In python state the recursive formula for this problem. Implement the algorithm with bottom-up approach dynamic programming and backtracking. Create an iterative function that prints the longest common subsequence(LCS).

If we are given with the two strings we have to find the longest common sub-sequence present in both of them.ExampleLCS for input Sequences "ABCDGH" and "AEDFHR" is "ADH" of length 3.LCS for input Sequences "AGGTAB" and "GXTXAYB" is "GTAB" of length 4.Implementation in Java

Solved in python

Suppose we have a recursive sequence f1, f2, f3, . . .. For the purposes of this problem, it does not matter exactly how the f; are defined, only that they are recursively defined. For integer n ≥ 1, let P(n) be the predicate that Σi-1 fi = 2ƒn+2 − 3. Don't worry about whether this predicate "makes sense"; we haven't defined the fi so you won't be able to "make sense" of the P(n). It's not important for this problem. Consider a proof by induction that Vn ≥ 1: P(n). Suppose we've gotten to the inductive step, and suppose that the first steps of the inductive step are Σfi = fk+1 + Σi=1 fi = fk + fk-1 + Σk=1 fi True or false: Based on the information given, we will need strong induction for this proof. True False

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Consider array A of n numbers. We want to design a dynamic programming algorithm to find the maximum sum of consecutive numbers with at least one number. Clearly, if all numbers are positive, the maximum will be the sum of all the numbers. On the other hand, if all of them are negative, the maximum will be the largest negative number. The complexity of your dynamic programming algorithm must be O(n2). However, the running time of the most efficient algorithm is O(n). Design the most efficient algorithm you can and answer the following questions based on it. To get the full points you should design the O(n) algorithm. However, if you cannot do that, still answer the following questions based on your algorithm and you will get partial credit. Write the recursion that computes the optimal solution recursively based on the solu- (a) tion(s) to subproblem(s). Briefly explain how it computes the solution. Do not forget the base case(s) of your recursion.