545 lines
41 KiB
HTML
545 lines
41 KiB
HTML
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<title>Zapiski #3 srečanja programerskega bralnega krožka SICP</title>
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</head>
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<body>
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<div id="content" class="content">
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<h1 class="title">Zapiski #3 srečanja programerskega bralnega krožka SICP</h1>
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<div id="outline-container-org5e882c4" class="outline-2">
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<h2 id="org5e882c4">Teme</h2>
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<div class="outline-text-2" id="text-org5e882c4">
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</div>
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<div id="outline-container-orgdaeae88" class="outline-3">
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<h3 id="orgdaeae88">Funkcije višjega reda</h3>
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</div>
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</div>
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<div id="outline-container-org401da87" class="outline-2">
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<h2 id="org401da87">Vaje</h2>
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<div class="outline-text-2" id="text-org401da87">
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</div>
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<div id="outline-container-org91ad66e" class="outline-3">
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<h3 id="org91ad66e">1.29 Simpsonovo pravilo</h3>
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<div class="outline-text-3" id="text-org91ad66e">
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<div class="org-src-container">
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<pre class="src src-scheme"><span style="color: #458588;">(</span><span style="color: #fb4933;">define</span><span style="color: #b16286;">(</span><span style="color: #fabd2f;">cube</span> x<span style="color: #b16286;">)</span>
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<span style="color: #b16286;">(</span>* x x x<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
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<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span><span style="color: #b16286;">(</span><span style="color: #fabd2f;">sum-integers</span> a b<span style="color: #b16286;">)</span>
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<span style="color: #b16286;">(</span><span style="color: #fb4933;">if</span> <span style="color: #8ec07c;">(</span> > a b<span style="color: #8ec07c;">)</span>
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0
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<span style="color: #8ec07c;">(</span>+ a <span style="color: #d65d0e;">(</span>sum-integers <span style="color: #458588;">(</span>+ a 1<span style="color: #458588;">)</span> b<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
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<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span><span style="color: #b16286;">(</span><span style="color: #fabd2f;">sum-cubes</span> a b<span style="color: #b16286;">)</span>
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<span style="color: #b16286;">(</span><span style="color: #fb4933;">if</span> <span style="color: #8ec07c;">(</span>> a b<span style="color: #8ec07c;">)</span>
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0
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<span style="color: #8ec07c;">(</span>+ <span style="color: #d65d0e;">(</span>cube a<span style="color: #d65d0e;">)</span> <span style="color: #d65d0e;">(</span>sum-cubes<span style="color: #458588;">(</span>+ a 1<span style="color: #458588;">)</span> b<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
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<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">sum</span> term a next b<span style="color: #b16286;">)</span>
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<span style="color: #b16286;">(</span><span style="color: #fb4933;">if</span> <span style="color: #8ec07c;">(</span>> a b<span style="color: #8ec07c;">)</span>
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0
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<span style="color: #8ec07c;">(</span>+ <span style="color: #d65d0e;">(</span>term a<span style="color: #d65d0e;">)</span>
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<span style="color: #d65d0e;">(</span>sum term <span style="color: #458588;">(</span>next a<span style="color: #458588;">)</span> next b<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
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<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">integral</span> f a b dx<span style="color: #b16286;">)</span>
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<span style="color: #b16286;">(</span><span style="color: #fb4933;">define</span> <span style="color: #8ec07c;">(</span><span style="color: #fabd2f;">add-dx</span> x<span style="color: #8ec07c;">)</span> <span style="color: #8ec07c;">(</span>+ x dx<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
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<span style="color: #b16286;">(</span>* <span style="color: #8ec07c;">(</span>sum f <span style="color: #d65d0e;">(</span>+ a <span style="color: #458588;">(</span>/ dx 2.0<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span> add-dx b<span style="color: #8ec07c;">)</span>
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dx<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
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<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">simpson</span> f a b n<span style="color: #b16286;">)</span>
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<span style="color: #b16286;">(</span><span style="color: #fb4933;">define</span> <span style="color: #fabd2f;">h</span> <span style="color: #8ec07c;">(</span>/ <span style="color: #d65d0e;">(</span>- b a<span style="color: #d65d0e;">)</span> n<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
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<span style="color: #b16286;">(</span><span style="color: #fb4933;">define</span> <span style="color: #8ec07c;">(</span><span style="color: #fabd2f;">add-hh</span> a<span style="color: #8ec07c;">)</span> <span style="color: #8ec07c;">(</span>+ a h h<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
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<span style="color: #b16286;">(</span>* <span style="color: #8ec07c;">(</span>+ <span style="color: #d65d0e;">(</span>- <span style="color: #458588;">(</span>f a<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span>
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<span style="color: #d65d0e;">(</span>* 2 <span style="color: #458588;">(</span>sum f a add-hh b<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span>
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<span style="color: #d65d0e;">(</span>* 4 <span style="color: #458588;">(</span>sum f <span style="color: #b16286;">(</span>+ a h<span style="color: #b16286;">)</span> add-hh b<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span>
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<span style="color: #d65d0e;">(</span>- <span style="color: #458588;">(</span>f b<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span>
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<span style="color: #8ec07c;">(</span>/ h 3.0<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
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<span style="color: #458588;">(</span>list <span style="color: #b16286;">(</span>simpson cube 1 2 100<span style="color: #b16286;">)</span>
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<span style="color: #b16286;">(</span>simpson cube 1 2 1000<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
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</pre>
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</div>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<colgroup>
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<col class="org-right" />
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<col class="org-right" />
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</colgroup>
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<tbody>
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<tr>
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<td class="org-right">3.7500000000000004</td>
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<td class="org-right">3.75</td>
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</tr>
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</tbody>
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</table>
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</div>
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</div>
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<div id="outline-container-org710ddb9" class="outline-3">
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<h3 id="org710ddb9">1.30 linearen sum</h3>
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<div class="outline-text-3" id="text-org710ddb9">
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<p>
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Rekurzivne procedure:
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</p>
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<div class="org-src-container">
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<pre class="src src-scheme"><span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">sum</span> term a next b<span style="color: #b16286;">)</span>
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<span style="color: #b16286;">(</span><span style="color: #fb4933;">if</span> <span style="color: #8ec07c;">(</span>> a b<span style="color: #8ec07c;">)</span>
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0
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<span style="color: #8ec07c;">(</span>+ <span style="color: #d65d0e;">(</span>term a<span style="color: #d65d0e;">)</span>
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<span style="color: #d65d0e;">(</span>sum term <span style="color: #458588;">(</span>next a<span style="color: #458588;">)</span> next b<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
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<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">cube</span> n<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>* n n n<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
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<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">inc</span> n<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>+ n 1<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
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<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">sum-cubes</span> a b<span style="color: #b16286;">)</span>
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<span style="color: #b16286;">(</span>sum cube a inc b<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
|
|
<span style="color: #458588;">(</span>sum-cubes 1 10<span style="color: #458588;">)</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<pre class="example">
|
|
3025
|
|
</pre>
|
|
|
|
|
|
<p>
|
|
Iterativne procedure:
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-scheme"><span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">sum-iter</span> term a next b<span style="color: #b16286;">)</span>
|
|
<span style="color: #b16286;">(</span><span style="color: #fb4933;">define</span> <span style="color: #8ec07c;">(</span><span style="color: #fabd2f;">iter</span> a result<span style="color: #8ec07c;">)</span>
|
|
<span style="color: #8ec07c;">(</span><span style="color: #fb4933;">if</span> <span style="color: #d65d0e;">(</span>> a b<span style="color: #d65d0e;">)</span>
|
|
result
|
|
<span style="color: #d65d0e;">(</span>iter <span style="color: #458588;">(</span>next a<span style="color: #458588;">)</span> <span style="color: #458588;">(</span>+ result <span style="color: #b16286;">(</span>term a<span style="color: #b16286;">)</span><span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
|
|
<span style="color: #b16286;">(</span>iter a 0<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
|
|
<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">cube</span> n<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>* n n n<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">inc</span> n<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>+ n 1<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
|
|
<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">sum-cubes-iter</span> a b<span style="color: #b16286;">)</span>
|
|
<span style="color: #b16286;">(</span>sum-iter cube a inc b<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
|
|
<span style="color: #458588;">(</span>sum-cubes-iter 1 10<span style="color: #458588;">)</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<pre class="example">
|
|
3025
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org7e0d0cf" class="outline-3">
|
|
<h3 id="org7e0d0cf">1.31 Produkt višjega reda</h3>
|
|
<div class="outline-text-3" id="text-org7e0d0cf">
|
|
<div class="org-src-container">
|
|
<pre class="src src-scheme"><span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">prod-iter</span> term a next b<span style="color: #b16286;">)</span>
|
|
<span style="color: #b16286;">(</span><span style="color: #fb4933;">define</span> <span style="color: #8ec07c;">(</span><span style="color: #fabd2f;">iter</span> a result<span style="color: #8ec07c;">)</span>
|
|
<span style="color: #8ec07c;">(</span><span style="color: #fb4933;">if</span> <span style="color: #d65d0e;">(</span>> a b<span style="color: #d65d0e;">)</span>
|
|
result
|
|
<span style="color: #d65d0e;">(</span>iter <span style="color: #458588;">(</span>next a<span style="color: #458588;">)</span> <span style="color: #458588;">(</span>* result <span style="color: #b16286;">(</span>term a<span style="color: #b16286;">)</span><span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
|
|
<span style="color: #b16286;">(</span>iter a 1<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
|
|
<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">piblizek</span> n<span style="color: #b16286;">)</span>
|
|
<span style="color: #b16286;">(</span><span style="color: #fb4933;">define</span> <span style="color: #8ec07c;">(</span><span style="color: #fabd2f;">stevec</span> m<span style="color: #8ec07c;">)</span>
|
|
<span style="color: #8ec07c;">(</span>+ m 2<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
|
|
<span style="color: #b16286;">(</span>* 4 <span style="color: #8ec07c;">(</span>/ <span style="color: #d65d0e;">(</span>prod-iter <span style="color: #458588;">(</span><span style="color: #fb4933;">lambda</span> <span style="color: #b16286;">(</span>a<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>* <span style="color: #8ec07c;">(</span>- a 1<span style="color: #8ec07c;">)</span> <span style="color: #8ec07c;">(</span>+ a 1<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
3
|
|
stevec
|
|
n<span style="color: #d65d0e;">)</span>
|
|
<span style="color: #d65d0e;">(</span>prod-iter <span style="color: #458588;">(</span><span style="color: #fb4933;">lambda</span> <span style="color: #b16286;">(</span>b<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>* b b<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
3
|
|
stevec
|
|
n<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
|
|
<span style="color: #458588;">(</span>+ <span style="color: #b16286;">(</span>piblizek 10000<span style="color: #b16286;">)</span> 0.0<span style="color: #458588;">)</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<pre class="example">
|
|
3.1417497371492673
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd135cab" class="outline-3">
|
|
<h3 id="orgd135cab">1.32 Akumulator (reduce funkcija)</h3>
|
|
<div class="outline-text-3" id="text-orgd135cab">
|
|
<div class="org-src-container">
|
|
<pre class="src src-scheme"><span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">accumulate</span> combiner null-value term a next b<span style="color: #b16286;">)</span>
|
|
<span style="color: #b16286;">(</span><span style="color: #fb4933;">if</span> <span style="color: #8ec07c;">(</span>> a b<span style="color: #8ec07c;">)</span>
|
|
null-value
|
|
<span style="color: #8ec07c;">(</span>combiner <span style="color: #d65d0e;">(</span>term a<span style="color: #d65d0e;">)</span> <span style="color: #d65d0e;">(</span>accumulate combiner null-value term <span style="color: #458588;">(</span>next a<span style="color: #458588;">)</span> next b<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
|
|
<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">sum</span> term a next b<span style="color: #b16286;">)</span>
|
|
<span style="color: #b16286;">(</span>accumulate + 0 term a next b<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
|
|
<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">cube</span> n<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>* n n n<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
|
|
<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">sum-cubes</span> a b<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>sum cube a <span style="color: #8ec07c;">(</span><span style="color: #fb4933;">lambda</span> <span style="color: #d65d0e;">(</span>n<span style="color: #d65d0e;">)</span> <span style="color: #d65d0e;">(</span>+ n 1<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span> b<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
|
|
<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">prod</span> term a next b<span style="color: #b16286;">)</span>
|
|
<span style="color: #b16286;">(</span>accumulate * 1 term a next b<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
|
|
<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">piblizek</span> n<span style="color: #b16286;">)</span>
|
|
<span style="color: #b16286;">(</span><span style="color: #fb4933;">define</span> <span style="color: #8ec07c;">(</span><span style="color: #fabd2f;">stevec</span> m<span style="color: #8ec07c;">)</span>
|
|
<span style="color: #8ec07c;">(</span>+ m 2<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
|
|
<span style="color: #b16286;">(</span>* 4 <span style="color: #8ec07c;">(</span>/ <span style="color: #d65d0e;">(</span>prod <span style="color: #458588;">(</span><span style="color: #fb4933;">lambda</span> <span style="color: #b16286;">(</span>a<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>* <span style="color: #8ec07c;">(</span>- a 1<span style="color: #8ec07c;">)</span> <span style="color: #8ec07c;">(</span>+ a 1<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
3
|
|
stevec
|
|
n<span style="color: #d65d0e;">)</span>
|
|
<span style="color: #d65d0e;">(</span>prod <span style="color: #458588;">(</span><span style="color: #fb4933;">lambda</span> <span style="color: #b16286;">(</span>b<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>* b b<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
3
|
|
stevec
|
|
n<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
|
|
<span style="color: #458588;">(</span>list <span style="color: #b16286;">(</span>sum-cubes 1 10<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>+ <span style="color: #8ec07c;">(</span>piblizek 10000<span style="color: #8ec07c;">)</span> 0.0<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-right" />
|
|
|
|
<col class="org-right" />
|
|
</colgroup>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-right">3025</td>
|
|
<td class="org-right">3.1417497371492673</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgacc9e22" class="outline-3">
|
|
<h3 id="orgacc9e22">1.32b Akumulator iterativno (reduce funkcija)</h3>
|
|
<div class="outline-text-3" id="text-orgacc9e22">
|
|
<div class="org-src-container">
|
|
<pre class="src src-scheme"><span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">accumulate-iter</span> combiner null-value term a next b<span style="color: #b16286;">)</span>
|
|
<span style="color: #b16286;">(</span><span style="color: #fb4933;">define</span> <span style="color: #8ec07c;">(</span><span style="color: #fabd2f;">combine</span> a combination<span style="color: #8ec07c;">)</span>
|
|
<span style="color: #8ec07c;">(</span><span style="color: #fb4933;">if</span> <span style="color: #d65d0e;">(</span>> a b<span style="color: #d65d0e;">)</span>
|
|
combination
|
|
<span style="color: #d65d0e;">(</span>combine <span style="color: #458588;">(</span>next a<span style="color: #458588;">)</span> <span style="color: #458588;">(</span>combiner combination <span style="color: #b16286;">(</span>term a<span style="color: #b16286;">)</span><span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
|
|
<span style="color: #b16286;">(</span>combine a null-value<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
|
|
<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">sum</span> term a next b<span style="color: #b16286;">)</span>
|
|
<span style="color: #b16286;">(</span>accumulate-iter + 0 term a next b<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
|
|
<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">cube</span> n<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>* n n n<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
|
|
<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">sum-cubes</span> a b<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>sum cube a <span style="color: #8ec07c;">(</span><span style="color: #fb4933;">lambda</span> <span style="color: #d65d0e;">(</span>n<span style="color: #d65d0e;">)</span> <span style="color: #d65d0e;">(</span>+ n 1<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span> b<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
|
|
<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">prod</span> term a next b<span style="color: #b16286;">)</span>
|
|
<span style="color: #b16286;">(</span>accumulate-iter * 1 term a next b<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
|
|
<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">piblizek</span> n<span style="color: #b16286;">)</span>
|
|
<span style="color: #b16286;">(</span><span style="color: #fb4933;">define</span> <span style="color: #8ec07c;">(</span><span style="color: #fabd2f;">stevec</span> m<span style="color: #8ec07c;">)</span>
|
|
<span style="color: #8ec07c;">(</span>+ m 2<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
|
|
<span style="color: #b16286;">(</span>* 4 <span style="color: #8ec07c;">(</span>/ <span style="color: #d65d0e;">(</span>prod <span style="color: #458588;">(</span><span style="color: #fb4933;">lambda</span> <span style="color: #b16286;">(</span>a<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>* <span style="color: #8ec07c;">(</span>- a 1<span style="color: #8ec07c;">)</span> <span style="color: #8ec07c;">(</span>+ a 1<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
3
|
|
stevec
|
|
n<span style="color: #d65d0e;">)</span>
|
|
<span style="color: #d65d0e;">(</span>prod <span style="color: #458588;">(</span><span style="color: #fb4933;">lambda</span> <span style="color: #b16286;">(</span>b<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>* b b<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
3
|
|
stevec
|
|
n<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
|
|
<span style="color: #458588;">(</span>list <span style="color: #b16286;">(</span>sum-cubes 1 10<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>+ <span style="color: #8ec07c;">(</span>piblizek 10000<span style="color: #8ec07c;">)</span> 0.0<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
|
|
|
|
|
|
<colgroup>
|
|
<col class="org-right" />
|
|
|
|
<col class="org-right" />
|
|
</colgroup>
|
|
<tbody>
|
|
<tr>
|
|
<td class="org-right">3025</td>
|
|
<td class="org-right">3.1417497371492673</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org8780c88" class="outline-3">
|
|
<h3 id="org8780c88">1.33 filtriran akumulator</h3>
|
|
<div class="outline-text-3" id="text-org8780c88">
|
|
</div>
|
|
<div id="outline-container-orgd3eb7fb" class="outline-4">
|
|
<h4 id="orgd3eb7fb">a) vsota kvadratov praštevil med a in b</h4>
|
|
<div class="outline-text-4" id="text-orgd3eb7fb">
|
|
<div class="org-src-container">
|
|
<pre class="src src-scheme"><span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">accumulate-filter</span> combiner null-value term a next b predikat?<span style="color: #b16286;">)</span>
|
|
<span style="color: #b16286;">(</span><span style="color: #fb4933;">if</span> <span style="color: #8ec07c;">(</span>> a b<span style="color: #8ec07c;">)</span>
|
|
null-value
|
|
<span style="color: #8ec07c;">(</span><span style="color: #fb4933;">if</span> <span style="color: #d65d0e;">(</span>predikat? a<span style="color: #d65d0e;">)</span>
|
|
<span style="color: #d65d0e;">(</span>combiner <span style="color: #458588;">(</span>term a<span style="color: #458588;">)</span> <span style="color: #458588;">(</span>accumulate-filter combiner null-value term <span style="color: #b16286;">(</span>next a<span style="color: #b16286;">)</span> next b predikat?<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span>
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<span style="color: #d65d0e;">(</span>accumulate-filter combiner null-value term <span style="color: #458588;">(</span>next a<span style="color: #458588;">)</span> next b predikat?<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
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<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">je-prastevilo?</span> a<span style="color: #b16286;">)</span>
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<span style="color: #b16286;">(</span><span style="color: #fb4933;">define</span> <span style="color: #8ec07c;">(</span><span style="color: #fabd2f;">preveri-prastevilo?</span> x a<span style="color: #8ec07c;">)</span>
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<span style="color: #8ec07c;">(</span><span style="color: #fb4933;">if</span> <span style="color: #d65d0e;">(</span>> x <span style="color: #458588;">(</span>/ a 2<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span>
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#t
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<span style="color: #d65d0e;">(</span><span style="color: #fb4933;">and</span> <span style="color: #458588;">(</span>not <span style="color: #b16286;">(</span>integer? <span style="color: #8ec07c;">(</span>/ a x<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
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<span style="color: #458588;">(</span>preveri-prastevilo? <span style="color: #b16286;">(</span>+ x 1<span style="color: #b16286;">)</span> a<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span>
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<span style="color: #b16286;">(</span>preveri-prastevilo? 2 a<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
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<span style="color: #7c6f64;">;; </span><span style="color: #7c6f64;">(vsota kvadratov praštevil med 1 in 12 je 209)</span>
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<span style="color: #458588;">(</span>= <span style="color: #b16286;">(</span>accumulate-filter + 0 <span style="color: #8ec07c;">(</span><span style="color: #fb4933;">lambda</span> <span style="color: #d65d0e;">(</span>n<span style="color: #d65d0e;">)</span> <span style="color: #d65d0e;">(</span>* n n<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span> 1 <span style="color: #8ec07c;">(</span><span style="color: #fb4933;">lambda</span> <span style="color: #d65d0e;">(</span>n<span style="color: #d65d0e;">)</span> <span style="color: #d65d0e;">(</span>+ n 1<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span> 12 je-prastevilo?<span style="color: #b16286;">)</span>
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209<span style="color: #458588;">)</span>
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-orga117f13" class="outline-4">
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<h4 id="orga117f13">a) produkt vseh naravnih števil manjših od n ki so "relativno pra-n" (torej si z n ne delijo skupnega delitelja razen n)</h4>
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<div class="outline-text-4" id="text-orga117f13">
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<div class="org-src-container">
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<pre class="src src-scheme"><span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">accumulate-filter</span> combiner null-value term a next b predikat?<span style="color: #b16286;">)</span>
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<span style="color: #b16286;">(</span><span style="color: #fb4933;">if</span> <span style="color: #8ec07c;">(</span>> a b<span style="color: #8ec07c;">)</span>
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null-value
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<span style="color: #8ec07c;">(</span><span style="color: #fb4933;">if</span> <span style="color: #d65d0e;">(</span>predikat? a<span style="color: #d65d0e;">)</span>
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<span style="color: #d65d0e;">(</span>combiner <span style="color: #458588;">(</span>term a<span style="color: #458588;">)</span> <span style="color: #458588;">(</span>accumulate-filter combiner null-value term <span style="color: #b16286;">(</span>next a<span style="color: #b16286;">)</span> next b predikat?<span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span>
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<span style="color: #d65d0e;">(</span>accumulate-filter combiner null-value term <span style="color: #458588;">(</span>next a<span style="color: #458588;">)</span> next b predikat?<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
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<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">id</span> a<span style="color: #b16286;">)</span> a<span style="color: #458588;">)</span>
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<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">inc</span> a<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span>+ a 1<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
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<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">IN</span> a b<span style="color: #b16286;">)</span> <span style="color: #b16286;">(</span><span style="color: #fb4933;">and</span> a b<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
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<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">relativni-prastevili?</span> a b<span style="color: #b16286;">)</span>
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<span style="color: #b16286;">(</span>accumulate-filter IN #t <span style="color: #8ec07c;">(</span><span style="color: #fb4933;">lambda</span> <span style="color: #d65d0e;">(</span>x<span style="color: #d65d0e;">)</span> <span style="color: #d65d0e;">(</span><span style="color: #fb4933;">and</span> <span style="color: #458588;">(</span>not <span style="color: #b16286;">(</span>integer? <span style="color: #8ec07c;">(</span>/ a x<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
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<span style="color: #458588;">(</span>not <span style="color: #b16286;">(</span>integer? <span style="color: #8ec07c;">(</span>/ b x<span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span><span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span>
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2 inc a id<span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
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<span style="color: #458588;">(</span><span style="color: #fb4933;">define</span> <span style="color: #b16286;">(</span><span style="color: #fabd2f;">produkt-relativnih-prastevil</span> n<span style="color: #b16286;">)</span>
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<span style="color: #b16286;">(</span>accumulate-filter * 1 id 1 inc n <span style="color: #8ec07c;">(</span><span style="color: #fb4933;">lambda</span> <span style="color: #d65d0e;">(</span>x<span style="color: #d65d0e;">)</span> <span style="color: #d65d0e;">(</span>relativni-prastevili? x n<span style="color: #d65d0e;">)</span><span style="color: #8ec07c;">)</span><span style="color: #b16286;">)</span><span style="color: #458588;">)</span>
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<span style="color: #458588;">(</span>produkt-relativnih-prastevil 9<span style="color: #458588;">)</span>
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</pre>
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</div>
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<p>
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TODO popravi!! ^
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</p>
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</div>
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</div>
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</div>
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</div>
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</div>
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<div id="postamble" class="status">
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<p class="author">Author: Jurij</p>
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<p class="date">Created: 2024-06-12 sre 19:35</p>
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<p class="validation"><a href="https://validator.w3.org/check?uri=referer">Validate</a></p>
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</div>
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</body>
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</html>
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