358 lines
16 KiB
HTML
358 lines
16 KiB
HTML
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#org-div-home-and-up
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</head>
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<body>
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<div id="content" class="content">
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<div id="table-of-contents" role="doc-toc">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents" role="doc-toc">
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<ul>
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<li><a href="#org93aaa17">1. rekurzivna procedura v Lisp-u odraža princip, da se pri klicanju procedure sklicuje na samo proceduro</a></li>
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<li><a href="#orgd5912a3">2. rekurziven proces opisuje obliko evolucije računskega postopka</a></li>
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<li><a href="#orgec1b0cf">3. procedura kliče samo sebe, dokler ni dosežen robni pogoj (aplikativni red)</a></li>
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<li><a href="#org76383d3">4. pri tem mora interpreter v spominu ohranjati zapis o potrebnih izvedbah procedure –> zaradi tega prostorska zahtevnost O(n)</a></li>
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<li><a href="#orgcb17a6f">5. to se imenuje veriga preloženih operacij (? chain of deferred operations)</a></li>
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<li><a href="#orgc80a02e">6. ko se funkcija kliče na vhodu, ki ustreza robnim pogojem, se nato v nasprotnem vrstnem redu funkcija aplicira na vhodno vrednost in izvede –> časovna zahtevnost O(n)</a></li>
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<li><a href="#org6b69e77">7. klasičen primer: fakulteta \[n!\]; rekurzivna definicija: \[n! = n(n-1)!\]</a></li>
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<li><a href="#org74a8e18">8. stanje procedure je enolično opisano na vsakem koraku: spremenljivke stanja</a></li>
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<li><a href="#org47384f6">9. poleg tega obstaja enoličen predpis za pripisovanje novih (posodobljenih) vrednosti spremenljivkam stanja po vsaki izvedbi procedure</a></li>
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<li><a href="#org549d0ea">10. prostorska zahtevnost je tako O(1) - stanje je vsakič shranjeno v istem številu spremenljivk</a></li>
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<li><a href="#orgf0a4623">11. časovna zahtevnost je O(n)</a></li>
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<li><a href="#orgd43928a">12. tudi pri iterativnih procesih procedura kliče sama sebe, vendar je razlika v postopku izvajanja; medtem ko se mora rekurzivni proces zaradi pomnenja verige preloženih operacij izvesti v celoti, lahko iterativni proces na katerikoli točki prekinemo in nato nadaljujemo na podlagi vrednosti spremenljivk stanja ob prekinitvi</a></li>
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<li><a href="#orgb04cf1f">13. v tem primeru govorimo o repni rekurziji (slovarček); zanke (while, for, …) v ostalih jezikih so tako samo posebne sintaktične oblike repne rekurzije</a></li>
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<li><a href="#org657a8b3">14. pri linearni rekurziji vsak korak vsebuje en klic procedure</a></li>
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<li><a href="#orgaf71f97">15. če se na posameznem koraku procedura kliče večkrat (korak je odvisen od večih prejšnjih vrednosti), je struktura procesa drevesna</a></li>
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<li><a href="#org55b55eb">16. eksponentna časovna zahtevnost: O(exp(n))</a></li>
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<li><a href="#orga834ed4">17. linearna prostorska zahtevnost: O(n) - v spominu moramo na vsakem koraku ohraniti samo vrednosti v vozliščih na prejšnjem nivoju globine drevesa</a></li>
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<li><a href="#orgf8bf024">18. klasični primer: Fibonaccijeva števila; \[Fib(n) = Fib(n-1) + Fib(n-2)\]</a></li>
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</ul>
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</div>
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</div>
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<p>
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## Vzorci evolucije procesov
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</p>
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<p>
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procedura: vzorec lokalne evolucije računalniškega procesa
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</p>
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<p>
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Kaj pa lahko rečemo o globalnih vzorcih?
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</p>
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<p>
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### 1.2.1 Linearna rekurzija in iteracija
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</p>
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<p>
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razlika med rekurzivno proceduro in rekurzivnim procesom:
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</p>
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<div id="outline-container-org93aaa17" class="outline-2">
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<h2 id="org93aaa17"><span class="section-number-2">1.</span> rekurzivna procedura v Lisp-u odraža princip, da se pri klicanju procedure sklicuje na samo proceduro</h2>
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</div>
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<div id="outline-container-orgd5912a3" class="outline-2">
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<h2 id="orgd5912a3"><span class="section-number-2">2.</span> rekurziven proces opisuje obliko evolucije računskega postopka</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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Rekurzivni procesi:
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</p>
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</div>
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</div>
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<div id="outline-container-orgec1b0cf" class="outline-2">
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<h2 id="orgec1b0cf"><span class="section-number-2">3.</span> procedura kliče samo sebe, dokler ni dosežen robni pogoj (aplikativni red)</h2>
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</div>
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<div id="outline-container-org76383d3" class="outline-2">
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<h2 id="org76383d3"><span class="section-number-2">4.</span> pri tem mora interpreter v spominu ohranjati zapis o potrebnih izvedbah procedure –> zaradi tega prostorska zahtevnost O(n)</h2>
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</div>
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<div id="outline-container-orgcb17a6f" class="outline-2">
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<h2 id="orgcb17a6f"><span class="section-number-2">5.</span> to se imenuje veriga preloženih operacij (? chain of deferred operations)</h2>
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</div>
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<div id="outline-container-orgc80a02e" class="outline-2">
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<h2 id="orgc80a02e"><span class="section-number-2">6.</span> ko se funkcija kliče na vhodu, ki ustreza robnim pogojem, se nato v nasprotnem vrstnem redu funkcija aplicira na vhodno vrednost in izvede –> časovna zahtevnost O(n)</h2>
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</div>
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<div id="outline-container-org6b69e77" class="outline-2">
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<h2 id="org6b69e77"><span class="section-number-2">7.</span> klasičen primer: fakulteta \[n!\]; rekurzivna definicija: \[n! = n(n-1)!\]</h2>
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<div class="outline-text-2" id="text-7">
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<p>
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Iterativni procesi:
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</p>
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</div>
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</div>
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<div id="outline-container-org74a8e18" class="outline-2">
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<h2 id="org74a8e18"><span class="section-number-2">8.</span> stanje procedure je enolično opisano na vsakem koraku: spremenljivke stanja</h2>
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</div>
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<div id="outline-container-org47384f6" class="outline-2">
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<h2 id="org47384f6"><span class="section-number-2">9.</span> poleg tega obstaja enoličen predpis za pripisovanje novih (posodobljenih) vrednosti spremenljivkam stanja po vsaki izvedbi procedure</h2>
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</div>
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<div id="outline-container-org549d0ea" class="outline-2">
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<h2 id="org549d0ea"><span class="section-number-2">10.</span> prostorska zahtevnost je tako O(1) - stanje je vsakič shranjeno v istem številu spremenljivk</h2>
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</div>
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<div id="outline-container-orgf0a4623" class="outline-2">
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<h2 id="orgf0a4623"><span class="section-number-2">11.</span> časovna zahtevnost je O(n)</h2>
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<div class="outline-text-2" id="text-11">
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<p>
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Razlike:
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</p>
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</div>
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</div>
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<div id="outline-container-orgd43928a" class="outline-2">
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<h2 id="orgd43928a"><span class="section-number-2">12.</span> tudi pri iterativnih procesih procedura kliče sama sebe, vendar je razlika v postopku izvajanja; medtem ko se mora rekurzivni proces zaradi pomnenja verige preloženih operacij izvesti v celoti, lahko iterativni proces na katerikoli točki prekinemo in nato nadaljujemo na podlagi vrednosti spremenljivk stanja ob prekinitvi</h2>
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</div>
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<div id="outline-container-orgb04cf1f" class="outline-2">
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<h2 id="orgb04cf1f"><span class="section-number-2">13.</span> v tem primeru govorimo o repni rekurziji (slovarček); zanke (while, for, …) v ostalih jezikih so tako samo posebne sintaktične oblike repne rekurzije</h2>
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||
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<div class="outline-text-2" id="text-13">
|
||
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<p>
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||
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### 1.2.2 Drevesna rekurzija
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</p>
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</div>
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</div>
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||
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<div id="outline-container-org657a8b3" class="outline-2">
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||
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<h2 id="org657a8b3"><span class="section-number-2">14.</span> pri linearni rekurziji vsak korak vsebuje en klic procedure</h2>
|
||
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</div>
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<div id="outline-container-orgaf71f97" class="outline-2">
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||
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<h2 id="orgaf71f97"><span class="section-number-2">15.</span> če se na posameznem koraku procedura kliče večkrat (korak je odvisen od večih prejšnjih vrednosti), je struktura procesa drevesna</h2>
|
||
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</div>
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||
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<div id="outline-container-org55b55eb" class="outline-2">
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||
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<h2 id="org55b55eb"><span class="section-number-2">16.</span> eksponentna časovna zahtevnost: O(exp(n))</h2>
|
||
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|
</div>
|
||
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<div id="outline-container-orga834ed4" class="outline-2">
|
||
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<h2 id="orga834ed4"><span class="section-number-2">17.</span> linearna prostorska zahtevnost: O(n) - v spominu moramo na vsakem koraku ohraniti samo vrednosti v vozliščih na prejšnjem nivoju globine drevesa</h2>
|
||
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|
</div>
|
||
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<div id="outline-container-orgf8bf024" class="outline-2">
|
||
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<h2 id="orgf8bf024"><span class="section-number-2">18.</span> klasični primer: Fibonaccijeva števila; \[Fib(n) = Fib(n-1) + Fib(n-2)\]</h2>
|
||
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|
</div>
|
||
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|
</div>
|
||
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</body>
|
||
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</html>
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