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1. Write a recursive algorithm to compute a+b, where a and b are nonnegative integers.;2. Let a be an array of integers. Write a recursive algorithm to compute the average of the elements of the array.;Solutions in which the sum is recursive (instead of the average) are worth fewer points. Note stopping case.;3. Ackerman's function is defined recursively on the nonnegative integers as follows;a(m, n) = n + 1 if m == 0;a(m, n) = a(m-1, 1) if m != 0, n == 0;a(m, n) = a(m-1, a(m, n-1)) if m != 0, n != 0;Using the above definition, show that a(2,2) equals 7.;4. If an array contains n elements, what is the maximum number of recursive calls made by the binary search algorithm?;5. The expression m % n yields the remainder of m upon division by n. Define the greatest common divisor (GCD) of two integers x and y by;gcd(x,y) = y if (y <= x && x % y == 0) if (y <= x && x % y == 0);gcd(x,y) = gcd(y, x) if (x 1;Write a recursive method to compute gfib(f0,f1,n).;7. Show how to transform the following iterative procedure into a recursive procedure. f(i) is a method returning a logical value based on the value of i, and g(i) is a method that returns a value with the same attributes as i. 605.202 Homework 3;void iter(int n);int i;i = n;while (f(i) == TRUE);/* any group of statement that */;/* does not change the value of i */;i = g(i);// end while;//end iter;8. Convert the following recursive program scheme into an iterative version that does not use a stack. f(n) is a method that returns TRUE or FALSE based on the value of n, and g(n) is a method that returns a value of the same type as n (without modifying n).;int rec(int n);if (f(n) == FALSE);/* any group of statement that */;/* do not change the value of n */;return (rec(g(n)));//end if;//end rec

 

Paper#65191 | Written in 18-Jul-2015

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