Question

question 4 show the steps that a radix sort takes when sorting the following array of 3-tuple integer keys (notice that each digit in the following values represent a key): 7,8,3 9,9,2 4,7,2 1,8,2 2,6,4 5,4,3 3,5,6 2,9,5 6,9,2 4,9,1 9,4,7

Answer 1

The radix sort algorithm works by sorting elements based on their individual digits or keys.

Step-by-step explanation:

The radix sort algorithm works by sorting elements based on their individual digits or keys. In this case, we have a 3-tuple of integer keys. The algorithm goes through each digit in the keys, starting from the least significant digit (rightmost) to the most significant digit (leftmost), and performs a stable sort based on that digit.

First, the algorithm focuses on the rightmost digit (the ones place). It sorts the elements based on this digit, creating sorted buckets for each possible digit value (0-9).

Next, the algorithm moves to the next digit (the tens place), and again sorts the elements into buckets based on this digit. However, this time the sort is done within each digit bucket, preserving the order established by the previous digit sort. After this step, the array is partially ordered based on the first two digits.

The process continues for the third digit (the hundreds place), further refining the order of the elements until the entire array is sorted.

Applying the radix sort algorithm to the given array of 3-tuple integer keys:

Sort based on the rightmost digit: 7,3, 2, 2, 4, 3, 6, 5, 2, 1, and 7.

Sort within each digit bucket based on the second digit (tens place): 1, 2, 2, 3, 3, 4, 5, 6, 7, and 7.

Sort within each digit bucket based on the third digit (hundreds place): 1, 2, 2, 2, 3, 4, 5, 6, 7, and 7.

After these steps, the array is now sorted in ascending order based on the 3-tuple integer keys.