(load "2d-table.scm")

;; space-saving fibonacci
(define fib-best
  (lambda (n)
    (if (< n 2)
        n 
        (do ((i 2 (+ i 1))
             (minus1 1 (+ minus1 minus2))
             (minus2 0 minus1))
          ((= i n) (+ minus1 minus2))))))

;; memoized choose
(define mchoose
  (lambda (n k)
    (let ((T (make-table (+ n 1) (+ k 1))))
      (define memoize
        (lambda (i j)
          (if (not (table-ref T i j))
              (table-set! T i j
                          (cond ((= i j) 1)
                                ((= j 0) 1)
                                (else (+ (memoize (- i 1) (- j 1))
                                         (memoize (- i 1) j))))))
          
          (table-ref T i j)))
      (table-fill! T #f)
      (memoize n k))))

;; computing 2^n by dynamic programing
(define dg
  (lambda (n)
    (let ((T (make-vector (+ n 1))))
      (do ((i 0 (+ i 1)))
        ((> i n) (vector-ref T n))
        (vector-set! T i
                     (if (= i 0)
                         1
                         (* 2 (vector-ref T (- i 1)))))))))