Ackermann’s Function is a recursive mathematical algorithm that can be used to test how well a computer performs
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java C++
Ackermann’s Function
Ackermann’s Function is a recursive mathematical
If m = 0 then return n + 1
If n = 0 then return A(m−1, 1) Otherwise, return A(m−1, A(m, n−1))
Test your function in a driver program that displays the following values:
A(0, 0) A(0, 1) A(1, 1) A(1, 2) A(1, 3) A(2, 2) A(3, 2)
SAMPLE RUN #0: ./AckermannRF
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- In Java 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 - 1, 1) Otherwise, return ackermann(m - 1, ackermann(m, n - 1)) Test your method in a program that displays the return values of the following method calls: ackermann(0, 0) ackermann(0, 1) ackermann(1, 1) ackermann(1, 2)ackermann(1, 3) ackermann(2, 2) ackermann(3, 2)(Using the programming language C, answer the following question) Write recursive C functions to do the following: Example: int summ(int n) returns the summation of integers from 0 to n. Here is the code. int summ(int n) { if(n < 0) return -1; if(n == 0) return 0; return n + summ(n - 1);} 1) If n is less than 0, the expression int bunnyEars(int n) returns -1; otherwise, it returns the number of ears for n bunnies. int factorial(int n) returns -1 if n is less than 0, otherwise returns the factorial of n. If n is greater than or equal to 0, the expression int fib(int n) returns -1; otherwise, it returns fib of n - 1 + fib of n - 2. (This will run quite slowly if you test it with more than roughly 50 digits.). int posPow(int base, int exp) returns -1 if exp is less than 0, otherwise returns base raised to the power exp. Write a main() that tests all the other functions thoroughly.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…
- Implement a recursive C++ function which takes a character (ch) and a positive integer (n) and prints thecharacter ch, n times on the screen. The prototype of your function should be:void printChar (char ch, int n)For example, calling printChar('*',5) should display ***** on screen.Note: There should NOT be any loop in your function.In lisp Write a simple recursive function to compute the f(n) for the following sequence: f(n) = f(n-1) + f(n-3) f(0) = 0, f(1) = f(2) = 1 Optimize this function using dynamic programming. You can assume that the number n in the function call for testing will be less than 20.Write 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…
- In Lisp Programming (Please show that it does work) Write a simple recursive function to compute the f(n) for the following sequence: f(n) = f(n-1) + f(n-3) f(0) = 0 f(1) = f(2) = 1 Optimize this function using dynamic programming. You can assume that the number n in the function call for testing will be less than 20.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…def sum ( lst ): """ Sums a list of numbers .""" if len ( lst ) == 0: return 0 return lst [0] + sum ( lst [1:]) def factorial ( number ): """ Returns the factorial value of any number """ if (( number == 0) or ( number == 1)): return 1 else : return number * factorial ( number - 1) Write down a tail recursive implementation of the function sum in python language. You can use the helper function in your solution. Write down a tail recursive implementation of the function factorial in python language.
- The Polish mathematician Wacław Sierpiński described the pattern in 1915, but it has appeared in Italian art since the 13th century. Though the Sierpinski triangle looks complex, it can be generated with a short recursive function. Your main task is to write a recursive function sierpinski() that plots a Sierpinski triangle of order n to standard drawing. Think recursively: sierpinski() should draw one filled equilateral triangle (pointed downwards) and then call itself recursively three times (with an appropriate stopping condition). It should draw 1 filled triangle for n = 1; 4 filled triangles for n = 2; and 13 filled triangles for n = 3; and so forth. API specification. When writing your program, exercise modular design by organizing it into four functions, as specified in the following API: public class Sierpinski { // Height of an equilateral triangle whose sides are of the specified length. public static double height(double length) // Draws a filled equilateral…In C language, implement two recursive versions of the linear search that gets an array of songs and a title and searches for a song with the given title in the array. 1. In this version the function returns the first index of the array containing the number. If the number is not in the array, the function returns -1. int linear_search_rec_first(int* ar, int length, int number); 2. In this version the function returns the last index of the array containing the number. If the number is not in the array, the function returns -1. int linear_search_rec_last(int* ar, int length, int number); Example of test for case 1: void test_q3() { int ar1[]={1,2,3,4,5,4,3,2,1}; if (linear_search_rec_first(ar1,9,2)==1) printf("Q3-1 ok\n"); else printf("Q3-1 ERROR\n"); } Example of test for case 2: void test_q3() { int ar1[]={1,2,3,4,5,4,3,2,1}; if (linear_search_rec_last(ar1,9,2) == 7) printf("Q3-3 ok\n"); else printf("Q3-3 ERROR\n"); }Write a recursive Fibonacci function that computes the Fibonacci number for input n and prints each value computed in the series at each recursive step in the sequence from 0 to n, all in one line on the console. (In python)