; compute nth fibonacci number using dynamic programming
(define df
  (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 2)
                         i
                         (+ (vector-ref T (- i 2))
                            (vector-ref T (- i 1)))))))))


(load "2d-table.scm")

;; compute choose(n, k) by dynamic programing
(define dpchoose
  (lambda (n k)
    (let ((T (make-table (+ n 1) (+ k 1))))
      (do ((i 0 (+ i 1)))
        ((> i n) (table-ref T n k))
        (do ((j 0 (+ j 1)))
          ((> j (min i k)))
          (table-set! T i j
                       (cond ((= j 0) 1)
                             ((= i j) 1)
                             (else (+ (table-ref T (- i 1) (- j 1))
                                      (table-ref T (- i 1) j))))))))))