Use Bubble Sort to sort the list:
7, 12, 5, 22, 13, 32
What is the maximum number of comparisons required for a list of 6 numbers?
How many vcomparisons did I actually need?
Number of comparisons for 6 numbers:
5+4+3+2+1=15
You need all 15 comparisons unless you modify the algorithm to keep track of exchanges.
There are 4 exchanges in this particular example.
Thanks for explaining this to me!
You're welcome!
To use Bubble Sort to sort the list [7, 12, 5, 22, 13, 32], we compare adjacent elements in the list and swap them if they are in the wrong order. We repeat this process until the list is sorted.
Now, let's determine the maximum number of comparisons required for a list of 6 numbers using Bubble Sort:
For a list of n numbers, Bubble Sort requires (n-1) passes through the list. In each pass, we compare adjacent elements and swap them if necessary. Since we have 6 numbers in this case, we will need (6-1) = 5 passes.
To calculate the maximum number of comparisons, we consider that in each pass, we compare each element with the adjacent element. In the first pass, we compare 6 pairs of elements. In the second pass, we compare 5 pairs of elements, and so on. Hence, the maximum number of comparisons is the sum of the first 5 numbers in the sequence {6, 5, 4, 3, 2}, which is equal to 6 + 5 + 4 + 3 + 2 = 20.
Now, let's determine how many comparisons were actually needed for this specific list:
During the Bubble Sort process, we compare adjacent elements and swap them if necessary. This means that the number of comparisons needed is equal to the number of times we compare adjacent elements.
In this case, we have the following comparisons:
7 and 12
12 and 5 (*will be swapped*)
12 and 22
22 and 13 (*will be swapped*)
22 and 32
Total comparisons: 5
Therefore, you needed 5 comparisons to sort the list [7, 12, 5, 22, 13, 32] using Bubble Sort.