a) Give a recursive algorithmto solve the following recursive function (hint: use Fibonacci as a reference) f(0) = 1; f(1) = 2; f(n) = 3 f(n-1) + 4 f(n-2); n> 1.

Suppose a recursive function f(n)=3f(n-1) + 2. If f(0)=1, what is f(2)? 53 17 13 O O O O

Write a recursive function to determine if an array of integers contains any even numbers: bool hasEvens(int nums[], int size)

Let recursive algorithm F be defined as follows: F(int n):if n=1 then    return 1else   return F(n-1)*n (a) i. Assuming x is a positive integer, what mathematical expression is returned by F(x)?ii. Repeat (i) but assume the line “return 1” is replaced by “return 0”? (b) Which of the following replacements for the last line will yield a function guaranteed to terminate for all valid inputs? i. return F(n-2)+2ii. return F( )*2iii. return F( )*2

SML programming Write a recursive function np(n) which takes a non negative n and  generates a list of numbers from n+1 down to 0. You may assume that input of n is always valid. Must use identical function name and parameter(s). np(4)⟶[5,4,3,2,1,0]

The solution can be handwritten b) Trace the following recursive method for the function call “isPalindrome(rotator)” and show the output result.

Write a recursive Python function named pgcd, to find and return the Greatest Common Divisor (GCD) of two numbers x and y passed in parameters. • Test it gcd (1234,4321) gcd (8192,192)

Determine the output of the following recursive function when n = 64. (show your working/steps) int func (int n) {             if (n ==1)                 return 0             else                 return 2 + func ( ) }

Solve the recursion by substitution: T(n) = 3T(n/2)+ 5n where T(1)=1

What does the following recursive function do? int f(int n){ if (n==1) return 1; else returm n*f(n-1); } O sum of numbers from 1 to n Factorial of numbern Square of numbers from 1 to n Print the numbers from 1 to n