() that picks out the ith
digit from item.
Test this using RadixSortTest.
Please copy Sorts.java
to your turn-in folder
/cslab/class/cs345/(your id)/linear-sort
.
To keep up with the course, this should be finished by Feb 8.