Problem 4
What is direct recursion?
Problem 5
What is indirect recursion?
Problem 6
What is tail recursion?
Problem 7
Consider the following recursive function: int mystery (int number) / / Line 1 \(f\) If (number = 0) / / Line 2 return number; else return (mystery (number +1 ) \(-\) number) \(;\) //Line 5\\} a. Identify the base case. b. Identify the general case. c. What valid values can be passed as parameters to the function mystery? d. If mystery (0) is a valid call, what is its value? If not, explain why. e. If mystery (10) is a valid call, what is its value? If not, explain why. f. If mystery (-3) is a valid call, what is its value? If not, explain why.
Problem 9
Consider the following recursive function:
void recrun (int x)
\(f\)\\[\begin{array}{l}\text { If }(x>0) \\\\\text { cout }
Problem 13
Consider the following function: int func (int x)\\{\\[\text { if } \quad(x=0)\\]return 2 else if \((x=1)\) return 3 else return \((\text { func }(x-1)+\text { func }(x-2))\)} What is the output of the following statements? a. \(\quad\) cout \(\langle\langle\text { func }(0)<<\text { end } 1\) b. \(\quad\) cout \(\langle\langle\text { func }(1)<<\text { end } 1\) c. cout \(<<\) func \((2)<<\) endl d. \(\quad\) cout \(<\langle\text { func }(5)<<\text { end } 1\)
Problem 14
Suppose that intArray is an array of integers, and length specifies the number of elements in intarray. Also, suppose that 1 ow and high are two integers such that \(0<=1\) ow \(<\) length, \(0<=\) high \(<\) length, and 1 ow \(<\) high. That is, low and high are two indices in intarray. Write a recursive definition that reverses the elements in intArray between low and high.
Problem 15
Write a recursive algorithm to multiply two positive integers \(m\) and \(n\) using repeated addition. Specify the base case and the recursive case.
Problem 16
Consider the following problem: How many ways can a committee of four people be selected from a group of 10 people? There are many other similar problems in which you are asked to find the number of ways to select a set of items from a given set of items. The general problem can be stated as follows: Find the number of ways \(r\) different things can be chosen from a set of \(n\) items, in which \(r\) and \(n\) are nonnegative integers and \(r \leq n .\) Suppose \(C(n, r)\) denotes the number of ways \(r\) different things can be chosen from a set of \(n\) items. Then, \(C(n, r)\) is given by the following formula: \(C(n, r)=\frac{n !}{r !(n-r) !}\) in which the exclamation point denotes the factorial function. Moreover, \(C(n, 0)=C(n, n)=1 .\) It is also known that \(C(n, r)=C(n-1, r-1)+C(n-1, r)\) a. Write a recursive algorithm to determine \(C(n, r)\). Identify the base case \((\mathrm{s})\) and the general case \((\mathrm{s})\) b. Using your recursive algorithm, determine \(C(5,3)\) and \(C(9,4)\)
