The following is a implementation of the Ackermann function: public static long Ackermann(int m, int n){ if (m == 0) return n + 1; else if (n == 0) return Ackermann(m - 1, 1); else return Ackermann(m - 1, Ackermann(m, n - 1)); }
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![The following is a
implementation of the Ackermann function:
public static long Ackermann(int m, int n){
0)
return n + 1;
if (m
==
else if (n
==
return Ackermann(m
1, 1);
else
return Ackermann(m
1, Ackermann(m, n - 1));](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe43c2282-ac24-4a1a-a0ac-abe5edbda3fc%2Fc34ee41c-a1a2-4491-95df-1fd255723ce2%2Felj21bh_processed.png&w=3840&q=75)
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- public static int Ack(int m, int n) { if (m == 0) { return n + 1; } else if (n == 0) { return Ack (m } else { } } return Ack (m - - 1, 1); 1, Ack (m, n- What is the return value of this function for a. Ack(0,0) b. Ack(0,3) c. Ack(0,6) Can you use the above three samples and come up with a formula for Ack(0,n)? 1));Write a recursive function that takes as a parameter a nonnegative integer and generates the following pattern of stars. If the nonnegative integer is 4, the pattern generated is as follows: **** *** ** * * ** *** **** Also, write a program that prompts the user to enter the number of lines in the pattern and uses the recursive function to generate the pattern. For example, specifying 4 as the number of lines generates the preceding pattern.Write a recursive function that takes as a parameter a nonnegative integer and generates the following pattern of stars. If the nonnegative integer is 4, then the pattern generated is: **** *** ** * ** *** ****
- Write a recursive function that takes as a parameter a nonnegative integer and generates the following pattern of stars. If the nonnegative integer is 4, then the pattern generated is:********************Also, write a program that prompts the user to enter the number of lines in the pattern and uses the recursive function to generate the pattern. For example, specifying 4 as the number of lines generates the above pattern.Explain the functionality of below recursive functions. static void fun1(int n) { int i = 0; if (n > 1) fun1(n - 1); for (i = 0; i<n; i++) System.out.print(" *"); } 2. int LIMIT = 1000; void fun2(int n) { if (n<=0)return; if (n>LIMIT)return; System.out.print( String.format("%d", n)); fun2(2*n); System.out.print( String.format("%d", n)) }9. 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 Otherwise, return ackermann(m 1, 1) 1, ackermann (m, n - 1))
- Which is the base case of the following recursion function: def mult3(n): if n == 1: return 3 else: return mult3(n-1) + 3 else n == 1 mult3(n) return mult3(n-1) + 3Write 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…Consider the following recursive function: if b = 0, if 6 > a > 0, a f(b, a) f (b, 2.(a mod b)) otherwise. f(a, b) = Estimate the number of recursive applications required to compute f(a, b).
- T/F 6. Consider the following recursive sum method:public int sum(int x){if (x == 0) return 0;else return sum(x - 1) + 1;}Write a recursive function for int powerOfTwo (int k). The function determines the value of 2k. (Note: k is a positive integer). Example, when k=0 the function returns 1 and when k-3 the function returns 8. To show that your code is correct, give the recursive trace for powerOfTwo (2) that returns 4.sum = 0; for (int i = 1; i< n; i = sum++ || 2*i)
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