Question

Recall the longest increasing subsequence algorithm discussed in class. Run this algorithm on the following array A of integers.

a) True
b) False

Answer 1

The longest increasing subsequence algorithm is a dynamic programming algorithm that finds the length of the longest subsequence in an array where the elements are in increasing order.

Step-by-step explanation:

The longest increasing subsequence algorithm is a dynamic programming algorithm that finds the length of the longest subsequence in an array where the elements are in increasing order. It can be implemented using an array to store the lengths of the longest increasing subsequences ending at each index of the input array.

To run this algorithm on the given array A of integers, you would start by initializing an array of the same length as A with all values set to 1. Then, you would iterate over each index i of A and compare A[i] with each previous index j. If A[i] is greater than A[j], you would update the value at index i in the array of lengths by adding 1 to the value at index j. Finally, you would find the maximum value in the array of lengths, which represents the length of the longest increasing subsequence.

Let's take an example:

• Array A: [5, 3, 4, 8, 6, 7]
• Initialize array of lengths: [1, 1, 1, 1, 1, 1]
• Iterate over A: 5, 3, 4, 8, 6, 7
• Update lengths: [1, 1, 2, 3, 2, 3]
• Maximum length: 3