Exercise 6: Let L be an Slist. Define a recursive function Flip as follows: B. Suppose L = x. Then Flip(L) = x R. Suppose L = (X, Y). Then Flip (L) = (Flip(Y), Flip(X)) Compute Flip [(2,3), (7,9)], showing all the steps
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Exercise 6: Let L be an Slist. Define a recursive function Flip as follows: B. Suppose L = x. Then Flip(L) = x R. Suppose L = (X, Y). Then Flip (L) = (Flip(Y), Flip(X)) Compute Flip [(2,3), (7,9)], showing all the steps
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- For function log, write the missing base case condition and the recursive call. This function computes the log of n to the base b. As an example: log 8 to the base 2 equals 3 since 8 = 2*2*2. We can find this by dividing 8 by 2 until we reach 1, and we count the number of divisions we make. You should assume that n is exactly b to some integer power. Examples: log(2, 4) -> 2 and log(10, 100) -> 2 public int log(int b, int n ) { if <<Missing base case condition>> { return 0; } else { return <<Missing a Recursive case action>> }}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…Write a recursive fibonacci (n) function with an expression body. The function should return an Int; it will be too slow to deal with inputs whose fibonacci numbers are too large anyway. You do *not* need to use memoization. Note that: fibonacci(0) = 0 fibonacci(1) = 1 fibonacci(n, where n is greater than 1) = fibonacci(n-2) + fibonacci(n - 1)
- A palindrome is a sentence that contains the same sequence of letters reading it either forwards or backwards. A classic example is '1\.ble was I, ereI saw Elba." Write a recursive function that detects whether a string is apalindrome. The basic idea is to check that the first and last letters of thestring are the same letter; if they are, then the entire string is a palindromeif everything between those letters is a palindrome.There are a couple of special cases to check for. If either the first orlast character of the string is not a letter, you can check to see if the restof the string is a palindrome with that character removed. Also, when youcompare letters, make sure that you do it in a case-insensitive way.Use your function in a program that prompts a user for a phrase andthen tells whether or not it is a palindrome. Here's another classic fortesting: '1\. man, a plan, a canal, Panama!"Question#1: Let P and Q be integers and suppose F (P, Q) is recursively defined by: F(int P, int Q) if (P == 0) return Q else return F(P- 1, P + Q) Find and Trace F(8,1)Write a recursive function to implement the recursive algorithm (determining the number of ways to select a set of things from a given set of things). Also, write a program to test your function.
- for C++ write a progam for the greatest common divisor of integers x and y is the largest integer that evenly divides both x and y. Write a recursive function gcd that returns the greatest common divisor of x and y. The gcd of x and y is defined recursively as follows. If y is 0 the answer is x; otherwise gcd(x, y) is gcd(y, x%y).Consider the recursive procedure which computes the nth Fibonacci number is the one below. procedure Fl (n) //a function which returns the nth Fibonacci number.// if n < 2 then return(n) else return (F2(2,n,1,1)) endif end Fl procedure F2(i,n,x,y) if iWrite a recursive function to implement the recursive algorithm (multiplying two positive integers using repeated addition). Also, write a program to test your function.
- Write a recursive function in f#, named specialSum, that has the followeing signature: int * int -> int, where sum(m,n) = m + (m +1) + (m+2) + ... + (m + (n-1)) + (m+n) for m >= 0 and n >= 0: (Hint use two clauses with (m,0) and (m,n) A PATTERNS.) start code with let rec specialSum (m,n) match m,n with | m,0 -> | m,n - >For function decToBinary, write the missing parts of the recursion case. This function should return a string that stores the binary equivalent for int variable num. Example: The binary equivalent of 13 may be found by repeatedly dividing 13 by 2. So, 13 in base 2 is represented by the string "1101". Examples: decToBinary(13) -> "1101" public String decToBinary (int num) { if (num < 2) return Integer.toString(num); else return <<Missing recursive call>> + <<Missing calculation>>;}Write a recursive function that returns true if the digits of a positive integer are in increasing order; otherwise, the function returns false. Also, write a program to test your function.
