Dynamic Programming: Determine a Longest Common Subsequence (LCS) for the following two strings using dynamic programming approach. You need to illustrate the step-by-step procedure based on a table. ‘ncaa tournament’ and ‘north carolina

T/F 12. If the Hanoi Towers puzzle was to be created with four towers rather than three with the rules modified accordingly, a recursive answer for a puzzle might be developed where one of the requirements is that any disc has to lie in one of the four towers at any stage in the solution.

Stuck need help! The class I'm taking is computer science discrete structures.  Problem is attached. please view attachment before answering.  Really struggling with this concept. Thank you so much.

a. Correctness of dynamic programming algorithm: Usually, a dynamic programming algorithm can be seen as a recursion and proof by induction is one of the easiest way to show its correctness. The structure of a proof by strong induction for one variable, say n, contains three parts. First, we define the Proposition P(n) that we want to prove for the variable n. Next, we show that the proposition holds for Base case(s), such as n = 0, 1, . . . etc. Finally, in the Inductive step, we assume that P(n) holds for any value of n strictly smaller than n' , then we prove that P(n') also holds. Use the proof by strong induction properly to show that the algorithm of the Knapsack problem above is correct.    b. Bounded Knapsack Problem: Let us consider a similar problem, in which each item i has ci > 0 copies (ci is an integer). Thus, xi is no longer a binary value, but a non-negative integer at most equal to ci , 0 ≤ xi ≤ ci . Modify the dynamic programming algorithm seen at class for this…