I was wondering anyone knew how to figure these problems out.
To, me it is hard and I really need this done by Sunday morning. If possible please reply, thanks!

1. Construct a recursive definition , where all variables are natural numbers.

f(n, k) = k + (k + 1) + (k + 2) + ... + (k + n).

2. Construct a recursive function definition for the following string functions for strings over the alphabet {a, b}.

f(x) = x, y, where y is the reverse of x.

3. Construct a recursive definition for each of the following functions that involve lists. Use the infix form of cons in the recursive part of each definition. In other words, write h ::t in place of cons(h,t).

(1, n = subscripts)
f(a, (<x1, y1),...(xn, yn)>) = <(x1 + a, y1), ..., (xn + a, yn)>

## All 5 Replies

Do you understand what recursive definitions are? The recursive definitions for 2 and 3 should come quite naturally.

1. Construct a recursive definition , where all variables are natural numbers.

f(n, k) = k + (k + 1) + (k + 2) + ... + (k + n).

Hint: f(n, k) = [k + (k + 1) + (k + 2) + ... + (k + (n - 1))] + (k + n)

2. Construct a recursive function definition for the following string functions for strings over the alphabet {a, b}.

f(x) = x, y, where y is the reverse of x.

Devise any means to break the string into substrings, and the recursion should be the obvious.

3. Construct a recursive definition for each of the following functions that involve lists. Use the infix form of cons in the recursive part of each definition. In other words, write h ::t in place of cons(h,t).

(1, n = subscripts)
f(a, (<x1, y1),...(xn, yn)>) = <(x1 + a, y1), ..., (xn + a, yn)>

Your recursive call will be on the tail of the list. (What else could it possibly be on?)

it helped me a little but not really. is there anyone to help me step by step process of these problems. please?

Look at your examples in class or your textbook, it should follow the same pattern...

The book totally sucks!
I am just being honest.

Well here's another hint. In general, recursive functions on lists follow the form

f(nil) = baseCase
f(h :: t) = g(h, f(t))

Be a part of the DaniWeb community

We're a friendly, industry-focused community of developers, IT pros, digital marketers, and technology enthusiasts meeting, learning, and sharing knowledge.