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04-zanke.html
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<h1>Zanke</h1>
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<h2> Contents </h2>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#zanka-while">Zanka <code class="docutils literal notranslate"><span class="pre">while</span></code></a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#zanka-for">Zanka <code class="docutils literal notranslate"><span class="pre">for</span></code></a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#stavki-break-continue-in-pass">Stavki <code class="docutils literal notranslate"><span class="pre">break</span></code>, <code class="docutils literal notranslate"><span class="pre">continue</span></code> in <code class="docutils literal notranslate"><span class="pre">pass</span></code></a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#metoda-monte-carlo">Metoda Monte-Carlo</a></li>
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<section class="tex2jax_ignore mathjax_ignore" id="zanke">
<h1>Zanke<a class="headerlink" href="#zanke" title="Permalink to this heading">#</a></h1>
<p>Rekurzivni klici nam omogočajo, da se pri izvajanju poljubno mnogokrat vrnemo na poljubne konce programa. V veliki večini primerov pa nam je dovolj že to, da ponovimo določen del programa. Temu so namenjene zanke.</p>
<section id="zanka-while">
<h2>Zanka <code class="docutils literal notranslate"><span class="pre">while</span></code><a class="headerlink" href="#zanka-while" title="Permalink to this heading">#</a></h2>
<p>Z zanko <code class="docutils literal notranslate"><span class="pre">while</span></code> določene ukaze izvajamo toliko časa, dokler velja dani pogoj. Pišemo jo kot</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">while</span> <span class="n">pogoj</span><span class="p">:</span>
<span class="c1"># stavki, ki jih ponavljamo</span>
<span class="c1"># od prvega do zadnjega,</span>
<span class="c1"># dokler velja pogoj</span>
</pre></div>
</div>
<p>Na primer, program</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">n</span> <span class="o">=</span> <span class="mi">12</span>
<span class="k">while</span> <span class="n">n</span> <span class="o"><</span> <span class="mi">1000</span><span class="p">:</span>
<span class="n">n</span> <span class="o">=</span> <span class="n">n</span> <span class="o">*</span> <span class="mi">2</span>
<span class="nb">print</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
</pre></div>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>24
48
96
192
384
768
1536
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<p>bo <code class="docutils literal notranslate"><span class="pre">n</span></code> nastavil na 12, nato pa ga toliko časa podvojeval in izpisoval, dokler njegova vrednost ne bo presegla 1000.</p>
<p>V programih bomo pogostokrat novo vrednost spremenljivke izračunali tako, da bomo spremenili staro (zato tudi govorimo o spremenljivkah). Na primer, ko bomo šteli vsa praštevila med 1 in 1000000, bomo imeli spremenljivko, ki bo imela na začetku vrednost 0, nato pa jo bomo ob vsakem praštevilu povečali za 1. V ta namen lahko namesto <code class="docutils literal notranslate"><span class="pre">n</span> <span class="pre">=</span> <span class="pre">n</span> <span class="pre">*</span> <span class="pre">2</span></code> pišemo kar operator <code class="docutils literal notranslate"><span class="pre">n</span> <span class="pre">*=</span> <span class="pre">2</span></code>, saj je <code class="docutils literal notranslate"><span class="pre">*=</span></code> operacija, ki spremenljivko na levi pomnoži z vrednostjo na desni. Tudi za ostale operacije obstajajo podobne bližnjice, na primer <code class="docutils literal notranslate"><span class="pre">-=</span></code>, <code class="docutils literal notranslate"><span class="pre">*=</span></code>, <code class="docutils literal notranslate"><span class="pre">//=</span></code> in tako naprej.</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">=</span> <span class="mi">3</span>
<span class="n">x</span> <span class="o">+=</span> <span class="mi">2</span>
<span class="n">x</span> <span class="o">*=</span> <span class="mi">4</span>
<span class="n">x</span>
</pre></div>
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>20
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<p>Zgornji program bi tako na krajše lahko napisali kot:</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">n</span> <span class="o">=</span> <span class="mi">12</span>
<span class="k">while</span> <span class="n">n</span> <span class="o"><</span> <span class="mi">1000</span><span class="p">:</span>
<span class="n">n</span> <span class="o">*=</span> <span class="mi">2</span>
<span class="nb">print</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
</pre></div>
</div>
</div>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>24
48
96
192
384
768
1536
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</div>
</div>
<p>Za primer izračunajmo stopnjo največje potence števila 2, ki še deli število 1580160. To storimo tako, da število zaporedoma celoštevilsko delimo z 2 in ob vsakem deljenju števec stopnje povečamo za 1. Ukaze ponavljamo toliko časa, dokler je ostanek pri deljenju z 2 enak 0:</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">n</span> <span class="o">=</span> <span class="mi">1580160</span>
<span class="n">stopnja</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">while</span> <span class="n">n</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">n</span> <span class="o">//=</span> <span class="mi">2</span>
<span class="n">stopnja</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="nb">print</span><span class="p">(</span><span class="n">stopnja</span><span class="p">)</span>
<span class="n">stopnja</span>
</pre></div>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>1
2
3
4
5
6
7
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>7
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<p>Program bi lahko pretvorili tudi v splošnejšo funkcijo:</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">celostevilski_logaritem</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">k</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Vrne stopnjo največje potence števila k, ki še deli n."""</span>
<span class="n">stopnja</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">while</span> <span class="n">n</span> <span class="o">%</span> <span class="n">k</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="n">n</span> <span class="o">//=</span> <span class="n">k</span>
<span class="n">stopnja</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">return</span> <span class="n">stopnja</span>
</pre></div>
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</div>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">celostevilski_logaritem</span><span class="p">(</span><span class="mi">81</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
</pre></div>
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</div>
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>4
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">celostevilski_logaritem</span><span class="p">(</span><span class="mi">1580160</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>7
</pre></div>
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<p>Isto funkcijo bi lahko napisali tudi z rekurzijo:</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">celostevilski_logaritem_rek</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">k</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Vrne stopnjo največje potence števila k, ki še deli n."""</span>
<span class="k">if</span> <span class="n">n</span> <span class="o">%</span> <span class="n">k</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="k">return</span> <span class="mi">1</span> <span class="o">+</span> <span class="n">celostevilski_logaritem_rek</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="n">k</span><span class="p">,</span> <span class="n">k</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="mi">0</span>
</pre></div>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">celostevilski_logaritem_rek</span><span class="p">(</span><span class="mi">81</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>4
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">celostevilski_logaritem_rek</span><span class="p">(</span><span class="mi">1580160</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>7
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<p>Vseeno v praksi za tiste programe, pri katerih neko stvar ponavljamo toliko časa, dokler velja določen pogoj, raje uporabimo zanko <code class="docutils literal notranslate"><span class="pre">while</span></code>, saj je učinkovitejša (vsaj v Pythonu, v drugih jezikih je rekurzija ravno tako učinkovita). Poleg tega se Python pritoži, če gremo pri rekurziji pregloboko. Običajno se to zgodi takrat, kadar smo rekurzijo napisali tako, da se ne ustavi. Vendar računalnik tega ne more vedeti, zato se Python ustavi po določenem številu klicev ustavi:</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">celostevilski_logaritem_rek</span><span class="p">(</span><span class="mi">2</span> <span class="o">**</span> <span class="mi">2950</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
</pre></div>
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<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>2950
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">celostevilski_logaritem_rek</span><span class="p">(</span><span class="mi">2</span> <span class="o">**</span> <span class="mi">2960</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
</pre></div>
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<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>2960
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<p>Pri zankah teh težav ni:</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">celostevilski_logaritem</span><span class="p">(</span><span class="mi">2</span> <span class="o">**</span> <span class="mi">2950</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
</pre></div>
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</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>2950
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</div>
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<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">celostevilski_logaritem</span><span class="p">(</span><span class="mi">2</span> <span class="o">**</span> <span class="mi">2960</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>2960
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">celostevilski_logaritem</span><span class="p">(</span><span class="mi">2</span> <span class="o">**</span> <span class="mi">10000</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
</pre></div>
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<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>10000
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<p>Se pa lahko pri zanki <code class="docutils literal notranslate"><span class="pre">while</span></code> zgodi, da se njeno izvajanje nikoli ne zaključi. Na primer, če bi poklicali <code class="docutils literal notranslate"><span class="pre">celostevilski_logaritem(12345,</span> <span class="pre">1)</span></code>,
bi bil ostanek pri deljenju z 1 v pogoju vedno enak 0 in zanka bi tekla v neskončnost. Ko se naveličamo čakanja, lahko pritisnemo <code class="docutils literal notranslate"><span class="pre">Ctrl-C</span></code> in izvajanje prekinemo.</p>
</section>
<section id="zanka-for">
<h2>Zanka <code class="docutils literal notranslate"><span class="pre">for</span></code><a class="headerlink" href="#zanka-for" title="Permalink to this heading">#</a></h2>
<p>Zanko <code class="docutils literal notranslate"><span class="pre">while</span></code> torej uporabimo takrat, kadar želimo ukaze ponavljati, dokler velja nek pogoj. Včasih pa že vnaprej vemo, kolikokrat bomo te ukaze ponovili. Na primer, funkcijo za izračun fakultete bi lahko pisali kot:</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">fakulteta</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Vrne fakulteto naravnega števila n."""</span>
<span class="n">produkt</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">i</span> <span class="o">=</span> <span class="mi">1</span>
<span class="k">while</span> <span class="n">i</span> <span class="o"><=</span> <span class="n">n</span><span class="p">:</span>
<span class="n">produkt</span> <span class="o">*=</span> <span class="n">i</span>
<span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">return</span> <span class="n">produkt</span>
</pre></div>
</div>
</div>
</div>
<p>vendar vemo, da se bo zanka izvedla natanko enkrat za vsako število od 1 do <code class="docutils literal notranslate"><span class="pre">n</span></code>. Poleg tega se nam hitro zgodi, da vrstico <code class="docutils literal notranslate"><span class="pre">i</span> <span class="pre">+=</span> <span class="pre">1</span></code> po nesreči pozabimo ali napišemo kot <code class="docutils literal notranslate"><span class="pre">i</span> <span class="pre">+</span> <span class="pre">1</span></code> ali kot <code class="docutils literal notranslate"><span class="pre">i</span> <span class="pre">=</span> <span class="pre">1</span></code>, zaradi česar se zanka izvaja v neskončnost. Za primere, ko vemo, kolikokrat izvedemo določeno kodo, raje uporabimo zanko <code class="docutils literal notranslate"><span class="pre">for</span></code>, ki jo pišemo kot:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">spremenljivka</span> <span class="ow">in</span> <span class="n">vrednosti</span><span class="p">:</span>
<span class="c1"># stavki, ki jih izvedemo</span>
<span class="c1"># po enkrat za vsako izmed</span>
<span class="c1"># podanih vrednost spremenljivke</span>
</pre></div>
</div>
<p>izvede pa se enako, kot če bi napisali</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1"># v spremenljivko shrani prvo vrednost</span>
<span class="c1"># izvedi vse stavke v telesu zanke</span>
<span class="c1"># v spremenljivko shrani drugo vrednost</span>
<span class="c1"># izvedi vse stavke v telesu zanke</span>
<span class="c1"># ...</span>
<span class="c1"># v spremenljivko shrani zadnjo vrednost</span>
<span class="c1"># izvedi vse stavke v telesu zanke</span>
</pre></div>
</div>
<p>Na primer, čez vse črke danega niza se sprehodimo kot:</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">znak</span> <span class="ow">in</span> <span class="s1">'to je en niz'</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="n">znak</span><span class="p">)</span>
</pre></div>
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<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>t
o
j
e
e
n
n
i
z
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<p>samoglasnike pa lahko preštejemo kot:</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">stevilo_samoglasnikov</span><span class="p">(</span><span class="n">niz</span><span class="p">):</span>
<span class="n">stevilo</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">znak</span> <span class="ow">in</span> <span class="n">niz</span><span class="p">:</span>
<span class="k">if</span> <span class="n">znak</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="ow">in</span> <span class="s1">'aeiou'</span><span class="p">:</span>
<span class="n">stevilo</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">return</span> <span class="n">stevilo</span>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">stevilo_samoglasnikov</span><span class="p">(</span><span class="s1">'Uvod v programiranje'</span><span class="p">)</span>
</pre></div>
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<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>7
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</div>
<p>Če se želimo sprehoditi po številih, uporabimo funkcijo <code class="docutils literal notranslate"><span class="pre">range</span></code>. Ta zaporedoma vrača vsa števila v danem razponu:</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">10</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
</pre></div>
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<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>25
36
49
64
81
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<p>Vidimo, da tako kot rezine tudi <code class="docutils literal notranslate"><span class="pre">range</span></code> ne doseže zgornje meje. Če funkciji <code class="docutils literal notranslate"><span class="pre">range</span></code> podamo en argument, bo začela šteti z 0, če pa ji podamo še tretji argument, ga bo uporabila za velikost koraka (kot pri rezinah).</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">5</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0
1
2
3
4
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</div>
</div>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">2</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>5
7
9
</pre></div>
</div>
</div>
</div>
<p>S pomočjo funkcije <code class="docutils literal notranslate"><span class="pre">range</span></code> bi fakulteto torej napisali kot:</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">fakulteta</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Vrne fakulteto naravnega števila n."""</span>
<span class="n">produkt</span> <span class="o">=</span> <span class="mi">1</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
<span class="n">produkt</span> <span class="o">*=</span> <span class="n">i</span>
<span class="k">return</span> <span class="n">produkt</span>
</pre></div>
</div>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">fakulteta</span><span class="p">(</span><span class="mi">20</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>2432902008176640000
</pre></div>
</div>
</div>
</div>
</section>
<section id="stavki-break-continue-in-pass">
<h2>Stavki <code class="docutils literal notranslate"><span class="pre">break</span></code>, <code class="docutils literal notranslate"><span class="pre">continue</span></code> in <code class="docutils literal notranslate"><span class="pre">pass</span></code><a class="headerlink" href="#stavki-break-continue-in-pass" title="Permalink to this heading">#</a></h2>
<p>V zankah lahko uporabimo tudi posebne ukaze, ki spreminjajo običajen potek programa. Stavek <code class="docutils literal notranslate"><span class="pre">break</span></code> prekine trenutno zanko. Na primer:</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">2</span> <span class="ow">or</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">3</span><span class="p">:</span>
<span class="k">break</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'x'</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>1
x
2
</pre></div>
</div>
</div>
</div>
<p>izmenično izpisuje števila od 1 do 4 ter znak <code class="docutils literal notranslate"><span class="pre">x</span></code>. V trenutku, ko pride do števila 2, ki zadošča pogoju <code class="docutils literal notranslate"><span class="pre">n</span> <span class="pre">==</span> <span class="pre">2</span> <span class="pre">or</span> <span class="pre">n</span> <span class="pre">==</span> <span class="pre">3</span></code>, izvajanje zanke v celoti prekine in preneha z izpisovanjem.</p>
<p>Primer je napisan za zanko <code class="docutils literal notranslate"><span class="pre">for</span></code>, vendar enako deluje tudi za zanko <code class="docutils literal notranslate"><span class="pre">while</span></code>.</p>
<p>Stavek <code class="docutils literal notranslate"><span class="pre">continue</span></code> zanke ne ustavi, temveč le preskoči preostanek trenutnega obhoda zanke in gre nazaj na začetek z naslednjo vrednostjo. Na primer:</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">2</span> <span class="ow">or</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">3</span><span class="p">:</span>
<span class="k">continue</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'x'</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>1
x
2
3
4
x
</pre></div>
</div>
</div>
</div>
<p>pri številih 2 in 3, ki zadoščata pogoju, preskoči izpis znaka <code class="docutils literal notranslate"><span class="pre">x</span></code>, ki bi moral slediti.</p>
<p>Tudi stavek <code class="docutils literal notranslate"><span class="pre">continue</span></code> deluje tako za zanko <code class="docutils literal notranslate"><span class="pre">for</span></code> kot za zanko <code class="docutils literal notranslate"><span class="pre">while</span></code>.</p>
<p>Stavek <code class="docutils literal notranslate"><span class="pre">pass</span></code> pa ne stori ničesar. Na primer:</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">):</span>
<span class="nb">print</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
<span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">2</span> <span class="ow">or</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">3</span><span class="p">:</span>
<span class="k">pass</span>
<span class="nb">print</span><span class="p">(</span><span class="s1">'x'</span><span class="p">)</span>
</pre></div>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>1
x
2
x
3
x
4
x
</pre></div>
</div>
</div>
</div>
<p>pri številih 2 in 3, ki zadoščata pogoju, vstopi v pogojni stavek, vendar tam ne stori ničesar, zato je izpis enak, kakor bi bil za program brez pogojnega stavka.</p>
<p>Stavek <code class="docutils literal notranslate"><span class="pre">pass</span></code> lahko uporabljamo kjerkoli v Pythonu, ne le v zankah. Najpogosteje ga uporabimo takrat, kadar Python zahteva, da napišemo vsaj en ukaz, vendar ne želimo storiti ničesar. Recimo, da imamo program:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">100</span><span class="p">):</span>
<span class="k">if</span> <span class="n">x</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s1">'je sod'</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s1">'je lih'</span><span class="p">)</span>
</pre></div>
</div>
<p>in za trenutek želimo izklopiti izpisovanje sodih števil. Če bi napisali le</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">100</span><span class="p">):</span>
<span class="k">if</span> <span class="n">x</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="c1"># print(x, 'je sod')</span>
<span class="k">else</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s1">'je lih'</span><span class="p">)</span>
</pre></div>
</div>
<p>bi se Python pritožil, da je prva veja pogojnega stavka prazna, saj komentarje ignorira. Seveda bi lahko celoten program preuredili v</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">100</span><span class="p">):</span>
<span class="k">if</span> <span class="n">x</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s1">'je lih'</span><span class="p">)</span>
</pre></div>
</div>
<p>vendar tega ne želimo (sploh pri večjih programih). S pomočjo stavka <code class="docutils literal notranslate"><span class="pre">pass</span></code> pa lahko napišemo</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">100</span><span class="p">):</span>
<span class="k">if</span> <span class="n">x</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
<span class="c1"># print(x, 'je sod')</span>
<span class="k">pass</span>
<span class="k">else</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="s1">'je lih'</span><span class="p">)</span>
</pre></div>
</div>
<p>Tudi če se odločimo, da bi zopet vklopili izpisovanje, lahko stavek <code class="docutils literal notranslate"><span class="pre">pass</span></code> pustimo v kodi, ker ne stori ničesar.</p>
</section>
<section id="metoda-monte-carlo">
<h2>Metoda Monte-Carlo<a class="headerlink" href="#metoda-monte-carlo" title="Permalink to this heading">#</a></h2>
<p><a class="reference external" href="https://en.wikipedia.org/wiki/Monte_Carlo_method">Metoda Monte-Carlo</a> je postopek, ki ga uporabljamo za približno izračunavanje numeričnih rezultatov s pomočjo naključnega vzorčenja. Njeni začetki segajo v 1940. leta, ko je bila uporabljena za simulacijo fizikalnih procesov v jedrskem orožju, kjer so bili natančni analitični izračuni prezapleteni. Za primer si oglejmo, kako ocenimo število <span class="math notranslate nohighlight">\(\pi\)</span>.</p>
<p>Želimo izračunati približno vrednost števila <span class="math notranslate nohighlight">\(\pi\)</span> z metodo Monte-Carlo. Vemo, da enotska krožnica v celoti leži v kvadratu <span class="math notranslate nohighlight">\([-1, 1] \times [-1, 1]\)</span>. Verjetnost, da naključno izbrana točka iz tega kvadrata leži v krogu, je enaka razmerju površin:</p>
<div class="math notranslate nohighlight">
\[
\frac{\text{površina kroga}}{\text{površina kvadrata}} = \frac{\pi}{4}
\]</div>
<p>Če bi torej naključno izbrali veliko število točk iz kvadrata, bi jih približno <span class="math notranslate nohighlight">\(\frac{\pi}{4}\)</span> ležalo v krogu. Obratno lahko <span class="math notranslate nohighlight">\(\pi\)</span> izračunamo tako, da delež točk, ki ležijo v krogu, pomnožimo s 4. Tudi če ne vemo, koliko je <span class="math notranslate nohighlight">\(\pi\)</span>, lahko enostavno izračunamo, ali točka leži v krogu ali ne. Napišimo funkcijo, ki naključno izbere <code class="docutils literal notranslate"><span class="pre">n</span></code> točk iz kvadrata, v spremenljivko <code class="docutils literal notranslate"><span class="pre">v_krogu</span></code> zabeleži število tistih, ki ležijo v krogu, ter vrne približek števila <span class="math notranslate nohighlight">\(\pi\)</span>. Pri tem bomo uporabili funkcijo <code class="docutils literal notranslate"><span class="pre">uniform(a,</span> <span class="pre">b)</span></code> iz knjižnice <code class="docutils literal notranslate"><span class="pre">random</span></code>, ki naključno izbere število s plavajočo vejico med <code class="docutils literal notranslate"><span class="pre">a</span></code> in <code class="docutils literal notranslate"><span class="pre">b</span></code>.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">random</span>
<span class="k">def</span> <span class="nf">oceni_pi</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
<span class="n">v_krogu</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="k">if</span> <span class="n">x</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">y</span> <span class="o">**</span> <span class="mi">2</span> <span class="o"><=</span> <span class="mi">1</span><span class="p">:</span>
<span class="n">v_krogu</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="nb">print</span><span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">v_krogu</span> <span class="o">/</span> <span class="n">i</span><span class="p">)</span>
<span class="n">delez_v_krogu</span> <span class="o">=</span> <span class="n">v_krogu</span> <span class="o">/</span> <span class="n">n</span>
<span class="k">return</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">delez_v_krogu</span>
</pre></div>
</div>
</div>
</div>
</section>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#zanka-while">Zanka <code class="docutils literal notranslate"><span class="pre">while</span></code></a></li>
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#zanka-for">Zanka <code class="docutils literal notranslate"><span class="pre">for</span></code></a></li>
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