title: “Sample LA: Vectors”
Design and write functions (potentially recursive functions) that utilize vectors.
Write a procedure, (vector-product nums) that finds the product of the numbers in in a vector that contains only numbers.
(test-= "normal case: short vector with 1"
(vector-product (vector 4 1 3))
12
0)
(test-= "normal case: includes negatives"
(vector-product (vector -3 1 7 2))
-42
0)
(test-= "normal case: mixed types, includes complex"
(vector-product (vector 2 3+4i))
6+8i
0)
(test-= "edge case: empty vector"
(vector-product (vector))
1
0)
(test-= "edge case: includes 0"
(vector-product (vector 1 2 3 0))
0
0)
Consider the following recursive procedure that adds all of the numbers in a vector of numbers.
(define vector-sum
(lambda (vec)
(vector-sum/helper vec 0)))
(define vector-sum/helper
(lambda (vec pos)
(if (< pos len)
(+ (vector-ref vec pos)
(vector-sum/helper vec (+ pos 1)))
0))]
Trace the evaluation of (vector-sum (vector 3 5 7 11)). You can skip to the consequent or alternate of the if without showing the if iteself. You can also do simple steps (e.g., adding one or looking up a value in a vector) in parallel.
(vector-sum '#(3 5 7 11))
--> (helper '#(3 5 7 11) 0)
; 0 < 4
--> (+ (vector-ref '#(3 5 7 11) 0) (helper '#(3 5 7 11) (+ 0 1)))
--> (+ 3 (helper '#(3 5 7 11) 1))
Consider the following recursive procedure that adds all of the numbers in a vector of numbers. (This one is a bit different than the previous one.)
(define vector-sum
(lambda (vec)
(let ([len (vector-length vec)])
(letrec ([helper
(lambda (pos sum-so-far)
(if (< pos len)
(helper (+ pos 1)
(+ sum-so-far (vector-ref vec pos)))
sum-so-far))])
(helper 0 0)))))
Trace the evaluation of (vector-sum (vector 3 5 7 11)). You can skip to the consequent or alternate of the if without showing the if iteself. You can also do simple steps (e.g., adding one or looking up a value in a vector) in parallel.
(vector-sum '#(3 5 7 11))
--> (helper 0 0)
; 0 < 4
--> (helper (+ pos 1) (+ 0 (vector-ref vec pos)))
--> (helper 1 (+ 0 3))
--> (helper 1 3)
Write a procedure, (vector-swap-neighbors! vec) that takes an even-length vector as a parameter and swaps the neighboring elements (those at indices 0 and 1, those at indices 2 and 3, etc.).
> (define vec (vector 'a 'b 'c 'd 'e 'f))
> (vector-swap-neighbors! (vector 'a 'b 'c 'd 'e 'f))
> vec
'#(b a d c f e)
Hint: You will find a let binding helpful.