#lang racket

;;;;**********************************************************************
;;; CS251 Spring 2017 PS6
;;; Your name:
;;;;**********************************************************************

;;;+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
;;; Solo Problem 1: Diagonal Duples

;;;-----------------------------------------------------------------------
;; You are given the following function.
;; In Problem 1a, explain what it returns
(define (diagonal-duples n)
  (foldr append null
         (map (λ (sum)
                (map (λ (fst) (list fst (- sum fst)))
                     (range 0 (+ sum 1))))
              (range 0 (+ n 1)))))

;;;-----------------------------------------------------------------------
;; Flesh out the following skeleton for Problem 1b
(define (diagonal-duples-genlist-apply n) ; Assume is n a nonnegative integer
  (genlist-apply 'next-function-goes-here
                 'done-function-goes-here
                 'keep-done-value-goes-here
                 'seed-goes-here
                 ))

;;;-----------------------------------------------------------------------
;; Flesh out the following skeleton for Problem 1c
(define (diagonal-duples-iterate-apply n) ; Assume is n a nonnegative integer
  (iterate-apply 'next-function-goes-here
                 'done?-function-goes-here
                 'finalize-function-goes-here
                 'initial-state-goes-here
                 ))

;;;-----------------------------------------------------------------------
;; Flesh out the following skeleton for Problem 1d
(define (diagonal-duples-iter n)
  (define (outer-tail ...outer-params...)
    (define (inner-tail ...inter-params...)
      ...inner-body...)
    ...outer-body...)
  (outer-tail ...args...))

;;;+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
;;; Helper Functions from PS5 and iteration lectures

(define (genlist-apply next done? keepDoneValue? seed)
  (if (apply done? seed)
      (if keepDoneValue? (list seed) null)
      (cons seed
            (genlist-apply next done? keepDoneValue? (apply next seed)))))

(define (iterate-apply next done? finalize state)
  (if (apply done? state)
      (apply finalize state)
      (iterate-apply next done? finalize (apply next state))))