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Exercises 1.11 - 1.12
| | (ns e1-11-12
(:use clojure.test))
1.11
A function f is defined by the rule that
$$f(n) = n \mbox{ if } n<3$$
and
$$f(n) = f(n - 1) + 2f(n - 2) + 3f(n - 3) \mbox{ if } n > 3$$
Write a procedure that computes f by means of a recursive process. Write a
procedure that computes f by means of an iterative process.
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| | (defn f [n]
(if (< n 3) n
(+ (f (- n 1)) (f (- n 2)) (f (- n 3)))))
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| | (defn f-iter [a b c n]
(if (< n 3) (+ a b c)
(f-iter b c (+ a b c) (- n 1))))
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| | (defn fi [n]
(if (< n 3) n
(f-iter 0 1 2 (- n 1))))
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| | (deftest fi-test
(is (= (fi 3) 3))
(is (= (fi 4) 6))
(is (= (fi 5) 11)))
1.12
The numbers at the edge of the Pascal triangle are all 1, and each number
inside the triangle is the sum of the two numbers above it. Write a
procedure that computes elements of Pascal's triangle by means of a
recursive process.
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| | (defn pascal [row col]
(if (or (= row col) (= col 1) (= row 1)) 1
(+ (pascal (- row 1) col)
(pascal (- row 1) (- col 1)))))
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| | (deftest test-pascal
(is (= (pascal 1 1) 1))
(is (= (pascal 3 2) 2))
(is (= (pascal 5 3) 6)))
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