#lang racket

; TODO 1
(define (all-equal? L)
  (or (null? L)
      (null? (cdr L))
      (and (equal? (first L) (second L)) (all-equal? (cdr L)))))

; TODO 2
(define (interchange A B pos)
  (list
   (append (take A pos) (list (list-ref B pos)) (drop A (add1 pos)))
   (append (take B pos) (list (list-ref A pos)) (drop B (add1 pos)))))

; TODO 3
(define (get-hole square)
  (define n (length square))
  (let loop ((s square) (row 0))
    (let ((res (member 0 (car s))))
      (if res
          (cons row (- n (length res)))
          (loop (cdr s) (add1 row))))))

; TODO 4
(define (magic-square? square)
  (define transposed (apply map list square))
  (all-equal?
   (map (λ (row) (apply + row)) (append square transposed))))


; TODO 5
(define (magic-stream square moves)
  (let loop ((seed (list square)))
    (stream-cons
     seed
     (loop (apply append ; concatenează listele interioare
                  (map (λ (sq) (filter identity (map (λ (move) (move sq)) moves)))
                       seed))))))

; TODO 6
(define (steps-to-destination final? s)
  (let loop ((s s)
             (step 0))
    (if (null? (filter final? (stream-first s)))
        (loop (stream-rest s)
              (add1 step))
        step)))