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<meta property="og:description" content="Într-un magazin sunt n obiecte; pentru fiecare se cunoaște greutatea G și valoarea V. Un hoț intră în magazin având un rucsac ce poate transporta o greutate maximă GMax. El va fura anumite obiecte, sau porțiuni de obiecte, astfel încât suma greutăților obiectelor furate să nu depășească GMax.
Să se stabilească câștigul maxim pe care îl poate obține hoțul. Câștigul este egal cu suma valorilor obiectelor furate. Câștigul adus de o fracțiune de obiect este direct proporțional cu greutatea fracțiunii.">
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<th>Postată de</th>
<th>Clasa</th>
<th>Intrare/ieșire</th>
<th>Limită timp</th>
<th>Limită memorie</th>
<th>Sursa problemei</th>
<th>Autor</th>
<th>Dificultate</th>
<th>Scorul tău</th>
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Candale Silviu (silviu) </a>
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<td class="center">
11 </td>
<td>
<span style="background: url('/img/32-terminal.png') no-repeat 3px center;background-size:16px;padding-left:34px;">tastatură / ecran</span> </td>
<td>
0.1 secunde
</td>
<td>
<span title="Memorie totală">64 MB</span> / <span title="Dimensiunea stivei">8 MB</span>
</td>
<td>
<div class="center">-</div> </td>
<td>
<div class="center">-</div> </td>
<td class="center">
medie </td>
<td id="scor_utilizator_problema" class="center"><a href="https://www.pbinfo.ro/detalii-evaluare/63127547" class="text-decoration-none badge bg-secondary" title="Cel mai mare scor la această problemă: 100">100</a></td>
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<span class="badge bg-primary">#1340</span>
<a href="https://www.pbinfo.ro/probleme/1340/rucsac" class="text-decoration-none me-3">
Rucsac </a>
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<h1>Cerința</h1>
<p>Într-un magazin sunt <code>n</code> obiecte; pentru fiecare se cunoaște greutatea <code>G</code> și valoarea <code>V</code>. Un hoț intră în magazin având un rucsac ce poate transporta o greutate maximă <code>GMax</code>. El va fura anumite obiecte, sau porțiuni de obiecte, astfel încât suma greutăților obiectelor furate să nu depășească <code>GMax</code>.</p>
<p>Să se stabilească câștigul maxim pe care îl poate obține hoțul. Câștigul este egal cu suma valorilor obiectelor furate. Câștigul adus de o fracțiune de obiect este direct proporțional cu greutatea fracțiunii.</p>
<h1>Date de intrare</h1>
<p>Programul citește de la tastatură numerele naturale <code>n GMax</code>, iar apoi <code>n</code> perechi de valori naturale <code>G V</code>, reprezentând greutatea, respectiv valoarea fiecărui obiect.</p>
<h1>Date de ieșire</h1>
<p>Programul va afișa pe ecran numărul <code>C</code>, reprezentând câștigul maxim pe care îl poate obține hoțul.</p>
<h1>Restricții și precizări</h1>
<ul>
<li><code>1 ≤ n ≤ 1000</code>;</li>
<li><code>1 ≤ GMax, G, V ≤ 10000</code>;</li>
<li>rezultatul va fi punctat dacă diferența dintre cel afișat de program și cel corect este mai mică decât <code>0.01</code>.</li>
</ul>
<h1>Exemplu:</h1>
<p><strong>Intrare</strong></p>
<pre contenteditable="true" editable="true">4 30
10 60
5 50
12 60
20 140</pre>
<p><strong>Ieșire</strong></p>
<pre contenteditable="true" editable="true">220</pre>
<h2>Explicație</h2>
<p>Hoțul va lua obiectele <code>2</code> și <code>4</code> în întregime și jumătate din obiectul <code>1</code>, obținând un câștig de <code>220</code>.</p> </article>
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Numele clasei Java care conține metoda <code>main</code> trebuie să fie <code>rucsac</code>.
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<textarea name="da5a2c2bf2808689282c87016511e09cb9ab8cc0" id="da5a2c2bf2808689282c87016511e09cb9ab8cc0" class="form-control" style="display: none;"></textarea><div class="CodeMirror cm-s-custom" style="width: 100%; height: auto;"><div style="overflow: hidden; position: relative; width: 3px; height: 0px; top: 661px; left: 42.7969px;"><textarea autocorrect="off" autocapitalize="off" spellcheck="false" style="position: absolute; padding: 0px; width: 1000px; height: 1em; outline: none;" tabindex="0"></textarea></div><div class="CodeMirror-vscrollbar" not-content="true"><div style="min-width: 1px; height: 0px;"></div></div><div class="CodeMirror-hscrollbar" not-content="true"><div style="height: 100%; min-height: 1px; width: 0px;"></div></div><div class="CodeMirror-scrollbar-filler" not-content="true"></div><div class="CodeMirror-gutter-filler" not-content="true"></div><div class="CodeMirror-scroll" tabindex="-1" draggable="false"><div class="CodeMirror-sizer" style="margin-left: 29px; margin-bottom: -15px; border-right-width: 15px; min-width: 561.203px; min-height: 696px; padding-right: 0px; padding-bottom: 0px;"><div style="position: relative; top: 0px;"><div class="CodeMirror-lines"><div style="position: relative; outline: none;"><div class="CodeMirror-measure"><pre>x</pre></div><div class="CodeMirror-measure"></div><div style="position: relative; z-index: 1;"></div><div class="CodeMirror-cursors" style="visibility: hidden;"><div class="CodeMirror-cursor" style="left: 12.7969px; top: 656px; height: 16px;"> </div></div><div class="CodeMirror-code" style=""><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">1</div></div><pre><span style="padding-right: 0.1px;"><span class="cm-meta">#include <fstream></span></span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">2</div></div><pre class=""><span style="padding-right: 0.1px;"><span class="cm-keyword">using</span> <span class="cm-keyword">namespace</span> <span class="cm-variable">std</span>;</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">3</div></div><pre class=""><span style="padding-right: 0.1px;"><span class="cm-keyword">float</span> <span class="cm-variable">cat</span>,<span class="cm-variable">valoare</span>[<span class="cm-number">1001</span>],<span class="cm-variable">greutate</span>[<span class="cm-number">1001</span>],<span class="cm-variable">sumfurat</span>,<span class="cm-variable">sumgreutate</span>;</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">4</div></div><pre class=""><span style="padding-right: 0.1px;"><span class="cm-keyword">int</span> <span class="cm-variable">n</span>,<span class="cm-variable">i</span>,<span class="cm-variable">j</span>,<span class="cm-variable">gmax</span>;</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">5</div></div><pre class=""><span style="padding-right: 0.1px;"><span class="cm-variable">ifstream</span> <span class="cm-variable">f</span>(<span class="cm-string">"rucsac.in"</span>);</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">6</div></div><pre><span style="padding-right: 0.1px;"><span class="cm-variable">ofstream</span> <span class="cm-variable">g</span>(<span class="cm-string">"rucsac.out"</span>);</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">7</div></div><pre class=""><span style="padding-right: 0.1px;"><span class="cm-keyword">int</span> <span class="cm-variable">main</span>()</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">8</div></div><pre class=""><span style="padding-right: 0.1px;">{</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">9</div></div><pre class=""><span style="padding-right: 0.1px;"> <span class="cm-variable">cin</span><span class="cm-operator">>></span><span class="cm-variable">n</span><span class="cm-operator">>></span><span class="cm-variable">gmax</span>;</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">10</div></div><pre class=""><span style="padding-right: 0.1px;"> <span class="cm-keyword">for</span> (<span class="cm-variable">i</span><span class="cm-operator">=</span><span class="cm-number">0</span>; <span class="cm-variable">i</span><span class="cm-operator"><</span><span class="cm-variable">n</span>; <span class="cm-variable">i</span><span class="cm-operator">++</span>)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">11</div></div><pre class=""><span style="padding-right: 0.1px;"> {</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">12</div></div><pre><span style="padding-right: 0.1px;"> <span class="cm-variable">f</span><span class="cm-operator">>></span><span class="cm-variable">greutate</span>[<span class="cm-variable">i</span>]<span class="cm-operator">>></span><span class="cm-variable">valoare</span>[<span class="cm-variable">i</span>];</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">13</div></div><pre class=""><span style="padding-right: 0.1px;"> }</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">14</div></div><pre class=""><span style="padding-right: 0.1px;"> <span class="cm-keyword">for</span> (<span class="cm-variable">i</span><span class="cm-operator">=</span><span class="cm-number">0</span>; <span class="cm-variable">i</span><span class="cm-operator"><</span><span class="cm-variable">n</span>; <span class="cm-variable">i</span><span class="cm-operator">++</span>)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">15</div></div><pre class=""><span style="padding-right: 0.1px;"> {</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">16</div></div><pre class=""><span style="padding-right: 0.1px;"> <span class="cm-keyword">for</span> (<span class="cm-variable">j</span><span class="cm-operator">=</span><span class="cm-variable">i</span><span class="cm-operator">+</span><span class="cm-number">1</span>; <span class="cm-variable">j</span><span class="cm-operator"><</span><span class="cm-variable">n</span>; <span class="cm-variable">j</span><span class="cm-operator">++</span>)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">17</div></div><pre class=""><span style="padding-right: 0.1px;"> {</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">18</div></div><pre class=""><span style="padding-right: 0.1px;"> <span class="cm-keyword">if</span> (<span class="cm-variable">valoare</span>[<span class="cm-variable">i</span>]<span class="cm-operator">/</span><span class="cm-variable">greutate</span>[<span class="cm-variable">i</span>]<span class="cm-operator"><</span><span class="cm-variable">valoare</span>[<span class="cm-variable">j</span>]<span class="cm-operator">/</span><span class="cm-variable">greutate</span>[<span class="cm-variable">j</span>])</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">19</div></div><pre class=""><span style="padding-right: 0.1px;"> {</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">20</div></div><pre class=""><span style="padding-right: 0.1px;"> <span class="cm-variable">swap</span> (<span class="cm-variable">valoare</span>[<span class="cm-variable">i</span>], <span class="cm-variable">valoare</span>[<span class="cm-variable">j</span>]);</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">21</div></div><pre class=""><span style="padding-right: 0.1px;"> <span class="cm-variable">swap</span> (<span class="cm-variable">greutate</span>[<span class="cm-variable">i</span>], <span class="cm-variable">greutate</span>[<span class="cm-variable">j</span>]);</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">22</div></div><pre class=""><span style="padding-right: 0.1px;"> }</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">23</div></div><pre class=""><span style="padding-right: 0.1px;"> }</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">24</div></div><pre class=""><span style="padding-right: 0.1px;"> }</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">25</div></div><pre class=""><span style="padding-right: 0.1px;"> <span class="cm-keyword">for</span> (<span class="cm-variable">i</span><span class="cm-operator">=</span><span class="cm-number">0</span>; <span class="cm-variable">i</span><span class="cm-operator"><</span><span class="cm-variable">n</span>; <span class="cm-variable">i</span><span class="cm-operator">++</span>)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">26</div></div><pre class=""><span style="padding-right: 0.1px;"> {</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">27</div></div><pre class=""><span style="padding-right: 0.1px;"> <span class="cm-keyword">if</span> (<span class="cm-variable">sumgreutate</span><span class="cm-operator"><=</span><span class="cm-variable">gmax</span> <span class="cm-operator">&&</span> <span class="cm-variable">greutate</span>[<span class="cm-variable">i</span>]<span class="cm-operator"><=</span><span class="cm-variable">gmax</span><span class="cm-operator">-</span><span class="cm-variable">sumgreutate</span>)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">28</div></div><pre class=""><span style="padding-right: 0.1px;"> {</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">29</div></div><pre class=""><span style="padding-right: 0.1px;"> <span class="cm-variable">sumgreutate</span><span class="cm-operator">+=</span><span class="cm-variable">greutate</span>[<span class="cm-variable">i</span>];</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">30</div></div><pre class=""><span style="padding-right: 0.1px;"> <span class="cm-variable">sumfurat</span><span class="cm-operator">+=</span><span class="cm-variable">valoare</span>[<span class="cm-variable">i</span>];</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">31</div></div><pre class=""><span style="padding-right: 0.1px;"> }</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">32</div></div><pre class=""><span style="padding-right: 0.1px;"> <span class="cm-keyword">else</span> <span class="cm-keyword">if</span> (<span class="cm-variable">sumgreutate</span><span class="cm-operator"><</span><span class="cm-variable">gmax</span>)</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">33</div></div><pre class=""><span style="padding-right: 0.1px;"> {</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">34</div></div><pre class=""><span style="padding-right: 0.1px;"> <span class="cm-variable">cat</span><span class="cm-operator">=</span>(<span class="cm-variable">gmax</span><span class="cm-operator">-</span><span class="cm-variable">sumgreutate</span>)<span class="cm-operator">/</span><span class="cm-variable">greutate</span>[<span class="cm-variable">i</span>];</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">35</div></div><pre class=""><span style="padding-right: 0.1px;"> <span class="cm-variable">sumfurat</span><span class="cm-operator">+=</span><span class="cm-variable">cat</span><span class="cm-operator">*</span><span class="cm-variable">valoare</span>[<span class="cm-variable">i</span>];</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">36</div></div><pre class=""><span style="padding-right: 0.1px;"> <span class="cm-variable">sumgreutate</span><span class="cm-operator">=</span><span class="cm-variable">gmax</span>;</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">37</div></div><pre class=""><span style="padding-right: 0.1px;"> <span class="cm-keyword">break</span>;</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">38</div></div><pre class=""><span style="padding-right: 0.1px;"> }</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">39</div></div><pre class=""><span style="padding-right: 0.1px;"> }</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">40</div></div><pre><span style="padding-right: 0.1px;"> <span class="cm-variable">g</span><span class="cm-operator"><<</span><span class="cm-variable">sumfurat</span>;</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">41</div></div><pre class=""><span style="padding-right: 0.1px;"> <span class="cm-keyword">return</span> <span class="cm-number">0</span>;</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">42</div></div><pre class=""><span style="padding-right: 0.1px;">}</span></pre></div><div style="position: relative;"><div class="CodeMirror-gutter-wrapper" style="left: -29px; width: 29px;"><div class="CodeMirror-linenumber CodeMirror-gutter-elt" style="left: 0px; width: 20px;">43</div></div><pre class=""><span style="padding-right: 0.1px;"><span></span></span></pre></div></div></div></div></div></div><div style="position: absolute; height: 15px; width: 1px; top: 696px;"></div><div class="CodeMirror-gutters" style="height: 711px;"><div class="CodeMirror-gutter CodeMirror-linenumbers" style="width: 28px;"></div></div></div></div>
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