Question

Consider an array, 'a', of 'n' distinct positive integers where the elements are sorted in ascending order. We want to find all subsequences of 'a' consisting of exactly 'm' elements. Once we have all of the m-element subsequences, we find the value of maximum of minimum absolute differences of any two elements in all m-element subsequences.

Answer 1

Consider an array a = [1, 2, 3, 4, 5].

Possible 2-element subsequences are [1, 2], [1, 3], [1, 4], [1, 5], [2, 3], [2, 4], [2, 5], [3, 4], [3, 5], [4, 5].

Minimum absolute differences for each subsequence are [1, 2, 3, 4, 1, 2, 3, 1, 2, 1] respectively.

Maximum of these minimum differences is 4.

Step-by-step explanation:

The question asks about finding all subsequences of an array of positive integers and then finding the maximum of the minimum absolute differences between any two elements in all of the m-element subsequences.

To solve this problem, we can start by generating all possible m-element subsequences of the given array.

Then, for each subsequence, we can find the absolute differences between all pairs of elements and determine the minimum among them.

Finally, we can find the maximum value among all of these minimum differences.

For example, let's consider an array a = [1, 2, 3, 4, 5] and we want to find all 2-element subsequences.

The possible subsequences are [1, 2], [1, 3], [1, 4], [1, 5], [2, 3], [2, 4], [2, 5], [3, 4], [3, 5], [4, 5].

The minimum absolute differences for each subsequence are [1, 2, 3, 4, 1, 2, 3, 1, 2, 1] respectively.

Then, the maximum of these minimum differences is 4.