How to count the digits of a given number in scheme?recursively and iteratively

Question

I know how to calculate the sum of the digits of a number:

(define (sum-of-digits x)  
  (if (= x 0) 0
      (+ (modulo x 10) 
         (sum-of-digits (/ (- x (modulo x 10))
                           10)))))`

But I just don't have a clue to make a count of the digits. And also don't know how to do that by a linear iterative progress.

Thanks!!

Answer 1

You are very close to the answer.

In order to figure out how to change sum-of-digits into count-of-digits, try writing some test cases. A test case must include an example of calling the function, and also the expected result.

As a side note, this is an example of generative recursion , and you shouldn't be tackling it until you've done a bunch of problems like "add the numbers in a list", "count the elements in a list", etc.

Answer 2

Some hints regarding each of your questions:

1. For counting digits, you don't need to add the current digit (as is the case in your code). Just add 1

2. There are several strategies for transforming a recursive solution (like yours) to a tail recursion (one that generates a linear iterative progress). Here's a short list:

   • Add an extra parameter to the function to hold the result accumulated so far
   • Pass the initial value for the accumulator the first time you call the procedure, typically this is the same value that you'd have returned at the base case in a "normal" (non-tail-recursive) recursion.
   • Return the accumulator at the base case of the recursion
   • At the recursive step, update the accumulated result with a new value and pass it to the recursive call
   • And the most important: when the time comes to call the recursion, make sure to call it as the last expression with no "additional work" to be performed.