3) What is the space complexity of the memoized dynamic programming algorithm f computing the nth Fibonacci Sequence that you have seen in the class? Explain.

Consider a scenario in which you are presented with a data set of length K. Write a simple recursive algorithm to choose all possible pairs of elements in the set. Assess the computational complexity and explain your calculations.

Can you describe how the Structured Programming Theorem clarifies the GOTO ambiguity and convoluted code? Write an appropriate-length essay using only your own words.

9. Explore the concept of recursion in user-defined functions, highlighting its advantages and potential pitfalls in programming.

Given three sequences of length m, n, and p each, you are to design and analyze an algorithm to find the longest common subsequence (LCSS) for the three sequence. Is it possible to use dynamic programming to find the LCSS between the three sequences? If yes, provide recursive solution to the above problem.

I need the answer as soon as possible

Problem 4 We can use lists of numbers like l to represent a mathematical vector. Recall from math classes that a vector is an object with a magnitude and direction. The magnitude is the sqrt of the sum of the squares (for a vector (x,y) it's the Pythagorean theorem for the magnitude (x^2 + y^2)**(1/2)). For a vector of any other length, the formula generalizes to (l[0]^2 + l[1]^2 + l[2]^2 + ... )**(1/2). For this problem use l from Problem 1 and a for loop to compute the magnitude of l with the result stored in l_mag. For l above, its magnitude is 12.96. Python gives you the ** exponentiation operator to raise a number to a power. You could also import math and use math.sqrt(). l = [1, 2, 3, 4, 5, 7, 8]  Please give proper explanation and typed answer only.