PAT/source/html/a1099.html

Build A Binary Search Tree
<div class="ques-view"><p>A Binary Search Tree (BST) is recursively defined as a binary tree which has the following properties:</p>
<ul>
<li>The left subtree of a node contains only nodes with keys less than the node's key.</li>
<li>The right subtree of a node contains only nodes with keys greater than or equal to the node's key.</li>
<li>Both the left and right subtrees must also be binary search trees.</li>
</ul>
<p>Given the structure of a binary tree and a sequence of distinct integer keys, there is only one way to fill these keys into the tree so that the resulting tree satisfies the definition of a BST. You are supposed to output the level order traversal sequence of that tree. The sample is illustrated by Figure 1 and 2.</p>
<p><img alt="figBST.jpg" src="https://images.ptausercontent.com/24c2521f-aaed-4ef4-bac8-3ff562d80a1b.jpg"/></p>
<h3 id="input-specification-">Input Specification:</h3>
<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>1</mn><mn>0</mn><mn>0</mn></mrow>\le 100</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">1</span><span class="mord mathrm">0</span><span class="mord mathrm">0</span></span></span></span>) which is the total number of nodes in the tree. The next <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 each contains the left and the right children of a node in the format <code>left_index right_index</code>, provided that 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>, and 0 is always the root. If one child is missing, then <span class="katex"><span class="katex-mathml"><math><mrow><mo>−</mo><mn>1</mn></mrow>-1</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="base textstyle uncramped"><span class="mord">−</span><span class="mord mathrm">1</span></span></span></span> will represent the NULL child pointer. Finally <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> distinct integer keys are given in the last line.</p>
<h3 id="output-specification-">Output Specification:</h3>
<p>For each test case, print in one line the level order traversal sequence of that tree. All the numbers must be separated by a space, with no extra space at the end of the line.</p>
<h3 id="sample-input-">Sample Input:</h3>
<pre><code class="lang-in">9
1 6
2 3
-1 -1
-1 4
5 -1
-1 -1
7 -1
-1 8
-1 -1
73 45 11 58 82 25 67 38 42
</code></pre>
<h3 id="sample-output-">Sample Output:</h3>
<pre><code class="lang-out">58 25 82 11 38 67 45 73 42
</code></pre>
</div>