Algorithms, Data Structures and Computability

A carpenter is cutting a long plank of wood of length N cm and fixed width of 2 cm into pieces of shorter lengths. Given that each length has a specific price, it is your job to help this carpenter to find the optimal cuts in order to maximize his profit.Consider following example showing different cut’s lengths and their equivalent prices

Answer the following questions:

a)Describe an algorithm that may examine all possible solutions using recursion to solve the above problem(6marks), and determine its complexity(4marks).

b)Develop a brief report (of max 250) words to explain the drawback of using such methods to solve similar problems. Describe a technique that can be efficiently used to save computational effort and hence resulting into a more efficient algorithm.(8marks)

c)Design an efficient algorithm that is more efficient with less complexity (8marks), and determine such complexity (4marks).

d)Implement the efficient algorithm using Python (10marks)[Note: The marks depend on the correctness of the code, indentation, comments, test-case]