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<h1 class="post-title">LeetCode 94 : Binary Tree Inorder Traversal</h1>
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<!-- <a href='/'>Ching Tsai</a> -->
<time class="post-date" datetime="2016-03-11">11 Mar 2016</time>
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<blockquote>
<p>Given a binary tree, return the inorder traversal of its nodes' values.</p>
<p>For example:
Given binary tree</p>
<div class="highlight"><pre><code class="language-python" data-lang="python"> <span class="mi">1</span>
\
<span class="mi">2</span>
<span class="o">/</span>
<span class="mi">3</span>
</code></pre></div>
<p>return [1,3,2]</p>
</blockquote>
<h3>Initial Though</h3>
<p>這題如果用 recursive 的話十分簡單，但是如果要用 iterative 作的話就不是這麼容易，最主要的原因是你無法用 call recursive 的順序來決定你 output value 的順序。</p>
<h3>Guide</h3>
<p>首先你需要有一個 Stack 來倒序記錄，由於 Inorder 是 中->左->右 ，所以必須有一個方式來記錄走到最左之間的所有 Node 。 所以作法就是每次 iteration 先看 <code>Stack Q</code> 的 top， 如果他有左子孫的話，就把它加上去。所以我們會走到樹的最左邊，並且 <code>Stack Q</code> 到目前為止的 Node 。 此時 top 就沒有左子孫，因為此時是作 Inorder ， 所以這時候我們要先把 top 的 value 輸出 。 並判斷他有沒有右子孫，如果有的話就要加到 <code>Stack Q</code> 上面。 這裡有一個很重要的步驟就是，要能標記哪些 Node 已經輸出，這樣才不會重複輸出， 所以在把 top 的 value 輸出後，除了要 removeFirst，並且把 <code>values</code> 設成 <code>Integer.MIN_VALUE</code> 來標示已經輸出了。如此做到 <code>Stack Q</code> 為空的時候後停止。以下就用跟上面一樣的例子，來看 <code>Stack Q</code> 在整個演算法之中的情況，應該就會比較好理解。</p>
<div class="highlight"><pre><code class="language-python" data-lang="python"><span class="p">[</span> <span class="p">]</span> <span class="p">[</span> <span class="p">]</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">2</span><span class="p">]</span>
<span class="o">|</span> <span class="o">|</span> <span class="o">|</span> <span class="o">|</span> <span class="o">|</span> <span class="o">|</span> <span class="o">|</span> <span class="o">|</span> <span class="o">|</span> <span class="o">|</span> <span class="o">|</span> <span class="o">|</span> <span class="o">|</span> <span class="o">|</span>
<span class="o">|</span> <span class="o">|</span> <span class="o">-></span> <span class="o">|</span> <span class="o">|</span> <span class="o">-></span> <span class="o">|</span> <span class="o">|</span> <span class="o">-></span> <span class="o">|</span> <span class="o">|</span> <span class="o">-></span> <span class="o">|</span><span class="mi">3</span><span class="o">|</span> <span class="o">-></span> <span class="o">|</span> <span class="o">|</span> <span class="o">-></span> <span class="o">|</span> <span class="o">|</span>
<span class="o">|</span> <span class="o">|</span> <span class="o">|</span><span class="mi">1</span><span class="o">|</span> <span class="o">|</span> <span class="o">|</span> <span class="o">|</span><span class="mi">2</span><span class="o">|</span> <span class="o">|</span><span class="mi">2</span><span class="o">|</span> <span class="o">|</span><span class="mi">2</span><span class="o">|</span> <span class="o">|</span> <span class="o">|</span>
<span class="o">|</span><span class="n">_</span><span class="o">|</span> <span class="o">|</span><span class="n">_</span><span class="o">|</span> <span class="o">|</span><span class="n">_</span><span class="o">|</span> <span class="o">|</span><span class="n">_</span><span class="o">|</span> <span class="o">|</span><span class="n">_</span><span class="o">|</span> <span class="o">|</span><span class="n">_</span><span class="o">|</span> <span class="o">|</span><span class="n">_</span><span class="o">|</span>
<span class="mi">1</span> <span class="mi">2</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span>
</code></pre></div>
<blockquote>
<ol>
<li>put root 1</li>
<li>top node 1 has no left child -> pop and output value, top node 1 has right child -> put right child 2</li>
<li>top node 2 has left child -> put left child 3 and skip the rest</li>
<li>top node 3 has no left child -> pop and output value, top node 3 has no right child then do nothing</li>
<li>top node 2 has no left child -> pop and output value, top node 2 has no right child then do nothing</li>
</ol>
</blockquote>
<h3>Code</h3>
<div class="highlight"><pre><code class="language-java" data-lang="java"><span class="cm">/**</span>
<span class="cm"> * Definition for a binary tree node.</span>
<span class="cm"> * public class TreeNode {</span>
<span class="cm"> * int val;</span>
<span class="cm"> * TreeNode left;</span>
<span class="cm"> * TreeNode right;</span>
<span class="cm"> * TreeNode(int x) { val = x; }</span>
<span class="cm"> * }</span>
<span class="cm"> */</span>
<span class="kd">public</span> <span class="kd">class</span> <span class="nc">Solution</span> <span class="o">{</span>
<span class="kd">public</span> <span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span> <span class="nf">inorderTraversal</span><span class="o">(</span><span class="n">TreeNode</span> <span class="n">root</span><span class="o">)</span> <span class="o">{</span>
<span class="n">LinkedList</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span> <span class="n">Q</span> <span class="o">=</span> <span class="k">new</span> <span class="n">LinkedList</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>();</span>
<span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span> <span class="n">result</span> <span class="o">=</span> <span class="k">new</span> <span class="n">ArrayList</span><span class="o"><</span><span class="n">Integer</span><span class="o">>();</span>
<span class="k">if</span><span class="o">(</span><span class="n">root</span><span class="o">!=</span><span class="kc">null</span><span class="o">)</span>
<span class="n">Q</span><span class="o">.</span><span class="na">addFirst</span><span class="o">(</span><span class="n">root</span><span class="o">);</span>
<span class="k">while</span><span class="o">(!</span><span class="n">Q</span><span class="o">.</span><span class="na">isEmpty</span><span class="o">()){</span>
<span class="n">TreeNode</span> <span class="n">iter</span> <span class="o">=</span> <span class="n">Q</span><span class="o">.</span><span class="na">get</span><span class="o">(</span><span class="mi">0</span><span class="o">);</span>
<span class="k">if</span><span class="o">(</span><span class="n">iter</span><span class="o">.</span><span class="na">left</span> <span class="o">!=</span> <span class="kc">null</span> <span class="o">){</span>
<span class="k">if</span><span class="o">(</span><span class="n">iter</span><span class="o">.</span><span class="na">left</span><span class="o">.</span><span class="na">val</span> <span class="o">!=</span> <span class="n">Integer</span><span class="o">.</span><span class="na">MIN_VALUE</span><span class="o">){</span>
<span class="n">Q</span><span class="o">.</span><span class="na">addFirst</span><span class="o">(</span><span class="n">iter</span><span class="o">.</span><span class="na">left</span><span class="o">);</span>
<span class="k">continue</span><span class="o">;</span>
<span class="o">}</span>
<span class="o">}</span>
<span class="n">TreeNode</span> <span class="n">output</span> <span class="o">=</span> <span class="n">Q</span><span class="o">.</span><span class="na">removeFirst</span><span class="o">();</span>
<span class="n">result</span><span class="o">.</span><span class="na">add</span><span class="o">(</span><span class="n">output</span><span class="o">.</span><span class="na">val</span><span class="o">);</span>
<span class="n">output</span><span class="o">.</span><span class="na">val</span> <span class="o">=</span> <span class="n">Integer</span><span class="o">.</span><span class="na">MIN_VALUE</span><span class="o">;</span>
<span class="k">if</span><span class="o">(</span><span class="n">iter</span><span class="o">.</span><span class="na">right</span> <span class="o">!=</span> <span class="kc">null</span><span class="o">){</span>
<span class="n">Q</span><span class="o">.</span><span class="na">addFirst</span><span class="o">(</span><span class="n">iter</span><span class="o">.</span><span class="na">right</span><span class="o">);</span>
<span class="o">}</span>
<span class="o">}</span>
<span class="k">return</span> <span class="n">result</span><span class="o">;</span>
<span class="o">}</span>
<span class="o">}</span>
</code></pre></div>
<h3>Postorder</h3>
<p>如此掌握 Inorder 的作法後，用類似的模式也可以做到 Postorder。</p>
<div class="highlight"><pre><code class="language-java" data-lang="java"><span class="kd">public</span> <span class="kd">class</span> <span class="nc">Solution</span> <span class="o">{</span>
<span class="kd">public</span> <span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span> <span class="nf">postorderTraversal</span><span class="o">(</span><span class="n">TreeNode</span> <span class="n">root</span><span class="o">)</span> <span class="o">{</span>
<span class="n">LinkedList</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">></span> <span class="n">Q</span> <span class="o">=</span> <span class="k">new</span> <span class="n">LinkedList</span><span class="o"><</span><span class="n">TreeNode</span><span class="o">>();</span>
<span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span> <span class="n">result</span> <span class="o">=</span> <span class="k">new</span> <span class="n">ArrayList</span><span class="o"><</span><span class="n">Integer</span><span class="o">>();</span>
<span class="k">if</span><span class="o">(</span><span class="n">root</span><span class="o">!=</span><span class="kc">null</span><span class="o">)</span>
<span class="n">Q</span><span class="o">.</span><span class="na">addFirst</span><span class="o">(</span><span class="n">root</span><span class="o">);</span>
<span class="k">while</span><span class="o">(!</span><span class="n">Q</span><span class="o">.</span><span class="na">isEmpty</span><span class="o">()){</span>
<span class="n">TreeNode</span> <span class="n">iter</span> <span class="o">=</span> <span class="n">Q</span><span class="o">.</span><span class="na">get</span><span class="o">(</span><span class="mi">0</span><span class="o">);</span>
<span class="k">if</span><span class="o">(</span><span class="n">iter</span><span class="o">.</span><span class="na">left</span> <span class="o">!=</span> <span class="kc">null</span> <span class="o">){</span>
<span class="k">if</span><span class="o">(</span><span class="n">iter</span><span class="o">.</span><span class="na">left</span><span class="o">.</span><span class="na">val</span> <span class="o">!=</span> <span class="n">Integer</span><span class="o">.</span><span class="na">MIN_VALUE</span><span class="o">){</span>
<span class="n">Q</span><span class="o">.</span><span class="na">addFirst</span><span class="o">(</span><span class="n">iter</span><span class="o">.</span><span class="na">left</span><span class="o">);</span>
<span class="k">continue</span><span class="o">;</span>
<span class="o">}</span>
<span class="o">}</span>
<span class="k">if</span><span class="o">(</span><span class="n">iter</span><span class="o">.</span><span class="na">right</span> <span class="o">!=</span> <span class="kc">null</span><span class="o">){</span>
<span class="k">if</span><span class="o">(</span><span class="n">iter</span><span class="o">.</span><span class="na">right</span><span class="o">.</span><span class="na">val</span> <span class="o">!=</span> <span class="n">Integer</span><span class="o">.</span><span class="na">MIN_VALUE</span><span class="o">){</span>
<span class="n">Q</span><span class="o">.</span><span class="na">addFirst</span><span class="o">(</span><span class="n">iter</span><span class="o">.</span><span class="na">right</span><span class="o">);</span>
<span class="k">continue</span><span class="o">;</span>
<span class="o">}</span>
<span class="o">}</span>
<span class="n">TreeNode</span> <span class="n">output</span> <span class="o">=</span> <span class="n">Q</span><span class="o">.</span><span class="na">removeFirst</span><span class="o">();</span>
<span class="n">result</span><span class="o">.</span><span class="na">add</span><span class="o">(</span><span class="n">output</span><span class="o">.</span><span class="na">val</span><span class="o">);</span>
<span class="n">output</span><span class="o">.</span><span class="na">val</span> <span class="o">=</span> <span class="n">Integer</span><span class="o">.</span><span class="na">MIN_VALUE</span><span class="o">;</span>
<span class="o">}</span>
<span class="k">return</span> <span class="n">result</span><span class="o">;</span>
<span class="o">}</span>
<span class="o">}</span>
</code></pre></div>
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