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.

X Bird(x)=Can- Fly(x) This universal quantifier used here implies that All reptiles cannot fly Oa. Ob. Ob. All that flies is a Bird All Birds can fly Oc. All chicken are birds d.

Note: Please Answer in C++ only Chef and his little brother are playing with sticks. They have total N sticks. Length of ith stick is Ai. Chef asks his brother to choose any four sticks and to make a rectangle with those sticks its sides. Chef warns his brother to not to break any of the sticks, he has to use sticks as a whole. Also, he wants that the rectangle formed should have the maximum possible area among all the rectangles that Chef's brother can make. Chef's little brother takes this challenge up and overcomes it. Can you also do so? That is, you have to tell whether it is even possible to create a rectangle? If yes, then you have to tell the maximum possible area of rectangle. Input Output 1 5 12312

Note: Please Answer in C++ only Chef and his little brother are playing with sticks. They have total N sticks. Length of ith stick is Ai. Chef asks his brother to choose any four sticks and to make a rectangle with those sticks its sides. Chef warns his brother to not to break any of the sticks, he has to use sticks as a whole. Also, he wants that the rectangle formed should have the maximum possible area among all the rectangles that Chef's brother can make. Chef's little brother takes this challenge up and overcomes it. Can you also do so? That is, you have to tell whether it is even possible to create a rectangle? If yes, then you have to tell the maximum possible area of rectangle. Input Output 1 5 12312