Question 3 (Longest palindrome subsequence A palindrome is a nonempty string over some alphabet that reads the same forward and backward. Examples of palindromes are all strings of length 1, civic, racecar, and aibohphobia (fear of palindromes). You need to design an efficient dynamic programming algorithm that finds the size of the longest palindrome subsequence of a given input string. For example, given the input character, your algorithm should return 5, since the longest palindrome subsequence is carac. 1. 2. 3. Define a recursive formula for the size of the longest palindrome subsequence. (Bonus) Argue for the cor- of your formula. rectness Use your formula to design a bottom-up algorithm that finds the size of the longest palindrome subsequence. Establish the running time of your algorithm.

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