# 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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