Code: num:=1; while(num=0) { num=num+1; Refer to the code given above, identify what is the computational problem of this code and explain in detail based on your understanding of complexity theory.
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- Format Requirement Algorithms in pseudo code MUST be placed in code blocks/fences, and use either the cpp or java syntax highlighter. Algorithms should follow the pseudo code standard described in handout 1. Your pseudo code should be placed in a code block, for example Algorithm alg_name(a, b) { // A description of the algorithm // input: a - a positive decimal integer; b - an integer // ouput: the sum of a and b c = a + b // or, c <- a + b return c } Do NOT change the template except the answer portion. Formulas and equations should be in math mode using Latex math symbols. Markdown math tutorial: http://tug.ctan.org/info/undergradmath/undergradmath.pdf Ways enter into the math mode in Notion: https://www.notion.so/help/math-equationsArtificial Intelligence (Part - 2) ==================== The Towers of Hanoi is a famous problem for studying recursion incomputer science and searching in artificial intelligence. We start with N discs of varying sizes on a peg (stacked in order according to size), and two empty pegs. We are allowed to move a disc from one peg to another, but we are never allowed to move a larger disc on top of a smaller disc. The goal is to move all the discs to the rightmost peg (see figure). To solve the problem by using search methods, we need first formulate the problem. Supposing there are K pegs and N disk. (2) What is the size of the state space?JAVA LANGUAGE The first examples of recursion are the mathematical functions factorial and fibonacci. These functions are defined for non-negative integers using the following recursive formulas:factorial(0) = 1factorial(N) = N*factorial(N-1) for N > 0fibonacci(0) = 1fibonacci(1) = 1fibonacci(N) = fibonacci(N-1) + fibonacci(N-2) for N > 1Write recursive functions to compute factorial(N) and fibonacci(N) for a given non-negative integer N, and write a main() routine to test your functions.(In fact, factorial and fibonacci are really not very good examples of recursion, since the most natural way to compute them is to use simple for loops. Furthermore, fibonacci is a particularly bad example, since the natural recursive approach to computing this function is extremely inefficient.) JAVA LANGUAGE
- int functionC (int n) { int i, j, sumC = 0; for (i=n; i > 0; i=i-5) for (j=1; j 0) { if (functionC(n) % 2 == 0) { for (i=m; i > 0; i=i/3) sumE++; } else (10) Asymptotic runtime of functionE { for (i=m; i > 0; i=i-3) sumE--; } n--; } return sumE;Artificial Intelligence (Part - 1) ==================== The Towers of Hanoi is a famous problem for studying recursion in computer science and searching in artificial intelligence. We start with N discs of varying sizes on a peg (stacked in order according to size), and two empty pegs. We are allowed to move a disc from one peg to another, but we are never allowed to move a larger disc on top of a smaller disc. The goal is to move all the discs to the rightmost peg (see figure). To solve the problem by using search methods, we need first formulate the problem. Supposing there are K pegs and N disk. (1) Propose a state representation for the problem?12.14 Zylab 3 - Single Procedure Call Given an array of at least one integer, write a program to create a new array with elements equal to the power of each element in the original array raised to the index, i.e., P[i] = A[i]^i. For this, write two functions that will be called in main function independently. ● power inputs: element (A[i]) and index (1) • task: returns the value of element raised to index (A[i]^i). } O • newElement inputs: base address of new array P (*P), current size of P (variable k) and the new element (A[i]^i) o task: add the new element at the end. o This function does not return any value (void). O Following is a sample C code to perform the required task. You may modify the code for the functions, but the task performed should not be changed. int main() { // Variable Declaration int *A, *P; int n, k; int pow; // Task of main function P[0] 1; for (int j = k = j; pow // Base addresses of A and P // Lengths of arrays A and B // Return value from power function }…
- Python question Analysis: Computational Complexity (Q14-15) In this section, you are asked to analyse the worst-case computational time complexity of Python functions. Always identify the order of growth in the tightest and simplest possible form using big-O notation, e.g., write O(n) instead of O(2n+n/2). Question 14 (Complexity 1) State the overall worst-case time complexity of the below function and provide a short explanation of your answer. The function accepts an integer n as input. def mystery(n): num = 1 count = 0 while num < n: num = num*2 count += 1 return count Question 15 (Complexity 2) State the overall worst-case time complexity of the below function and provide a short explanation of your answer. The function is supposed to return a list, res, containing the duplicated elements in the given list , lst, of size n. Analyse the function in terms of the length of the list, n. def duplicate_values(lst): res = [] for i in range(len(lst)):…9. Ackermann's Function Ackermann's function is a recursive mathematical algorithm that can be used to test how well a computer performs recursion. Write a method ackermann (m, n), which solves Ackermann's function. Use the following logic in your method: If m = 0 then return n + 1 If n = 0 then return ackermann (m Otherwise, return ackermann(m 1, 1) 1, ackermann (m, n - 1))T/F 3. Iteratively traversing a labyrinth is much faster than recursively traversing one.
- Why does dynamic programming provide faster solutions that recursive algorithms solving the same problem? 1.avoids resolving overlapping subproblems 2.dynamic programming uses dynamic memory that is more efficient than stack memory 3.loops are always faster than recursion 4.dynamic uses arrays that are faster than function callsWrite a program that performs the following functionalities:1. Fibonacci: a recursive function that computes the fibonacci series, which is defined as followsfibonacci (n) = fibonacci(n-2) + fibonacci(n-1)fibonacci(0) = 0fibonacci(1) = 1 So the fibonacci looks like: 0 1 1 2 3 5 8 13 21 34 …. Therefore, fibonacci(4) = 3, fibonacci(5) = 5, fibonacci(7)=13 2. Sum: a recursive function that computes the sum of integers 1, 2, 3, …., n for a given number n. So Sum(6) should return 1 + 2 + 3 + 4 + 5 + 6 , i.e. 21.sum(n) = n + sum(n-1) 3. Largest: a recursive function that computes the largest value for an integer array of positiveand negative values. For example, for the array below, the function largest should return 22,which is the largest value in the array. You can assume there are no more 20 integers in thearray. Think of how to formulate the recurrence relation in this problem yourself. 4. The 4th problem mimics the situation where eagles flying in the sky can be spotted and…Pascal's triangle is a useful recursive definition that tells us the coefficients in the expansion of the polynomial (x + a)^n. Each element in the triangle has a coordinate, given by the row it is on and its position in the row (which you could call a column). Every number in Pascals triangle is defined as the sum of the item above it and the item above it and to the left. If there is a position that does not have an entry, we treat it as if we had a 0 there. *picture of the pascals triangle* Given the following recursive function signature, write the recursive function that takes a row and a column and finds the value at that position in the triangle. Assume that the triangle starts at row 0 and column 0. Examples: pascal(2, 1) -> 2, pascal(1, 2) -> 0 public int pascal(int row, int column) { }