Dynamic Programming

When solving the question, can you explain all the steps in detail? I mean, can you show me all 4 steps when solving the question? I wrote the steps below. Pseudocode should be in C. Also, a bottom-up approach must be used not memoization. It is a bit urgent.

Steps:

1. Characterize the structure of an optimal solution.

2. Recursively define the value of an optimal solution.

3. Compute the value of an optimal solution, typically in a bottom-up fashion.

4. Construct an optimal solution from computed information.

Q1. As an avid NBA fan, you have decided to play a simplified form of YAHOO fantasy basketball game with friends for the 2019-2020 season. In this version of fantasy basketball, each participant is given 100 credits and selects 5 NBA players prior to the start of the season. Each NBA player has a price that is calculated according to their form throughout their careers. Players earn a score for their performance in each game they play. A participant's score is the sum of the scores of players they have selected. After the end of the season, participant with highest score wins. After the season ends, you have 2 questions in your mind. First one is what would be the maximum number of scores that can be earned if you could select as much players as you want with 100 credits. Secondly, you wonder what would be the best team, i.e., which combination of 5 players would earn the maximum score. For these questions, you think you can use dynamic programming. You are given an array P[1...n), each P[i] is in the 3-tuple form (). Example: Assume that you are given a list of 11 basketball players in the table below: Player Name Price Score Tony Parker 15 120 Manu Ginobili Rajon Rondo Kobe Bryant 220 Damian Lillard 60 Tim Duncan 25 250 David Robinson 20 120 Lebron James 27 300 Charles Barkley 15 150 Kevin Garnett Joakim Noah 20 To answer the first question, selecting Kobe Bryant, Manu Ginobili, Tim Duncan, Lebron James, Charles Barkley and Joakim Noah, a total of 6 players, costs 20+10+25+27+15+3=100 credits which yields the max- imum score 220+90+250 +300+150+20=1030. 55 To answer the second question, selecting Kobe Bryant, Manu Ginobili, Tim Duncan, Lebron James and Charles Barkley costs 20+10+25+27+15=97 credits which yields the maximum score 220-90+250+300+150=1010. Note that optimal solution can be achieved by spending less than 100 credits. Qla. For a dynamic programming solution: Recursively define the maximum score Sij that can be obtained by using the first i players and j credits. Write the pseudocode for the algorithm that computes and returns the maximum score that can be obtained by using at most 100 credits. Qib. For a dynamic programming solution: Recursively define the maximum score Sij,k that can be obtained by selecting exactly k players from first i players using credits. Write the pseudocode for the algorithm that computes and returns the maximum score that can be obtained by using at most 100 credits and selecting exactly 5 players