;; TRAINING BIAS #4:  Prefer codes with more colors.
;; Specifically, for a code of length N, the probability that a randomly
;; chosen code has K different colors is:
;;    p(+ | K) = (K/N) * (2/(N+1))
;; So:
;;    p(+ | N) = 2 / (N+1)
;;    p(+ | 1) = 2 / (N(N+1))
;; Codes consistent with this probability distribution are
;; generated by randomly generating a number in the range
;; [0,1], and using the cumulative probability distribution
;; function to map this probability to a number of colors in [1,N].
;;
;; Note that this bias is only meaningful when there are at
;; least as many colors as pegs.
;;
;; Negative instances are generated by using the inverse
;; cumulative probability distribution function (i.e., using
;; (1-p) for each probability.

(defun train-bias4-pos (&optional (colors *colors*) 
				  (code-length *code-length*))
  (setf numcolors (bias4-colors code-length t))
  (train-bias-flag colors code-length
		   #'(lambda (code flag)
		       (check-train-bias4 code flag numcolors))
		   t))


(defun train-bias4-neg (&optional (colors *colors*) 
				  (code-length *code-length*))
  (setf numcolors (bias4-colors code-length nil))
  (train-bias-flag colors code-length
		   #'(lambda (code flag)
		       (check-train-bias4 code flag numcolors))
		   nil))


(defun bias4-colors (code-length posflag)
  (let ((p (random 1.0)) (cumprob 0) (pnext 0)
	(norm (* (/ 1 code-length) (/ 2 (+ 1 code-length)))))
    (if posflag
	(loop for i from code-length downto 1
	      do (progn
		   (setf pnext (* i norm))
		   (incf cumprob pnext)
		   (if (> cumprob p)
		       (return-from bias4-colors i))))
      (loop for i from 1 to code-length
	    do (progn
		 (setf pnext (* i norm))
		 (incf cumprob pnext)
		 (if (> cumprob p)
		     (return-from bias4-colors i)))))))




(defun check-train-bias4 (code flag numcolors &aux (colors nil))
  (loop for c in code
	do (setf colors (adjoin c colors)))
  (if flag
      (eq (length colors) numcolors)
    (not (eq (length colors) numcolors))))