;; A NEL is one of: 
;; --- (cons Number empty)
;; --- (cons Number NEL)

;; NEL  →  Number
;; find the largest number in l
;; examples: (list 1 2 3) produces 3
(define (largest l)
  (cond
    [(empty? (rest l)) (first l)]
    [else (cond
	    [(> (first l) (largest (rest l))) (first l)]
	    [else (largest (rest l))])]))

;; test: 
(= (largest (list 1 2 3)) 3)

;; run program run 

(largest (list 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17)) ; produces
17

(largest
 (list 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23)) 

;; NEL  →  Number
;; find the largest number in l
;; examples: (list 1 2 3) produces 3
(define (largest l)
  (cond
    [(empty? (rest l)) (first l)]
    [else (local ((define max-in-rest (largest (rest l))))
	    (cond [(> (first l) max-in-rest) (first l)]
	          [else max-in-rest])])))

;;  N  →   Matrix
;; create a 1 diagonal in an n x n square
(define (diagonal n)
  (local (;;  N  →  Matrix
          ;; produce i rows of width n with 1’s in the diagonal positions
          ;; example: (aux n) produces (list (list 0 0 ... 1))
          (define (aux i)
            (cond
              [(zero? i) empty]
              [else (cons (row n i) (aux (sub1 i)))]))
          ;;  N  →  NumberList
          ;; produce one row of width n with a 1 in position i
          ;; example: (row 3 1) produces (list 1 0 0)
          (define (row n i)
            (cond
              [(zero? n) empty]
              [else (cond [(= i n) (cons 1 (row (sub1 n) i))]
                          [else (cons 0 (row (sub1 n) i))])])))
    (aux n)))

;; tests: 
(equal? (diagonal 3)
        (list (list 1 0 0)
              (list 0 1 0)
              (list 0 0 1)))

(equal? (diagonal 1)
        (list (list 1)))

(equal? (diagonal 0)
        empty)