a) Explain why the recursive equation |B = |B+ |B-1| holds for any k <3. b) List all the elements of B and B3 in the set notation. c) Compute |BŹ| using part a) and b). Explain. %3D
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- In c++ please help me answer this question I will give you a good rating :) implement the three versions of the addupto20() function: iterative, recursive, and divide-and-conquer approach test these functions with a few inputs from your main() Iterative solution * check if there exsits two numbers from vector data that add up to 20 e.g., if data=[2,5,3,15], the function returns true, as data [0] +data [3]==20 e.g., if data=[3,4,0,8], the function return false precondition: vector data has been initialized postcondition: if there are two numbers from list add up to 20, return true; otherwise, return false */ bool AddupTo20 (const vector‹int> & data){ } Come up with a recursive solution to the problem, following the hints given below: * check if there exsits two numbers from vector data[first...right] add up to 20 e.g., if data=[2,5,3,15], first=0, last=3, the function returns true, as data [0] +data [3]==20 e.g., if data=[2,5,3,15], first=2, last=3, the function returns…Each case below gives a recursive definition of LS{a, b}*. Give a simple nonrecursive definiton of L in each case. Example: a e L; VXEL axE L can be defined as "The set of all non-empty strings that do not contain b." Handwriting solutions all three subparts 1. а€ L; VxєL ха,xbe L 2. ae L; VxeL bx,xbe L 3. а€ L; VxEL ax,xbє LGive a recursive definition for the set of all strings of a’s and b’s that begins with an a and ends in a b. Say, S = { ab, aab, abb, aaab, aabb, abbb, abab..} Let S be the set of all strings of a’s and b’s that begins with a and ends in a b. The recursive definition is as follows – Base:... Recursion: If u ∈ S, then... Restriction: There are no elements of S other than those obtained from the base and recursion of S.
- QUESTION 6 A proper recursive solution requires at least two parts: a recursive function that calls the recursive function with a smaller problem, and a base, or stopping case. O True O FalseProvide a recursive definition for the following set S. S={2k3m5n EN | k, m, n E Z+} Z+ is the set of all positive integers (1, 2, 3, ..) N is a set of numbers so 2^1 * 3^1 * 5^1 = 35 Not in Code format. Base Case and Constructor CaseWrite an iterative function that determines the number of even elements in an array a of integers of size n. The function should return the number of elements that are even in array a of size n. Propose an appropriate prototype for your function and then write its code. Write a recursive function to solve the above problem. Propose an appropriate prototype for your function and then write its code.
- Let ∑={a,b} and T be the set of words in ∑* that have no consecutive a’s (i.e. there cannot be 2 or more a’s in a row). (a) Give a recursive definition for the set T. (b) Use your recursive definition to show that the string “abbaba” is in T. (c) Is your recursive definition uniquely determined? Explain why or why not.Write a recursive function that, given a sequence of comparable values, returns the count of elements where the current element is less than the following ( next ) element in the given sequence. See the examples given below. def count_ordered ( seq ) : """ Input : A sequence of comparable elements Output : The number of elements that are less than the following element in the sequence Example : >>> count_ordered ( [ 1 , 2 , 3 , 4 , 5 , 6 ] ) 5 >>> count_ordered ( ( 1 , 12, 7.3 , -2,4 ) ) 2 >>> count_ordered ( 'Python' ) 2 >>> count_ordered ( [ 6 ] ) 0 >>> count_ordered ( [ ] ) 0 """ In the first example above , count_ordered ( [ 1,2,3,4,5,6 ] )the returned answer is 5 because for all the first 5 numbers the current number is less than the next number. In the second example above, count_ordered ( ( 1,12,7.3 , -2,4 ) )the…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?
- •rewrite calculateSum function as a recursive function. m(i) = m(i-1) + i/(i+1), where i >=1Practice recursion on lists Practice multiple base conditions Combine recursion call with and,or not operators Search for an element in a list using recursion Instructions In this lab, we will write a recursive function for searching a list of integers/strings. Write a recursive function to determine if a list contains an element. Name the function recursive_search(aList, value), where aList is a list and value if primitive type is the object we want to search for. Return a boolean, specifically True if and only if value is an element of aList else return False from the function Examples: recursive_search([1,2,3], 2) == True recursive_search([1,2,3], 4) == False recursive_search([ ], 4) == False recursive_search([ [ 1 ], 2 ], 1) == False # -----> (because the list contains [ 1 ] and 2, not 1) Hint: Think about what the base case is? When is it obvious that the element is not in the list? If we are not at the base case, how can you use the information about the first element of the…Recursive Max! Write a recursive function rc_max(L:List[int]) -> int that takes a list L and returns an element with highest value in the list. For example, rc_max([1,2,3]) returns 3. Note that L is not necessarily sorted. You may assume that the input L is not empty. You cannot use the built-in max() Your Answer: 1 # Put your answer here 2 Submit