CSCI 152 Program 2
Fall 2005 Due: Friday, 30 Sep
Emphasis on: Two-dimensional array processing
A radix sort (commonly known as a bucket sort) of integers begins with a one-dimensional array of
integers to be sorted, and a two-dimensional array of integers with 10 rows and n columns, where
n is the number of values in the one-dimensional array to be sorted. Each row of the two-
dimensional array is known as a bucket.
Alternatively you could use an array with n rows and 10 columns (buckets), though that is more
difficult to program.
Write a function to bucket sort an array of integers and a program to test your function.
The sort algorithm is as follows:
1) Loop through the one-dimensional array and place each of its values in the bucket whose
subscript corresponds to the value of its one's digit. For example, 97 is placed in bucket 7,
3 is placed in bucket 3, 140 is placed in bucket 0, 47 is placed in bucket 7, and 93 is placed in
bucket 3.
2) Loop through the buckets and copy the values back to the original array (from bucket 0 to
bucket 9, and from first value entered into the bucket to last). The new order of the example
values in the one-dimensional array is 140, 3, 93, 97, 47.
3) Repeat this process for each subsequent digit position (tens, hundreds, etc.) until all possible
digit positions have been processed.
On the second pass of the array (looking at the tens position), 140 is placed in bucket 4,
3 in bucket 0, 93 in bucket 9, 97 in bucket 9, and 47 in bucket 4. The order of the values in the
one-dimensional array is now 3, 140, 47, 93, 97.
On the third pass, 3 is placed in bucket 0, 140 in bucket 1, 47 in bucket 0, 93 in bucket 0, and
97 in bucket 0. The bucket sort is guaranteed to have all the values properly sorted after
processing the leftmost digit of the largest number. The bucket sort knows it is done when all
the values are copied into bucket 0.
The bucket sort requires one pass through the array for each possible digit in the numbers to be
sorted. If you don't know the maximum number of digits in your largest number, you'd have to
make another pass. When all the numbers are in the 0 bucket, you know they are sorted.
Note that the memory required for the ten buckets is ten times the size of the array being sorted.
This sorting technique provides better performance in terms of speed than many sorts, but
requires much larger data storage capacity. Bucket sort is an example of a time-space tradeoff.
It performs faster than many sorts, but uses considerably more memory.
You are to use a random number generator to fill an array with integers in the range 0 to 32,000,
Inclusive. This array should be passed to your Bucket Sort function to be sorted into ascending
order. Print the values in their original order first and then again after each pass through the
array, ending with the values in their sorted order.
Program Requirements:
1. The bucket sort must be written as a function. Parameters passed are the one-dimensional
array to be sorted and the number of elements in the array.
2. The bucket array must be implemented as a two-dimensional array.
