;; The first three lines of this file were inserted by DrRacket. They record metadata
;; about the language level of this file in a form that our tools can easily process.
#reader(lib "htdp-intermediate-lambda-reader.ss" "lang")((modname tables) (read-case-sensitive #t) (teachpacks ()) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ())))

;; DEMO: Lines and Tables

;; A Table is a (listof Line)

;; A Line is a (listof Number)

empty
(list empty)
(list (list 1 2 3) (list 1 2 3))
(list (list 1 2 4) (list 2 4 5 6))

;; table-summary: Table -> Line
;; table-summary: aggregates the columns of the given table as a line

;; (table-summary (list empty)) ==> empty
;; (table-summary (list (list empty))) => empty
;; (table-summary (list (list 1 2 3) (list 1 2 3))) => (list 2 4 6)
;; (table-summary (list (list 1 2 4) (list 2 4 5 6))) => (list 3 6 9 6)


#;(define (table-summary a-table)
    (cond [(empty? a-table) (... a-table ...)]
          [else 
           ( ... a-table ...
             ... (first a-table) ...
             ... (rest a-table) ...
             ... (table-summary (rest a-table)) ...)]))


(define (table-summary a-table)
  (cond [(empty? a-table) empty]
        [else (add-lines (first a-table) (table-summary (rest a-table)))]))

#;(define (table-summary a-table) (foldr add-lines empty a-table))

(check-expect (table-summary empty) empty)
(check-expect (table-summary (list empty)) empty)
(check-expect (table-summary (list (list 1 2 3) (list 1 2 3))) (list 2 4 6))
(check-expect (table-summary (list (list 1 2 4) (list 2 4 5 6))) (list 3 6 9 6))

;; add-lines: Line Line -> Line
;; add-lines: aggregates the two given lines in a single line

;; (add-lines empty empty) ==> empty
;; (add-lines empty (list 1 2 3)) => (list 1 2 3)
;; (add-lines (list 1 2 3) empty) => (list 1 2 3)
;; (add-lines (list 1 2 4) (list 2 4 5)) => (list 3 6 9)
;; (add-lines (list 1 2 4 10) (list 2 4 5)) => (list 3 6 9 10)
;; (add-lines (list 1 2 4) (list 2 4 5 10)) => (list 3 6 9 10)


#;(define (add-lines a-line b-line)
    (cond [(and (empty? a-line) (empty? b-line)) (... a-line ... b-line ...)]
          [(and (empty? a-line) (cons? b-line))
           (... a-line ...
            ... b-line ...
            ... (first b-line) ... 
            ... (rest b-line) ...)]
          [(and (empty? b-line) (cons? a-line))
           (... b-line ...
            ... a-line ...
            ... (first a-line) ... 
            ... (rest a-line) ...)]
          [else
           (... a-line ...
            ... (first a-line) ... 
            ... (rest a-line) ...
            ... b-line ...
            ... (first b-line) ...
            ... (rest b-line)
            ... (add-lines (rest a-line) (rest b-line)) ...)]))


(define (add-lines a-line b-line)
    (cond [(and (empty? a-line) (empty? b-line)) empty]
          [(empty? a-line) b-line]
          [(empty? b-line) a-line]
          [else (cons (+ (first a-line) (first b-line))
                      (add-lines (rest a-line) (rest b-line)))]))

(check-expect (add-lines empty empty) empty)
(check-expect (add-lines empty (list 1 2 3)) (list 1 2 3))
(check-expect (add-lines (list 1 2 3) empty) (list 1 2 3))
(check-expect (add-lines (list 1 2 4) (list 2 4 )) (list 3 6 4))
(check-expect (add-lines (list 1 2 4 10) (list 2 4 5)) (list 3 6 9 10))
(check-expect (add-lines (list 1 2 4) (list 2 4 5 10)) (list 3 6 9 10))