(define (largest-two-square-sum x y z) (if (= x (larger x y)) (sum-of-squares x (larger y z)) (sum-of-squares y (larger x z)) ) ) (define (larger x y) (if (> x y) x y) ) (define (sum-of-squares x y) (+ (square x) (square y)) ) (define (square x) (* x x) )
;; ex1.3: Define a procedure that takes three numbers as arguments ;; and returns the sum of the squares of the two larger numbers. (define (square x) (* x x)) (define (sum-of-squares x y) (+ (square x) (square y))) (define (sum-of-squared-largest-two x y z) (cond ((= (min x y z) x) (sum-of-squares y z)) ((= (min x y z) y) (sum-of-squares x z)) ((= (min x y z) z) (sum-of-squares x y)))) ;; Testing (sum-of-squared-largest-two 1 3 4) (sum-of-squared-largest-two 4 1 3) (sum-of-squared-largest-two 3 4 1)
;; ex 1.3 ;; implemented using only techniques covered to this point (define (square x) (* x x)) (define (sum-of-squares x y) (+ (square x) (square y))) (define (largest-two-of-three x y z) (if (>= x y) (sum-of-squares x (if (>= y z) y z)) (sum-of-squares y (if (>= x z) x z)))) ;; tests (largest-two-of-three 2 3 4) (largest-two-of-three 4 2 3) (largest-two-of-three 3 4 2)
(define (smallest-two-of-three a b c) (if (< a b) (if (< a c) a c) (if (< b c) b c))) (define (square a) (* a a)) (define (sum-of-squares-largest-two-of-three a b c) (+ (square a) (square b) (square c) (- (square (smallest-two-of-three a b c)))))
(define (sum-of-squares x y) (+ (* x x) (* y y))) (define (sum-of-squares-of-two-largest a b c) (cond ((and (<= a b) (<= a c)) (sum-of-squares b c)) ((<= a b) (sum-of-squares a b)) (else (sum-of-squares a c)))) ;; wrong when (and (> a b) (> b c))
(define (sum-of-squared-largest-two a b c)
(- (+ (square a) (square b) (square c)) (square (min a b c))))
;; a recursive solution (define (sum-of-squares-of-two-largest a b c) (define (>= x y) (or (> x y) (= x y))) (define (square x) (* x x)) (cond ((and (>= a b) (>= b c)) (+ (square a) (square b))) ; a >= b >= c ((and (>= b a) (>= c b)) (+ (square b) (square c))) ; a <= b <= c (else (sum-of-squares-of-two-largest b c a))))
;; Exercise 1.3 ;; Uses no helper functions (define (sumsqrs-largest x y z) (cond ((and (>= x z) (>= y z)) (+ (* x x) (* y y))) ((and (>= x y) (>= z y)) (+ (* x x) (* z z))) ((and (>= y x) (>= z x)) (+ (* y y) (* z z)))))
;; ex1.3: does not implement helper functions nor techniques yet covered in book (define (sum-max2-sqr a b c) (cond ((and (not (> c a)) (not (> c b))) (+ (* a a) (* b b))) ((and (not (> b a)) (not (> b c))) (+ (* a a) (* c c))) ((and (not (> a b)) (not (> a c))) (+ (* b b) (* c c))) ) ) ;; testing (sum-max2-sqr 3 4 5) (sum-max2-sqr 3 5 4) (sum-max2-sqr 5 3 4) (sum-max2-sqr 5 4 3) (sum-max2-sqr 4 3 5) (sum-max2-sqr 4 5 3) (sum-max2-sqr -1 -2 -3) (sum-max2-sqr -3 -2 -1) (sum-max2-sqr 0 0 -1) (sum-max2-sqr 1 0 -1) (sum-max2-sqr 3 3 5) (sum-max2-sqr 3 5 5)
;; ex1.3: Another variation not used yet (define (if-you-want-to-get-the-sum-of-two-numbers-where-those-two-numbers-are-chosen-by-finding-the-largest-of-two-out-of-three-numbers-and-squaring-them-which-is-multiplying-them-by-itself-then-you-should-input-three-numbers-into-this-function-and-it-will-do-that-for-you x y z) (if (>= x y) (if (>= y z) (+ (* x x) (* y y)) (+ (* x x) (* z z))) (if (>= x z) (+ (* y y) (* x x)) (+ (* y y) (* z z)))))
(define (largest-two-square-sum x y z) (sum-of-squares (mid x y z) (biggest x y z))) (define (sum-of-squares x y) (+ (square x) (square y))) (define (square x) (* x x)) (define (bigger x y) (if (> x y) x y)) (define (biggest x y z) (if (> (bigger x y) z) (bigger x y) z)) (define (mini x y) (if (> x y) y x)) (define (mid x y z) (bigger (mini x y) (mini (bigger x y) z)))
;; no min used (define (square x) (* x x)) (define (sum-of-squares x y) (+ (square x) (square y))) (define (biggest x y) (if (> x y) x y)) (define (input x y z) (sum-of-squares (biggest x y) (biggest y z))) ;; output > (input 1 2 3) 13 > (input 5 6 7) 85 > (input 9 10 11) 221 ;; gives wrong answer when (and (> y x) (> y z))
(define (sum-of-squares x y z) (+ (square (max x y)) (square (max (min x y) z)))) (define (square x) (* x x)) ;; test > (sum-of-squares 1 2 3) 13 > (sum-of-squares 3 2 1) 13 > (sum-of-squares 3 1 2) 13 > (sum-of-squares 2 3 1) 13 > (sum-of-squares 1 3 2) 13 > (sum-of-squares 1 3 2) 13 > (sum-of-squares 2 2 1) 8 > (sum-of-squares 1 2 2) 8 > (sum-of-squares 2 2 2) 8
;; make it clearly (define (square x) (* x x)) (define (larger x y) (if (> x y) x y)) (define (smaller x y) (if (< x y) x y)) (define (largest-two-square-sum x y z) (+ (square (larger x y)) (square (smaller x y)))) ;; output > (largest-two-square-sum 4 5 6) 41 ;; this program is wrong, answer should be 61.
;; drop thru' cond (define (fun x y z) (define (square x) (* x x)) (define (sumsq x y) (+ (square x) (square y))) (cond ((>= x y) (sumsq x (if (>= y z) y z))) ((>= x z) (sumsq x y)) (else (sumsq z y)) ) )
(define (square a) (* a a)) (define (square-sum a b) (+ (square a) (square b))) (define (compare a b c) (if (> a b) (if (> b c) (square-sum a b) (square-sum a c)) (if (> a c) (square-sum a b) (square-sum b c))))
(define (square a) (* a a)) (define (sum-of-squares a b) (+ (square a) (square b))) (define (sum-sq-max2 a b c) (cond ((and (< a b) (< a c)) (sum-of-squares b c)) ((and (< b a) (< b c)) (sum-of-squares a c)) (else (sum-of-squares a b)) ) ) (define (sumsq a b c) (define sum (+ a b c)) (define x (max a b c)) (define y (- sum x (min a b c))) (sum-of-squares x y) )
;; Doesn't use helper functions. A bit neater than sum-max2-sqr defined above. (define (sum a b c) (cond ((not (or (< b a) (< c a))) (+ (* b b) (* c c))) ((not (or (< a b) (< c b))) (+ (* a a) (* c c))) ((not (or (< a c) (< b c))) (+ (* a a) (* b b)))))
(define (square x) (* x x)) (define (exam x y z) (if (or (> x y) (> x z)) (if (> y z) (+ (square x) (square y)) (+ (square x) (square z))) (+ (square y) (square z))))
;; Different approach, where square of the lowest term is deducted. (define (f a b c) (- (+ (* a a) (* b b) (* c c)) (* (cond ((and (< a b) (< a c)) (* a a)) ((and (< b c) (< b a)) (* b b)) (else (* c c))))))
;; Using sorting networks (define (max a b) (cond ((< a b) b) (else a)) ) (define (min a b) (cond ((> a b) b) (else a)) ) (define (square a) (* a a) ) (define (sorting-network-3 a b c) (let* ((stage1-b (max b c)) (stage1-c (min b c)) (stage2-a (max a stage1-c))) (list (max stage2-a stage1-b) (min stage2-a stage1-b) (min a stage1-c)) ) ) (define (ex13 a b c) (let* ((sorted (sorting-network-3 a b c)) (maximal (first sorted)) (middle (second sorted))) (+ (square maximal) (square middle)) ) )
;; Doesn't use helper functions. (define (ex13 x y z) (+ (if (or (>= x y) (>= x z)) (* x x) 0) (if (or (> y x) (>= y z)) (* y y) 0) (if (or (> z x) (> z y)) (* z z) 0)))
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