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yanfeng42/view_money_order.scm

Last active September 10, 2021 12:41
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sicp 2.19: 可视化的方式, 展示零钱本身的顺序, 对计算过程的不同影响.
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view_money_order.scm
; 源码 1.14.scm 中有一部分.
; 既有实现的输出: 4.
(count-change 10)
; 新的实现...
(define us-coins (list 50 25 10 5 1))
(define us-coins-0 (list 1 5 10 25 50))
(define us-coins-1 (list 50 5 10 1 25))
(define uk-coins (list 100 50 20 10 5 2 1 0.5))
; 与旧版实现等价的输入. 4.
(cc 10 us-coins 0)
; 尝试不同的顺序.
(cc 10 us-coins-0 0)
(cc 10 us-coins-1 0)
; 新的实现.
(define (cc amount coin-values depth)
(define kinds-of-coins (length coin-values))
(define from-node (cc-node-depth amount kinds-of-coins depth))
(display (cc-node-depth-label amount kinds-of-coins depth))
(cond
((= amount 0) 1)
((or (< amount 0) (no-more? coin-values)) 0)
(else (let ((to-node (cc-node-depth amount (- kinds-of-coins 1) (+ depth 1)))) (display (cc-link from-node to-node)))
(let ((to-node (cc-node-depth (- amount (first-denomination coin-values)) kinds-of-coins (+ depth 1)))) (display (cc-link from-node to-node)))
(+
;除第一种硬币之外的所有其他硬币的不同方式的数目.
(cc amount (except-first-denomination coin-values) (+ depth 1))
; 将现金 a - d 换成所有种类的硬币的不同方式的数目.
(cc (- amount (first-denomination coin-values)) coin-values (+ depth 1))
)
)
)
)
; 需要定义的方法.
(define (no-more? l) (= (length l) 0))
(define (except-first-denomination l) (cdr l))
(define (first-denomination l) (car l))
@yanfeng42
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截屏2021-09-10 20 35 03

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@yanfeng42
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截屏2021-09-10 20 38 02

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"[12] (cc 1 2)" [label="(cc 1 2)"];
"[12] (cc 1 2)" ->  "[13] (cc 1 1)";
"[12] (cc 1 2)" ->  "[13] (cc -24 2)";
"[13] (cc 1 1)" [label="(cc 1 1)"];
"[13] (cc 1 1)" ->  "[14] (cc 1 0)";
"[13] (cc 1 1)" ->  "[14] (cc -49 1)";
"[14] (cc 1 0)" [label="(cc 1 0)"];
"[14] (cc -49 1)" [label="(cc -49 1)"];
"[13] (cc -24 2)" [label="(cc -24 2)"];
"[12] (cc -9 3)" [label="(cc -9 3)"];
"[11] (cc -4 4)" [label="(cc -4 4)"];
"[10] (cc 0 5)" [label="(cc 0 5)",color=gray80];
}

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截屏2021-09-10 20 39 23

digraph G {
node [color = gray95,style=filled];
graph [ranksep=0.3,size=7];
node [color = gray95,style=filled,fontsize=9,shape=box, margin=.08, width=0, height=0 ];
edge [penwidth=.1, arrowsize=0.5];
"[0] (cc 10 5)" [label="(cc 10 5)"];
"[0] (cc 10 5)" ->  "[1] (cc 10 4)";
"[0] (cc 10 5)" ->  "[1] (cc -40 5)";
"[1] (cc 10 4)" [label="(cc 10 4)"];
"[1] (cc 10 4)" ->  "[2] (cc 10 3)";
"[1] (cc 10 4)" ->  "[2] (cc 5 4)";
"[2] (cc 10 3)" [label="(cc 10 3)"];
"[2] (cc 10 3)" ->  "[3] (cc 10 2)";
"[2] (cc 10 3)" ->  "[3] (cc 0 3)";
"[3] (cc 10 2)" [label="(cc 10 2)"];
"[3] (cc 10 2)" ->  "[4] (cc 10 1)";
"[3] (cc 10 2)" ->  "[4] (cc 9 2)";
"[4] (cc 10 1)" [label="(cc 10 1)"];
"[4] (cc 10 1)" ->  "[5] (cc 10 0)";
"[4] (cc 10 1)" ->  "[5] (cc -15 1)";
"[5] (cc 10 0)" [label="(cc 10 0)"];
"[5] (cc -15 1)" [label="(cc -15 1)"];
"[4] (cc 9 2)" [label="(cc 9 2)"];
"[4] (cc 9 2)" ->  "[5] (cc 9 1)";
"[4] (cc 9 2)" ->  "[5] (cc 8 2)";
"[5] (cc 9 1)" [label="(cc 9 1)"];
"[5] (cc 9 1)" ->  "[6] (cc 9 0)";
"[5] (cc 9 1)" ->  "[6] (cc -16 1)";
"[6] (cc 9 0)" [label="(cc 9 0)"];
"[6] (cc -16 1)" [label="(cc -16 1)"];
"[5] (cc 8 2)" [label="(cc 8 2)"];
"[5] (cc 8 2)" ->  "[6] (cc 8 1)";
"[5] (cc 8 2)" ->  "[6] (cc 7 2)";
"[6] (cc 8 1)" [label="(cc 8 1)"];
"[6] (cc 8 1)" ->  "[7] (cc 8 0)";
"[6] (cc 8 1)" ->  "[7] (cc -17 1)";
"[7] (cc 8 0)" [label="(cc 8 0)"];
"[7] (cc -17 1)" [label="(cc -17 1)"];
"[6] (cc 7 2)" [label="(cc 7 2)"];
"[6] (cc 7 2)" ->  "[7] (cc 7 1)";
"[6] (cc 7 2)" ->  "[7] (cc 6 2)";
"[7] (cc 7 1)" [label="(cc 7 1)"];
"[7] (cc 7 1)" ->  "[8] (cc 7 0)";
"[7] (cc 7 1)" ->  "[8] (cc -18 1)";
"[8] (cc 7 0)" [label="(cc 7 0)"];
"[8] (cc -18 1)" [label="(cc -18 1)"];
"[7] (cc 6 2)" [label="(cc 6 2)"];
"[7] (cc 6 2)" ->  "[8] (cc 6 1)";
"[7] (cc 6 2)" ->  "[8] (cc 5 2)";
"[8] (cc 6 1)" [label="(cc 6 1)"];
"[8] (cc 6 1)" ->  "[9] (cc 6 0)";
"[8] (cc 6 1)" ->  "[9] (cc -19 1)";
"[9] (cc 6 0)" [label="(cc 6 0)"];
"[9] (cc -19 1)" [label="(cc -19 1)"];
"[8] (cc 5 2)" [label="(cc 5 2)"];
"[8] (cc 5 2)" ->  "[9] (cc 5 1)";
"[8] (cc 5 2)" ->  "[9] (cc 4 2)";
"[9] (cc 5 1)" [label="(cc 5 1)"];
"[9] (cc 5 1)" ->  "[10] (cc 5 0)";
"[9] (cc 5 1)" ->  "[10] (cc -20 1)";
"[10] (cc 5 0)" [label="(cc 5 0)"];
"[10] (cc -20 1)" [label="(cc -20 1)"];
"[9] (cc 4 2)" [label="(cc 4 2)"];
"[9] (cc 4 2)" ->  "[10] (cc 4 1)";
"[9] (cc 4 2)" ->  "[10] (cc 3 2)";
"[10] (cc 4 1)" [label="(cc 4 1)"];
"[10] (cc 4 1)" ->  "[11] (cc 4 0)";
"[10] (cc 4 1)" ->  "[11] (cc -21 1)";
"[11] (cc 4 0)" [label="(cc 4 0)"];
"[11] (cc -21 1)" [label="(cc -21 1)"];
"[10] (cc 3 2)" [label="(cc 3 2)"];
"[10] (cc 3 2)" ->  "[11] (cc 3 1)";
"[10] (cc 3 2)" ->  "[11] (cc 2 2)";
"[11] (cc 3 1)" [label="(cc 3 1)"];
"[11] (cc 3 1)" ->  "[12] (cc 3 0)";
"[11] (cc 3 1)" ->  "[12] (cc -22 1)";
"[12] (cc 3 0)" [label="(cc 3 0)"];
"[12] (cc -22 1)" [label="(cc -22 1)"];
"[11] (cc 2 2)" [label="(cc 2 2)"];
"[11] (cc 2 2)" ->  "[12] (cc 2 1)";
"[11] (cc 2 2)" ->  "[12] (cc 1 2)";
"[12] (cc 2 1)" [label="(cc 2 1)"];
"[12] (cc 2 1)" ->  "[13] (cc 2 0)";
"[12] (cc 2 1)" ->  "[13] (cc -23 1)";
"[13] (cc 2 0)" [label="(cc 2 0)"];
"[13] (cc -23 1)" [label="(cc -23 1)"];
"[12] (cc 1 2)" [label="(cc 1 2)"];
"[12] (cc 1 2)" ->  "[13] (cc 1 1)";
"[12] (cc 1 2)" ->  "[13] (cc 0 2)";
"[13] (cc 1 1)" [label="(cc 1 1)"];
"[13] (cc 1 1)" ->  "[14] (cc 1 0)";
"[13] (cc 1 1)" ->  "[14] (cc -24 1)";
"[14] (cc 1 0)" [label="(cc 1 0)"];
"[14] (cc -24 1)" [label="(cc -24 1)"];
"[13] (cc 0 2)" [label="(cc 0 2)",color=gray80];
"[3] (cc 0 3)" [label="(cc 0 3)",color=gray80];
"[2] (cc 5 4)" [label="(cc 5 4)"];
"[2] (cc 5 4)" ->  "[3] (cc 5 3)";
"[2] (cc 5 4)" ->  "[3] (cc 0 4)";
"[3] (cc 5 3)" [label="(cc 5 3)"];
"[3] (cc 5 3)" ->  "[4] (cc 5 2)";
"[3] (cc 5 3)" ->  "[4] (cc -5 3)";
"[4] (cc 5 2)" [label="(cc 5 2)"];
"[4] (cc 5 2)" ->  "[5] (cc 5 1)";
"[4] (cc 5 2)" ->  "[5] (cc 4 2)";
"[5] (cc 5 1)" [label="(cc 5 1)"];
"[5] (cc 5 1)" ->  "[6] (cc 5 0)";
"[5] (cc 5 1)" ->  "[6] (cc -20 1)";
"[6] (cc 5 0)" [label="(cc 5 0)"];
"[6] (cc -20 1)" [label="(cc -20 1)"];
"[5] (cc 4 2)" [label="(cc 4 2)"];
"[5] (cc 4 2)" ->  "[6] (cc 4 1)";
"[5] (cc 4 2)" ->  "[6] (cc 3 2)";
"[6] (cc 4 1)" [label="(cc 4 1)"];
"[6] (cc 4 1)" ->  "[7] (cc 4 0)";
"[6] (cc 4 1)" ->  "[7] (cc -21 1)";
"[7] (cc 4 0)" [label="(cc 4 0)"];
"[7] (cc -21 1)" [label="(cc -21 1)"];
"[6] (cc 3 2)" [label="(cc 3 2)"];
"[6] (cc 3 2)" ->  "[7] (cc 3 1)";
"[6] (cc 3 2)" ->  "[7] (cc 2 2)";
"[7] (cc 3 1)" [label="(cc 3 1)"];
"[7] (cc 3 1)" ->  "[8] (cc 3 0)";
"[7] (cc 3 1)" ->  "[8] (cc -22 1)";
"[8] (cc 3 0)" [label="(cc 3 0)"];
"[8] (cc -22 1)" [label="(cc -22 1)"];
"[7] (cc 2 2)" [label="(cc 2 2)"];
"[7] (cc 2 2)" ->  "[8] (cc 2 1)";
"[7] (cc 2 2)" ->  "[8] (cc 1 2)";
"[8] (cc 2 1)" [label="(cc 2 1)"];
"[8] (cc 2 1)" ->  "[9] (cc 2 0)";
"[8] (cc 2 1)" ->  "[9] (cc -23 1)";
"[9] (cc 2 0)" [label="(cc 2 0)"];
"[9] (cc -23 1)" [label="(cc -23 1)"];
"[8] (cc 1 2)" [label="(cc 1 2)"];
"[8] (cc 1 2)" ->  "[9] (cc 1 1)";
"[8] (cc 1 2)" ->  "[9] (cc 0 2)";
"[9] (cc 1 1)" [label="(cc 1 1)"];
"[9] (cc 1 1)" ->  "[10] (cc 1 0)";
"[9] (cc 1 1)" ->  "[10] (cc -24 1)";
"[10] (cc 1 0)" [label="(cc 1 0)"];
"[10] (cc -24 1)" [label="(cc -24 1)"];
"[9] (cc 0 2)" [label="(cc 0 2)",color=gray80];
"[4] (cc -5 3)" [label="(cc -5 3)"];
"[3] (cc 0 4)" [label="(cc 0 4)",color=gray80];
"[1] (cc -40 5)" [label="(cc -40 5)"];
}

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