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36 lines
3.0 KiB
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Complete Binary Tree
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<div class="ques-view"><p>Given a tree, you are supposed to tell if it is a complete binary tree.</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 gives 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>2</mn><mn>0</mn></mrow>\le 20</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.78041em;vertical-align:-0.13597em;"></span><span class="base textstyle uncramped"><span class="mrel">≤</span><span class="mord mathrm">2</span><span class="mord mathrm">0</span></span></span></span>) which is the total number of nodes in the tree -- and hence the nodes are numbered from 0 to <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>. Then <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> lines follow, each corresponds to a node, and gives the indices of the left and right children of the node. If the child does not exist, a <code>-</code> will be put at the position. Any pair of children are separated by a space.</p>
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<h3 id="output-specification-">Output Specification:</h3>
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<p>For each case, print in one line <code>YES</code> and the index of the last node if the tree is a complete binary tree, or <code>NO</code> and the index of the root if not. There must be exactly one space separating the word and the number.</p>
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<h3 id="sample-input-1-">Sample Input 1:</h3>
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<pre><code class="lang-in">9
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7 8
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- -
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- -
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- -
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0 1
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2 3
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4 5
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- -
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- -
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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">YES 8
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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">8
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- -
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4 5
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0 6
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- -
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2 3
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- 7
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- -
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- -
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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">NO 1
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</code></pre>
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</div> |