Question

In Lisp, I have to create a program that does the following (please visit link):

http://uva.onlinejudge.org/external/103/10328.html

I have code to create the tree

(defun head-tail (n  &optional (total 0))
  (if (< total n)
      (list(cons 'H (head-tail n (1+ total)))
             (cons 'T (head-tail n (1+ total))))
    nil))

and then code to check the sequence of H = heads

(defun head-search2 (tree n &optional (total 0) (check 0))
  (cond ((null tree)
         check)
        ((listp (first tree))
         (+ (head-search2 (first tree) n total)
            (head-search2 (rest tree) n total check)))
        ((and (eq (first tree) 'H)
              (>= (1+ total) n))
         (head-search2 (rest tree) n (1+ total) 1))
        ((and (eq (first tree) 'H)
              (< (1+ total) n))
         (head-search2 (rest tree) n (1+ total) check))
        ((eq (first tree) 'T)
         (head-search2 (rest tree) n 0 check ))))

and a last function to combine those two

(defun head-check (m n)
  (head-search2(head-tail m) n))

The code is not working with large numbers of trees, any help would be great!

Answer 1

There are two problems:

1. In the function head-search2, second clause of cond, first recursive call to head-search2 fails to propagate the check down.

2. Same clause, second recursive call gets (rest tree) as first parameter, which results in an extra layer of list; it should be (second tree) instead.

That said, you traverse the tree twice: first when constructing, and then counting it. With a little bit more careful thinking, you can save a lot of work traversing it just once, without constructing it explicitly:

(defun count-n-runs (m n &optional (k n))
  "Count all possible binary sequences with n consecutive 1s."
  (cond ((= 0 n) (expt 2 m))
        ((= 0 m) 0)
        ((+ (count-n-runs (1- m) k k)
            (count-n-runs (1- m) (1- n) k)))))

Rewriting this further for dynamic programming is left as an exercise for the reader. 😉