Consider the following problems for recursive definition/solution. Answer the following questions. [Remember that a recursive definition/solution requires base case and recursive case] 3.1. We learned that its power set has 2" elements when a set has n elements. Define it in a recursive solution. 3.2. Consider a set of odd natural numbers. Make a recursive definition for the set.

Consider the following problems for recursive definition/solution. Answer the following questions. [Remember that a recursive definition/solution requires base case and recursive case] 3.1. We learned that its power set has 2" elements when a set has n elements. Define it in a recursive solution. 3.2. Consider a set of odd natural numbers. Make a recursive definition for the set.

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 7SA

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Consider the following problems for recursive definition/solution. Answer the following questions. [Remember that a recursive definition/solution requires base case and recursive case] We learned that its power set has 2" elements when a set has n elements. Define it in a recursive solution.
Consider the following problems for recursive definition/solution. Answer the following questions. [Remember that a recursive definition/solution requires base case and recursive case] Consider a set of odd natural numbers. Make a recursive definition for the set.
16. Give a recursive definition for the set of all strings of 0's and l's for which all the O's precede all the l's.
Give 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.
a) Give a recursive deﬁnition for the set of all strings of a’s and b’s where n a’s followed by n b’s (where n= 0, 1, 2, 3, ...). (Assume, S is set of all strings of a’s and b’s. Then S = {λ, ab, aabb, aaabbb, ... ) b) Give a recursive deﬁnition for the set of all strings of 'a' 's and 'b' 's that ends with an 'ab'. (Assume, S is set of all strings of a’s and b’s. Then S = {ab, aab, bab, abab, baab, aaab, bbab, ... ).
2. Let E be the alphabet E = {0, 1, 2, 3, 4}. Then using Definition 1 of section 5.3, (a) Give a recursive definition of the set of strings E". (b) Prior to the first iteration of the recursion, list all the elements then in E*. (c) After the first iteration of the recursion, list all the elements then in E*. (d) After the second iteration of the recursion, list all the elements then in E*. Definition 1 The set E* of strings over the alphabet E is defined recursively by BASIS STEP: À e E* (where à is the empty string containing no symbols). RECURSIVE STEP: fw ε amd x Σ, then wx E Σ'.
Give a recursive deﬁnition for the set of all strings of a’s and b’s where all the strings are of odd lengths. (Assume, S is set of all strings of a’s and b’s where all the strings are of odd lengths. Then S = { a, b, aaa, aba, aab, abb, baa, bba, bab, bbb, aaaaa, ... )
2.1. Answer the following True/False questions about Recursion. A. Every recursive method must have a base case or a stopping condition. Without it, infinite recursion occurs and causes StackOverflowError. A. B. Every recursive call reduces the original problem, bringing it increasingly closer to a base case until it becomes that case. C. Infinite recursion can occur if recursion does not reduce the problem in a manner that allows it to eventually converge into the base case. D. Every recursive method must have a return value. D. E. A recursive method is invoked differently from a non-recursive method. B. C. E.
Iteration versus one-friend recursion. 1. Your job is to accept the tuple a1, a2,..., a and return the tuple an, an1,..., a1 that has been reversed. You will only take an element off of one end or put an element back on one end because you are being indolent. But you have allies in recursion who can assist you.Please include the recursive code as well as a paragraph with the friend's description of the algorithm. 2. Now imagine that you lack pals but have a stack. (Refer to Chapter 3. Quickly design an incremental programme to address this issue. Include loop invariants and other crucial stages that are necessary to describe an iterative algorithm. 3. Trace both of these scripts separately. Compare and contrast their computerised calculations step by step.
Consider the following sequence and answer the questions 2, 7, 14, 23, 34, . (1) Develop the recursive solution to identify numbers in the list. (2) Develop the closed-form solution of the recursive solution you made in the previous question.
Draw the results of using the recursive ruler-drawing algorithm for thesevalues of the arguments: rule(0, 11, 4), rule(4, 20, 4), and rule(7, 30, 5).
Recursion can be direct or indirect. It is direct when a function calls itself and it is indirect recursion when a function calls another function that then calls the first function. To illustrate solving a problem using recursion, consider the Fibonacci series: - 1,1,2,3,5,8,13,21,34...The way to solve this problem is to examine the series carefully. The first two numbers are 1. Each subsequent number is the sum of the previous two numbers. Thus, the seventh number is the sum of the sixth and fifth numbers. More generally, the nth number is the sum of n - 2 and n - 1, as long as n > 2.Recursive functions need a stop condition. Something must happen to cause the program to stop recursing, or it will never end. In the Fibonacci series, n < 3 is a stop condition. The algorithm to use is this: 1. Ask the user for a position in the series.2. Call the fib () function with that position, passing in the value the user entered.3. The fib () function examines the argument (n). If n < 3…