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<span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg> <span class="sr-only">(opens new window)</span></span></a></nav> <ul class="sidebar-links"><li><section class="sidebar-group depth-0"><p class="sidebar-heading open"><span>Algorithm</span> <!----></p> <ul class="sidebar-links sidebar-group-items"><li><a href="/algorithm/" aria-current="page" class="sidebar-link">Disclaimer</a></li><li><a href="/algorithm/getting-started-with-algorithm.html" class="sidebar-link">Getting started with algorithm</a></li><li><a href="/algorithm/algorithm-complexity.html" 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Tree</a></li></ul></li><li><a href="/algorithm/lowest-common-ancestor-of-a-binary-tree.html" class="sidebar-link">Lowest common ancestor of a Binary Tree</a></li><li><a href="/algorithm/graph.html" class="sidebar-link">Graph</a></li><li><a href="/algorithm/graph-traversals.html" class="sidebar-link">Graph Traversals</a></li><li><a href="/algorithm/dijkstras-algorithm.html" class="sidebar-link">Dijkstra’s Algorithm</a></li><li><a href="/algorithm/a-pathfinding.html" class="sidebar-link">A* Pathfinding</a></li><li><a href="/algorithm/a-pathfinding-algorithm.html" class="sidebar-link">A* Pathfinding Algorithm</a></li><li><a href="/algorithm/dynamic-programming.html" class="sidebar-link">Dynamic Programming</a></li><li><a href="/algorithm/applications-of-dynamic-programming.html" class="sidebar-link">Applications of Dynamic Programming</a></li><li><a href="/algorithm/kruskal-s-algorithm.html" class="sidebar-link">Kruskal's Algorithm</a></li><li><a href="/algorithm/greedy-algorithms.html" 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Search</a></li><li><a href="/algorithm/breadth-first-search.html" class="sidebar-link">Breadth-First Search</a></li><li><a href="/algorithm/depth-first-search.html" class="sidebar-link">Depth First Search</a></li><li><a href="/algorithm/hash-functions.html" class="sidebar-link">Hash Functions</a></li><li><a href="/algorithm/travelling-salesman.html" class="sidebar-link">Travelling Salesman</a></li><li><a href="/algorithm/shortest-common-supersequence-problem.html" class="sidebar-link">Shortest Common Supersequence Problem</a></li><li><a href="/algorithm/knapsack-problem.html" class="sidebar-link">Knapsack Problem</a></li><li><a href="/algorithm/equation-solving.html" class="sidebar-link">Equation Solving</a></li><li><a href="/algorithm/longest-common-subsequence.html" class="sidebar-link">Longest Common Subsequence</a></li><li><a href="/algorithm/longest-increasing-subsequence.html" class="sidebar-link">Longest Increasing Subsequence</a></li><li><a href="/algorithm/check-two-strings-are-anagrams.html" class="sidebar-link">Check two strings are anagrams</a></li><li><a href="/algorithm/pascal-s-triangle.html" class="sidebar-link">Pascal's Triangle</a></li><li><a href="/algorithm/algo-print-a-m-n-matrix-in-square-wise.html" class="sidebar-link">Algo:- Print a m*n matrix in square wise</a></li><li><a href="/algorithm/matrix-exponentiation.html" class="sidebar-link">Matrix Exponentiation</a></li><li><a href="/algorithm/polynomial-time-bounded-algorithm-for-minimum-vertex-cover.html" class="sidebar-link">polynomial-time bounded algorithm for Minimum Vertex Cover</a></li><li><a href="/algorithm/dynamic-time-warping.html" class="sidebar-link">Dynamic Time Warping</a></li><li><a href="/algorithm/fast-fourier-transform.html" class="sidebar-link">Fast Fourier Transform</a></li><li><a href="/algorithm/pseudocode.html" class="sidebar-link">Pseudocode</a></li><li><a href="/algorithm/contributors.html" class="sidebar-link">The Contributors</a></li></ul></section></li></ul> </aside> <main class="page"> <div class="theme-default-content content__default"><h1 id="binary-tree-traversals"><a href="#binary-tree-traversals" class="header-anchor">#</a> Binary Tree traversals</h1> <p>Visiting a node of a binary tree in some particular order is called traversals.</p> <h2 id="level-order-traversal-implementation"><a href="#level-order-traversal-implementation" class="header-anchor">#</a> Level Order traversal - Implementation</h2> <p>For example if the given tree is:</p> <p><a href="https://i.stack.imgur.com/7Kz71.png" target="_blank" rel="noopener noreferrer"><img src="https://i.stack.imgur.com/7Kz71.png" alt="enter image description here"><span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg> <span class="sr-only">(opens new window)</span></span></a></p> <p><strong>Level order traversal will be</strong></p> <p>1 2 3 4 5 6 7</p> <p>Printing node data level by level.</p> <p>Code:</p> <div class="language-cpp extra-class"><pre class="language-cpp"><code><span class="token macro property"><span class="token directive-hash">#</span><span class="token directive keyword">include</span><span class="token string"><iostream></span></span>
<span class="token macro property"><span class="token directive-hash">#</span><span class="token directive keyword">include</span><span class="token string"><queue></span></span>
<span class="token macro property"><span class="token directive-hash">#</span><span class="token directive keyword">include</span><span class="token string"><malloc.h></span></span>
<span class="token keyword">using</span> <span class="token keyword">namespace</span> std<span class="token punctuation">;</span>
<span class="token keyword">struct</span> <span class="token class-name">node</span><span class="token punctuation">{</span>
<span class="token keyword">int</span> data<span class="token punctuation">;</span>
node <span class="token operator">*</span>left<span class="token punctuation">;</span>
node <span class="token operator">*</span>right<span class="token punctuation">;</span>
<span class="token punctuation">}</span><span class="token punctuation">;</span>
<span class="token keyword">void</span> <span class="token function">levelOrder</span><span class="token punctuation">(</span><span class="token keyword">struct</span> <span class="token class-name">node</span> <span class="token operator">*</span>root<span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>root <span class="token operator">==</span> <span class="token constant">NULL</span><span class="token punctuation">)</span> <span class="token keyword">return</span><span class="token punctuation">;</span>
queue<span class="token operator"><</span>node <span class="token operator">*</span><span class="token operator">></span> Q<span class="token punctuation">;</span>
Q<span class="token punctuation">.</span><span class="token function">push</span><span class="token punctuation">(</span>root<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">while</span><span class="token punctuation">(</span><span class="token operator">!</span>Q<span class="token punctuation">.</span><span class="token function">empty</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">struct</span> <span class="token class-name">node</span><span class="token operator">*</span> curr <span class="token operator">=</span> Q<span class="token punctuation">.</span><span class="token function">front</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
cout<span class="token operator"><<</span> curr<span class="token operator">-></span>data <span class="token operator"><<</span><span class="token string">" "</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>curr<span class="token operator">-></span>left <span class="token operator">!=</span> <span class="token constant">NULL</span><span class="token punctuation">)</span> Q<span class="token punctuation">.</span><span class="token function">push</span><span class="token punctuation">(</span>curr<span class="token operator">-></span> left<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">if</span><span class="token punctuation">(</span>curr<span class="token operator">-></span>right <span class="token operator">!=</span> <span class="token constant">NULL</span><span class="token punctuation">)</span> Q<span class="token punctuation">.</span><span class="token function">push</span><span class="token punctuation">(</span>curr<span class="token operator">-></span> right<span class="token punctuation">)</span><span class="token punctuation">;</span>
Q<span class="token punctuation">.</span><span class="token function">pop</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token punctuation">}</span>
<span class="token keyword">struct</span> <span class="token class-name">node</span><span class="token operator">*</span> <span class="token function">newNode</span><span class="token punctuation">(</span><span class="token keyword">int</span> data<span class="token punctuation">)</span>
<span class="token punctuation">{</span>
<span class="token keyword">struct</span> <span class="token class-name">node</span><span class="token operator">*</span> node <span class="token operator">=</span> <span class="token punctuation">(</span><span class="token keyword">struct</span> <span class="token class-name">node</span><span class="token operator">*</span><span class="token punctuation">)</span>
<span class="token function">malloc</span><span class="token punctuation">(</span><span class="token keyword">sizeof</span><span class="token punctuation">(</span><span class="token keyword">struct</span> <span class="token class-name">node</span><span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
node<span class="token operator">-></span>data <span class="token operator">=</span> data<span class="token punctuation">;</span>
node<span class="token operator">-></span>left <span class="token operator">=</span> <span class="token constant">NULL</span><span class="token punctuation">;</span>
node<span class="token operator">-></span>right <span class="token operator">=</span> <span class="token constant">NULL</span><span class="token punctuation">;</span>
<span class="token keyword">return</span><span class="token punctuation">(</span>node<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span class="token keyword">int</span> <span class="token function">main</span><span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">{</span>
<span class="token keyword">struct</span> <span class="token class-name">node</span> <span class="token operator">*</span>root <span class="token operator">=</span> <span class="token function">newNode</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
root<span class="token operator">-></span>left <span class="token operator">=</span> <span class="token function">newNode</span><span class="token punctuation">(</span><span class="token number">2</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
root<span class="token operator">-></span>right <span class="token operator">=</span> <span class="token function">newNode</span><span class="token punctuation">(</span><span class="token number">3</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
root<span class="token operator">-></span>left<span class="token operator">-></span>left <span class="token operator">=</span> <span class="token function">newNode</span><span class="token punctuation">(</span><span class="token number">4</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
root<span class="token operator">-></span>left<span class="token operator">-></span>right <span class="token operator">=</span> <span class="token function">newNode</span><span class="token punctuation">(</span><span class="token number">5</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
root<span class="token operator">-></span>right<span class="token operator">-></span>left <span class="token operator">=</span> <span class="token function">newNode</span><span class="token punctuation">(</span><span class="token number">6</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
root<span class="token operator">-></span>right<span class="token operator">-></span>right <span class="token operator">=</span> <span class="token function">newNode</span><span class="token punctuation">(</span><span class="token number">7</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token function">printf</span><span class="token punctuation">(</span><span class="token string">"Level Order traversal of binary tree is \n"</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token function">levelOrder</span><span class="token punctuation">(</span>root<span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token keyword">return</span> <span class="token number">0</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
</code></pre></div><p>Queue data structure is used to achieve the above objective.</p> <h2 id="pre-order-inorder-and-post-order-traversal-of-a-binary-tree"><a href="#pre-order-inorder-and-post-order-traversal-of-a-binary-tree" class="header-anchor">#</a> Pre-order, Inorder and Post Order traversal of a Binary Tree</h2> <p>Consider the Binary Tree:</p> <p><a href="https://i.stack.imgur.com/4oxnI.png" target="_blank" rel="noopener noreferrer"><img src="https://i.stack.imgur.com/4oxnI.png" alt="enter image description here"><span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg> <span class="sr-only">(opens new window)</span></span></a></p> <p><strong>Pre-order traversal(root)</strong> is traversing the node then left sub-tree of the node and then the right sub-tree of the node.</p> <p>So the pre-order traversal of above tree will be:</p> <p>1 2 4 5 3 6 7</p> <p><strong>In-order traversal(root)</strong> is traversing the left sub-tree of the node then the node and then right sub-tree of the node.</p> <p>So the in-order traversal of above tree will be:</p> <p>4 2 5 1 6 3 7</p> <p><strong>Post-order traversal(root)</strong> is traversing the left sub-tree of the node then the right sub-tree and then the node.</p> <p>So the post-order traversal of above tree will be:</p> <p>4 5 2 6 7 3 1</p></div> <footer class="page-edit"><div class="edit-link"><a href="https://github.com/devtut/generate/edit/master/docs/algorithm/binary-tree-traversals.md" target="_blank" rel="noopener noreferrer">Edit this page on GitHub</a> <span><svg xmlns="http://www.w3.org/2000/svg" aria-hidden="true" focusable="false" x="0px" y="0px" viewBox="0 0 100 100" width="15" height="15" class="icon outbound"><path fill="currentColor" d="M18.8,85.1h56l0,0c2.2,0,4-1.8,4-4v-32h-8v28h-48v-48h28v-8h-32l0,0c-2.2,0-4,1.8-4,4v56C14.8,83.3,16.6,85.1,18.8,85.1z"></path> <polygon fill="currentColor" points="45.7,48.7 51.3,54.3 77.2,28.5 77.2,37.2 85.2,37.2 85.2,14.9 62.8,14.9 62.8,22.9 71.5,22.9"></polygon></svg> <span class="sr-only">(opens new window)</span></span></div> <!----></footer> <div class="page-nav"><p class="inner"><span class="prev">
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