;; =============== Q3 a) ===============
(check-expect (absolutely-odd (cons -10 (cons 22 (cons 43 empty)))) 43)
(check-expect (absolutely-odd (cons -13 (cons 3 (cons 7 empty)))) 23)
(check-expect (absolutely-odd (cons 11 (cons -6 (cons 2 empty)))) 11)

(check-expect (absolutely-odd (cons -7 (cons 2 (cons 5 empty)))) 12)
(check-expect (absolutely-odd (cons 0 (cons 176489 (cons -997789 empty))))
              1174278)
(check-expect (absolutely-odd (cons 4876 (cons -238762 (cons 11 empty))))
              11)
(check-expect (absolutely-odd (cons -123421 (cons 332233 empty))) 455654)
(check-expect (absolutely-odd (cons 3 (cons -7 (cons 1 (cons 8 empty))))) 11)
(check-expect (absolutely-odd (cons 12 (cons 22 (cons 8 empty)))) 0)
(check-expect (absolutely-odd empty) 0)
(check-expect (absolutely-odd
               (cons -223
                     (cons 12345
                           (cons 6 (cons -123421 (cons 123 empty))))))
              136112)
(check-expect (absolutely-odd (cons 0 (cons 0 (cons 0 empty)))) 0)

;; =============== Q3 b) ===============

(check-expect
 (spiraling? (cons 100 (cons -1000 (cons -10000 empty))))
 false)
(check-expect
 (spiraling? (cons 1 (cons -324 (cons 30000 empty))))
 true)
(check-expect
 (spiraling? (cons 23 (cons -142 (cons 0 empty))))
 false)
(check-expect
 (spiraling? (cons 54 (cons 100 (cons 240 empty))))
 false)
(check-expect
 (spiraling? (cons -1 (cons 24 (cons -10000 empty))))
 true)
(check-expect
 (spiraling? (cons 0 (cons -10 (cons 100 empty))))
 false)
(check-expect
 (spiraling? (cons 100 (cons -10 (cons 1 empty))))
 false)
(check-expect
 (spiraling? (cons 3 (cons 2 (cons -1 empty))))
 false)
(check-expect
 (spiraling? (cons 123454 (cons -1012345 (cons 12456124 empty))))
 true)
(check-expect
 (spiraling? (cons 1 empty))
 true)
(check-expect
 (spiraling? empty)
 true)

;; =============== Q3 c) ===============

(check-within
 (geometric-mean (cons 14(cons 0.2 (cons 45 empty))))
 5.0133 0.0001)
(check-within
 (geometric-mean (cons 123 (cons 425 (cons 0.41 empty))))
 27.7774 0.0001)
(check-within
 (geometric-mean (cons 55 (cons 212 (cons 4 empty))))
 35.9959 0.0001)
(check-within
 (geometric-mean (cons 132 (cons 23 (cons 6.23 empty))))
 26.6438 0.0001)
(check-within
 (geometric-mean (cons 2.5 (cons 14.2 (cons 46.2 empty))))
 11.7929 0.0001)
(check-within
 (geometric-mean (cons 123 (cons 2.5 (cons 0.01 empty))))
 1.4541 0.0001)
(check-within
 (geometric-mean (cons 5.4 (cons 21 (cons 55.2 empty))))
 18.4296 0.0001)
(check-within
 (geometric-mean (cons 98 (cons 25.1 (cons 1.1 empty))))
 13.9346 0.0001)
(check-within
 (geometric-mean (cons 1 empty))
 1 0.0001)
(check-within
 (geometric-mean (cons 9 (cons 0.5 empty)))
 2.1213 0.0001)

;; ================ Q4 a) ================
(check-expect
 (rainbow? (cons 'orange (cons 'yellow (cons 'violet empty))))
 true)
(check-expect
 (rainbow? (cons 'cars (cons 'planes (cons 'train empty))))
 false)
(check-expect
 (rainbow? (cons 'blue (cons 'indigo (cons 'violet empty))))
 true)
(check-expect
 (rainbow? (cons 'red empty))
 true)
(check-expect
 (rainbow? (cons 'orange (cons 'green empty)))
 true)
(check-expect
 (rainbow? (cons 'red (cons 'red (cons 'red empty))))
 false)
(check-expect
 (rainbow? empty)
 true)

;; ================ Q4 b) ================
(check-expect
 (unicorn 'green (cons 'red (cons 'green (cons 'blue empty))))
 (cons 'red (cons 'blue empty)))
(check-expect
 (unicorn 'orange (cons 'red (cons 'green (cons 'violet empty))))
 (cons 'red (cons 'green (cons 'violet empty))))
(check-expect
 (unicorn 'red (cons 'red (cons 'yellow (cons 'blue empty))))
 (cons 'yellow (cons 'blue empty)))
(check-expect
 (unicorn 'green (cons 'green empty)) empty)
(check-expect
 (unicorn 'blue empty) empty)
(check-expect
 (unicorn 'yellow (cons 'red
                        (cons 'orange
                              (cons 'yellow (cons 'green (cons 'blue empty))))))
 (cons 'red (cons 'orange (cons 'green (cons 'blue empty)))))

;; ================ Q4 c) ================
(check-expect
 (leprechaun 'red (cons 'yellow (cons 'blue empty)))
 (cons 'red (cons 'yellow (cons 'blue empty))))
(check-expect
 (leprechaun 'green (cons 'red (cons 'yellow (cons 'blue empty))))
 (cons 'red (cons 'yellow (cons 'green (cons 'blue empty)))))
(check-expect
 (leprechaun 'orange (cons 'orange (cons 'yellow (cons 'violet empty))))
 (cons 'orange (cons 'yellow (cons 'violet empty))))
(check-expect
 (leprechaun 'yellow (cons 'red (cons 'green (cons 'blue empty))))
 (cons 'red (cons 'yellow (cons 'green (cons 'blue empty)))))
(check-expect
 (leprechaun 'violet (cons 'yellow (cons 'blue empty)))
 (cons 'yellow (cons 'blue (cons 'violet empty))))
(check-expect
 (leprechaun 'violet (cons 'blue empty))
 (cons 'blue (cons 'violet empty)))
(check-expect
 (leprechaun 'orange empty)
 (cons 'orange empty))
(check-expect
 (leprechaun 'indigo (cons 'red
                           (cons 'yellow (cons 'blue (cons 'violet empty)))))
 (cons 'red (cons 'yellow (cons 'blue (cons 'indigo (cons 'violet empty))))))
(check-expect
 (leprechaun 'violet (cons 'red empty))
 (cons 'red (cons 'violet empty)))