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29 lines
3.6 KiB
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29 lines
3.6 KiB
HTML
Deepest Root
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<div class="ques-view"><p>A graph which is connected and acyclic can be considered a tree. The hight of the tree depends on the selected root. Now you are supposed to find the root that results in a highest tree. Such a root is called <strong>the deepest root</strong>.</p>
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<h3 id="input-specification-">Input Specification:</h3>
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<p>Each input file contains one test case. For each case, the first line contains a positive integer <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi></mrow>N</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span></span></span></span> (<span class="katex"><span class="katex-mathml"><math><mrow><mo>≤</mo><mn>1</mn><msup><mn>0</mn><mn>4</mn></msup></mrow>\le 10^4</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.8141079999999999em;"></span><span class="strut bottom" style="height:0.950078em;vertical-align:-0.13597em;"></span><span class="base textstyle uncramped"><span class="mrel">≤</span><span class="mord mathrm">1</span><span class="mord"><span class="mord mathrm">0</span><span class="msupsub"><span class="vlist"><span style="top:-0.363em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathrm mtight">4</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span></span></span></span></span></span></span></span>) which is the number of nodes, and hence the nodes are numbered from 1 to <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi></mrow>N</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span></span></span></span>. Then <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi><mo>−</mo><mn>1</mn></mrow>N-1</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.76666em;vertical-align:-0.08333em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span><span class="mbin">−</span><span class="mord mathrm">1</span></span></span></span> lines follow, each describes an edge by given the two adjacent nodes' numbers.</p>
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<h3 id="output-specification-">Output Specification:</h3>
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<p>For each test case, print each of the deepest roots in a line. If such a root is not unique, print them in increasing order of their numbers. In case that the given graph is not a tree, print <code>Error: K components</code> where <code>K</code> is the number of connected components in the graph.</p>
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<h3 id="sample-input-1-">Sample Input 1:</h3>
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<pre><code class="lang-in">5
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1 2
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1 3
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1 4
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2 5
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</code></pre>
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<h3 id="sample-output-1-">Sample Output 1:</h3>
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<pre><code class="lang-out">3
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4
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5
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</code></pre>
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<h3 id="sample-input-2-">Sample Input 2:</h3>
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<pre><code class="lang-in">5
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1 3
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1 4
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2 5
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3 4
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</code></pre>
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<h3 id="sample-output-2-">Sample Output 2:</h3>
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<pre><code class="lang-out">Error: 2 components
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</code></pre>
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</div> |