SICP-1.2.2节练习
练习 1.11 - 1.13
练习 1.11：
A function f is defined by the rule that f(n) = n if n<3 and f(n) = f(n - 1) + 2f(n - 2) + 3f(n - 3) 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.
我的解答：
递归计算过程：
(define (f n)
(if (< n 3)
n
(+ (f (- n 1))
(* 2 (f (- n 2)))
(* 3 (f (- n 3))))))
迭代计算过程：
(define (f n)
(define (iter a b c count)
(if (= count 0)
c
(iter (+ a (* 2 b) (* 3 c)) a b (- count 1))))
(iter 2 1 0 n))
练习 1.12：
The following pattern of numbers is called Pascal's triangle.
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
The numbers at the edge of the 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.
我的解答：
(define (pascal row col)
(if (or (= col 1) (= row col))
1
(+ (pascal (- row 1) col)
(pascal (- row 1) (- col 1)))))
练习 1.13：
我没证明出来，在网上搜的：http://pro.panxingzhi.net/wp/?p=519
答案如下：
Feb 22, 2011 02:04:57 PM
刚刚开始看SICP，1.11写的也没写得像博主漂亮
Feb 22, 2020 03:22:58 AM
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