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USACO 1.2
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<div class="post-body" itemprop="articleBody"><h2 id="Brief"><a href="#Brief" class="headerlink" title="Brief"></a>Brief</h2><p>本章節的題目也是沒有什麼特定演算法，有些可以使用DP來處理，有些則是根據題目敘述來解即可</p>
<span id="more"></span>
<h2 id="Milking-Cows"><a href="#Milking-Cows" class="headerlink" title="Milking Cows"></a><a target="_blank" rel="noopener" href="http://cerberus.delos.com:790/usacoprob2?a=Gss1EzStiBH&S=milk2">Milking Cows</a></h2><p>此提使用DP來解，思考過程如下</p>
<ul>
<li>將所有farmers的工作時間依據其起點由早到晚排序</li>
</ul>
<figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">0</span>;i<n;i++){</span><br><span class="line"> farmers* f = <span class="keyword">new</span> <span class="built_in">farmers</span>();</span><br><span class="line"> fin >> f->low >> f->high;</span><br><span class="line"> data.<span class="built_in">push_back</span>(f);</span><br><span class="line">}</span><br><span class="line"><span class="built_in">sort</span>(data.<span class="built_in">begin</span>(),data.<span class="built_in">end</span>(),compare);</span><br></pre></td></tr></table></figure>
<ul>
<li>掃過所有farmers的工作時間，判斷當前的farmers是否有跟上一個farmers的時間有重疊，如果有重疊，就更新當前紀錄的工作時間，如果沒有重疊，就代表此時需要閒置，因此就要更新當前閒置時間，每次更新的同時，也順便紀錄最大值</li>
</ul>
<figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br></pre></td><td class="code"><pre><span class="line">currLow = data[<span class="number">0</span>]->low;</span><br><span class="line">currHigh= data[<span class="number">0</span>]->high;</span><br><span class="line">maxMilked = currHigh - currLow;</span><br><span class="line">maxNotMilked = <span class="number">0</span>;</span><br><span class="line"><span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i<data.<span class="built_in">size</span>();++i){</span><br><span class="line"> <span class="keyword">if</span>(data[i]->low > currHigh){ <span class="comment">//沒有重疊</span></span><br><span class="line"> maxNotMilked = <span class="built_in">max</span>(maxNotMilked,data[i]->low - currHigh);</span><br><span class="line"> currLow = data[i]->low;</span><br><span class="line"> currHigh = data[i]->high;</span><br><span class="line"> maxMilked = <span class="built_in">max</span>(maxMilked,currHigh-currLow);</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">else</span> <span class="keyword">if</span> (data[i]->high > currHigh){ <span class="comment">//有重疊</span></span><br><span class="line"> currHigh = data[i]->high;</span><br><span class="line"> maxMilked = <span class="built_in">max</span>(maxMilked,(currHigh - currLow));</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"></span><br></pre></td></tr></table></figure>
<ul>
<li>全部掃過一遍及可找到答案</li>
</ul>
<h2 id="Transformations"><a href="#Transformations" class="headerlink" title="Transformations"></a><a target="_blank" rel="noopener" href="http://cerberus.delos.com:790/usacoprob2?a=Gss1EzStiBH&S=transform">Transformations</a></h2><ul>
<li>此題不難，只要想好如何將一個矩陣給順時針旋轉90即可</li>
</ul>
<figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="type">void</span> <span class="title">turn90</span><span class="params">(<span class="type">char</span>* data,<span class="type">int</span> n)</span></span>{</span><br><span class="line"> <span class="type">char</span> *tmp = <span class="keyword">new</span> <span class="type">char</span>[n*n];</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">0</span>;i<n;i++){</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> j=<span class="number">0</span>;j<n;j++){</span><br><span class="line"> tmp[j*n+(n-i<span class="number">-1</span>)] = data[i*n + j];</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="built_in">memcpy</span>(data,tmp,n*n);</span><br><span class="line"> <span class="keyword">delete</span> tmp;</span><br><span class="line"> <span class="keyword">return</span> ;</span><br><span class="line">}</span><br></pre></td></tr></table></figure>
<ul>
<li>根據題目所規定的順序，每種都去嘗試，若符合就印出答案，不合就繼續嘗試下一種即可。</li>
</ul>
<figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//#1</span></span><br><span class="line"><span class="built_in">turn90</span>(src,n);</span><br><span class="line"><span class="keyword">if</span>( <span class="number">0</span> == <span class="built_in">memcmp</span>(src,dst,n*n)){</span><br><span class="line"> fout <<<span class="string">"1"</span><<endl;</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br><span class="line"><span class="comment">//#2</span></span><br><span class="line"><span class="built_in">turn90</span>(src,n);</span><br><span class="line"><span class="keyword">if</span>( <span class="number">0</span> == <span class="built_in">memcmp</span>(src,dst,n*n)){</span><br><span class="line"> fout <<<span class="string">"2"</span><<endl;</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br><span class="line"><span class="comment">//#3</span></span><br><span class="line"><span class="built_in">turn90</span>(src,n);</span><br><span class="line"><span class="keyword">if</span>( <span class="number">0</span> == <span class="built_in">memcmp</span>(src,dst,n*n)){</span><br><span class="line"> fout <<<span class="string">"3"</span><<endl;</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br><span class="line"><span class="comment">//#4</span></span><br><span class="line"><span class="built_in">turn90</span>(src,n);</span><br><span class="line"><span class="built_in">reflect</span>(src,n);</span><br><span class="line"><span class="keyword">if</span>( <span class="number">0</span> == <span class="built_in">memcmp</span>(src,dst,n*n)){</span><br><span class="line"> fout <<<span class="string">"4"</span><<endl;</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br><span class="line"><span class="comment">//#5</span></span><br><span class="line"><span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">0</span>;i<<span class="number">3</span>;i++){</span><br><span class="line"> <span class="built_in">turn90</span>(src,n);</span><br><span class="line"> <span class="keyword">if</span>( <span class="number">0</span> == <span class="built_in">memcmp</span>(src,dst,n*n)){</span><br><span class="line"> fout <<<span class="number">5</span><<endl;</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"><span class="comment">//#6</span></span><br><span class="line"><span class="built_in">turn90</span>(src,n);</span><br><span class="line"><span class="built_in">reflect</span>(src,n);</span><br><span class="line"><span class="keyword">if</span>( <span class="number">0</span> == <span class="built_in">memcmp</span>(src,dst,n*n)){</span><br><span class="line"> fout <<<span class="string">"6"</span><<endl;</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br><span class="line"><span class="comment">//#7</span></span><br><span class="line">fout<<<span class="string">"7"</span><<endl;</span><br><span class="line"></span><br></pre></td></tr></table></figure>
<h2 id="Name-That-Number"><a href="#Name-That-Number" class="headerlink" title="Name That Number"></a><a target="_blank" rel="noopener" href="http://cerberus.delos.com:790/usacoprob2?a=Gss1EzStiBH&S=namenum">Name That Number</a></h2><ul>
<li>一開始先讀取<code>dict.txt</code>，只將長度符合題目要求的單字給存起來</li>
</ul>
<figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">while</span>(din >> tmp){</span><br><span class="line"> <span class="keyword">if</span>(tmp.<span class="built_in">size</span>() == input.<span class="built_in">size</span>())</span><br><span class="line"> data.<span class="built_in">push_back</span>(tmp);</span><br><span class="line">}</span><br></pre></td></tr></table></figure>
<ul>
<li>接下來依據位數來一個一個檢查。先針對單字內所有的第一位進行檢查是否符合規則，若不合就將其從字典內刪除，以此往下即可找到所有符合的答案<figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">0</span>;i<input.<span class="built_in">size</span>();++i){</span><br><span class="line"> <span class="keyword">for</span>(list<string>::iterator itr = data.<span class="built_in">begin</span>(); itr != data.<span class="built_in">end</span>() ; ){</span><br><span class="line"> <span class="keyword">if</span>(<span class="built_in">check</span>(input[i]-<span class="string">'0'</span>,(*itr)[i])){</span><br><span class="line"> ++itr;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">else</span>{</span><br><span class="line"> itr = data.<span class="built_in">erase</span>(itr);</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> }</span><br><span class="line"> }</span><br></pre></td></tr></table></figure></li>
</ul>
<h2 id="Palindromic-Squares"><a href="#Palindromic-Squares" class="headerlink" title="Palindromic Squares"></a><a target="_blank" rel="noopener" href="http://cerberus.delos.com:790/usacoprob2?a=Gss1EzStiBH&S=palsquare">Palindromic Squares</a></h2><ul>
<li>對於1~300之間的每個數字都去進行驗證</li>
<li>首先將先該數字給平方，接者去判斷是否迴文，若是就印出答案即可</li>
</ul>
<figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="type">void</span> <span class="title">PalindromesSquare</span><span class="params">(<span class="type">int</span> n,<span class="type">int</span> base)</span></span>{</span><br><span class="line"> string baseString;</span><br><span class="line"> string squareString;</span><br><span class="line"> <span class="type">int</span> tmp = n;</span><br><span class="line"> n = n *n;</span><br><span class="line"> <span class="keyword">while</span>(n){ <span class="comment">//計算平方後的字串</span></span><br><span class="line"> squareString.<span class="built_in">push_back</span>(<span class="built_in">getBaseChar</span>(n%base));</span><br><span class="line"> n/=base;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">while</span>(tmp){ <span class="comment">//計算當前的字串</span></span><br><span class="line"> baseString.<span class="built_in">push_back</span>(<span class="built_in">getBaseChar</span>(tmp%base));</span><br><span class="line"> tmp/=base;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span> ( <span class="built_in">checkPalin</span>(squareString) ){</span><br><span class="line"> n = baseString.<span class="built_in">size</span>();</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">0</span>;i<baseString.<span class="built_in">size</span>();++i)</span><br><span class="line"> fout<<baseString[n-i<span class="number">-1</span>];</span><br><span class="line"> fout<<<span class="string">" "</span><<squareString<<endl;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> }</span><br><span class="line"></span><br></pre></td></tr></table></figure>
<h2 id="Dual-Palindromes"><a href="#Dual-Palindromes" class="headerlink" title="Dual Palindromes"></a><a target="_blank" rel="noopener" href="http://cerberus.delos.com:790/usacoprob2?a=Gss1EzStiBH&S=dualpal">Dual Palindromes</a></h2><ul>
<li>這題跟 <em>Dual Palindromes</em>非常類似，先根據題目的需求對每個數字去做處理</li>
<li>每次處理都以2~10進位去試試看有沒有迴文，若能夠產生迴文的base數量超過兩個就直接印出結果，直接測是下一個數字即可</li>
</ul>
<figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span> </span>{</span><br><span class="line"> <span class="function">ifstream <span class="title">fin</span> <span class="params">(<span class="string">"dualpal.in"</span>)</span></span>;</span><br><span class="line"> <span class="type">int</span> limit;</span><br><span class="line"> <span class="type">int</span> start;</span><br><span class="line"> <span class="type">int</span> count;</span><br><span class="line"> fin >> limit >> start;</span><br><span class="line"> <span class="keyword">while</span>(limit){</span><br><span class="line"> ++start;</span><br><span class="line"> count =<span class="number">0</span>;</span><br><span class="line"> <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">2</span>;i<=<span class="number">10</span>;++i){</span><br><span class="line"> <span class="keyword">if</span>( <span class="built_in">PalindromesSquare</span>(start,i)){</span><br><span class="line"> ++count;</span><br><span class="line"> <span class="keyword">if</span>( <span class="number">2</span> == count){</span><br><span class="line"> fout<<start<<endl;</span><br><span class="line"> --limit;</span><br><span class="line"> <span class="keyword">break</span>;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br><span class="line"></span><br></pre></td></tr></table></figure>
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