Design a transform-and-conquer algorithm for finding the minimum and the maximum element of n numbers using no more than 3n/2 comparisons. Justify the number of comparisons of your algorithm.
- Design a transform-and-conquer
algorithm for finding the minimum and the maximum element of n numbers using no more than 3n/2 comparisons.
Justify the number of comparisons of your algorithm.
The transform-and-conquer algorithm for finding the minimum and the maximum element of n numbers is as follows:
1. If n is odd, compare the first element with the last element. If the first element is smaller, it is the new minimum. If the last element is smaller, it is the new maximum.
2. If n is even, compare the first element with the second element. If the first element is smaller, it is the new minimum. If the second element is smaller, it is the new maximum.
3. Repeat the above steps until all n elements have been compared.
The number of comparisons in this algorithm is 3n/2. This is because each comparison involves comparing two elements, and there are n/2 pairs of elements to compare.
Step by step
Solved in 2 steps
