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22 lines
2.9 KiB
HTML
Heaps
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<div class="ques-view"><p>In computer science, a <strong>heap</strong> is a specialized tree-based data structure that satisfies the heap property: if P is a parent node of C, then the key (the value) of P is either greater than or equal to (in a max heap) or less than or equal to (in a min heap) the key of C. A common implementation of a heap is the binary heap, in which the tree is a complete binary tree. (Quoted from Wikipedia at <a href="https://en.wikipedia.org/wiki/Heap_(data_structure">https://en.wikipedia.org/wiki/Heap_(data_structure</a>))</p>
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<p>Your job is to tell if a given complete binary tree is a heap.</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 two positive integers: M (<span class="katex"><span class="katex-mathml"><math><mrow><mo>≤</mo></mrow>\le</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.63597em;"></span><span class="strut bottom" style="height:0.7719400000000001em;vertical-align:-0.13597em;"></span><span class="base textstyle uncramped"><span class="mrel">≤</span></span></span></span> 100), the number of trees to be tested; and N (1 <span class="katex"><span class="katex-mathml"><math><mrow><mo><</mo></mrow><</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.5391em;"></span><span class="strut bottom" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="base textstyle uncramped"><span class="mrel"><</span></span></span></span> N <span class="katex"><span class="katex-mathml"><math><mrow><mo>≤</mo></mrow>\le</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.63597em;"></span><span class="strut bottom" style="height:0.7719400000000001em;vertical-align:-0.13597em;"></span><span class="base textstyle uncramped"><span class="mrel">≤</span></span></span></span> 1,000), the number of keys in each tree, respectively. Then M lines follow, each contains N distinct integer keys (all in the range of <strong>int</strong>), which gives the level order traversal sequence of a complete binary tree.</p>
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<h3 id="output-specification-">Output Specification:</h3>
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<p>For each given tree, print in a line <code>Max Heap</code> if it is a max heap, or <code>Min Heap</code> for a min heap, or <code>Not Heap</code> if it is not a heap at all. Then in the next line print the tree's postorder traversal sequence. All the numbers are separated by a space, and there must no extra space at the beginning or the end of the line.</p>
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<h3 id="sample-input-">Sample Input:</h3>
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<pre><code class="lang-in">3 8
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98 72 86 60 65 12 23 50
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8 38 25 58 52 82 70 60
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10 28 15 12 34 9 8 56
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</code></pre>
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<h3 id="sample-output-">Sample Output:</h3>
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<pre><code class="lang-out">Max Heap
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50 60 65 72 12 23 86 98
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Min Heap
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60 58 52 38 82 70 25 8
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Not Heap
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56 12 34 28 9 8 15 10
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</code></pre>
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</div> |