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Adding back Graph and Heap sections #110

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Expand Up @@ -303,4 +303,164 @@ <h2 id="sorting">Array Sorting Algorithms</h2>
<td><code class="yellow">O(n)</code></td>
</tr>

<table class="table table-bordered table-striped">
<tr>
<th>Data Structure</th>
<th colspan="7">Time Complexity</th>
</tr>
<tr>
<th></th>
<th>Storage</th>
<th>Add Vertex</th>
<th>Add Edge</th>
<th>Remove Vertex</th>
<th>Remove Edge</th>
<th>Query</th>
</tr>
<h2 id="graph-operations">Graph Data Structure Operations</h2>
<tr>
<td><a href="http://en.wikipedia.org/wiki/Adjacency_list">Adjacency list</a></td>
<td><code class="yellow">O(|V|+|E|)</code></td>
<td><code class="green">O(1)</code></td>
<td><code class="green">O(1)</code></td>
<td><code class="yellow">O(|V| + |E|)</code></td>
<td><code class="yellow">O(|E|)</code></td>
<td><code class="yellow">O(|V|)</code></td>
</tr>
<tr>
<td><a href="http://en.wikipedia.org/wiki/Incidence_list">Incidence list</a></td>
<td><code class="yellow">O(|V|+|E|)</code></td>
<td><code class="green">O(1)</code></td>
<td><code class="green">O(1)</code></td>
<td><code class="yellow">O(|E|)</code></td>
<td><code class="yellow">O(|E|)</code></td>
<td><code class="yellow">O(|E|)</code></td>
</tr>
<tr>
<td><a href="http://en.wikipedia.org/wiki/Adjacency_matrix">Adjacency matrix</a></td>
<td><code class="red">O(|V|^2)</code></td>
<td><code class="red">O(|V|^2)</code></td>
<td><code class="green">O(1)</code></td>
<td><code class="red">O(|V|^2)</code></td>
<td><code class="green">O(1)</code></td>
<td><code class="green">O(1)</code></td>
</tr>
<tr>
<td><a href="http://en.wikipedia.org/wiki/Incidence_matrix">Incidence matrix</a></td>
<td><code class="red">O(|V| &sdot; |E|)</code></td>
<td><code class="red">O(|V| &sdot; |E|)</code></td>
<td><code class="red">O(|V| &sdot; |E|)</code></td>
<td><code class="red">O(|V| &sdot; |E|)</code></td>
<td><code class="red">O(|V| &sdot; |E|)</code></td>
<td><code class="yellow">O(|E|)</code></td>
</tr>
</table>

<h2 id="heaps">Heap Data Structure Operations</h2>
<table class="table table-bordered table-striped">
<tr>
<th>Data Structure</th>
<th colspan="7">Time Complexity</th>
</tr>
<tr>
<th></th>
<th>Find Max</th>
<th>Extract Max</th>
<th>Increase Key</th>
<th>Insert</th>
<th>Delete</th>
<th>Merge</th>
</tr>

<tr>
<td><a href="http://en.wikipedia.org/wiki/Binary_heap">Binary Heap</a></td>
<td><code class="green">O(1)</code></td>
<td><code class="yellow-green">O(log(n))</code></td>
<td><code class="yellow-green">O(log(n))</code></td>
<td><code class="yellow-green">O(log(n))</code></td>
<td><code class="yellow-green">O(log(n))</code></td>
<td><code class="yellow">O(m+n)</code></td>
</tr>
<tr>
<td><a href="http://en.wikipedia.org/wiki/Pairing_heap">Pairing Heap</a></td>
<td><code class="green">O(1)</code></td> <!-- find max -->
<td><code rel="tooltip" title="Amortized" class="yellow-green">O(log(n))</code></td> <!-- extract max -->
<td><code rel="tooltip" title="Amortized; tight bound not precisely known. See Wikipedia-article." class="yellow-green">O(log(n))</code></td> <!-- increase key -->
<td><code class="green">O(1)</code></td> <!-- insert -->
<td><code rel="tooltip" title="Amortized; increase key to infinity followed by extract max." class="yellow-green">O(log(n))</code></td> <!-- delete -->
<td><code class="green">O(1)</code></td> <!-- merge -->
</tr>
<tr>
<td><a href="http://en.wikipedia.org/wiki/Binomial_heap">Binomial Heap</a></td>
<td><code rel="tooltip" title="With aux pointer" class="green">O(1)</code></td>
<td><code class="yellow-green">O(log(n))</code></td>
<td><code class="yellow-green">O(log(n))</code></td>
<td><code rel="tooltip" title="Amortized" class="green">O(1)</code></td>
<td><code class="yellow-green">O(log(n))</code></td>
<td><code class="yellow-green">O(log(n))</code></td>
</tr>
<tr>
<td><a href="http://en.wikipedia.org/wiki/Fibonacci_heap">Fibonacci Heap</a></td>
<td><code class="green">O(1)</code></td>
<td><code rel="tooltip" title="Amortized" class="yellow-green">O(log(n))</code></td>
<td><code rel="tooltip" title="Amortized" class="green">O(1)</code></td>
<td><code class="green">O(1)</code></td>
<td><code rel="tooltip" title="Amortized" class="yellow-green">O(log(n))</code></td>
<td><code class="green">O(1)</code></td>
</tr>

</table>

<h2 id="graph-algorithms">Graph Algorithms</h2>
<table class="table table-bordered table-striped">

<tr>
<th>Algorithm</th>
<th colspan="2">Time Complexity</th>
<th>Space Complexity</th>
</tr>
<tr>
<th></th>
<th>Average</th>
<th>Worst</th>
<th>Worst</th>
</tr>

<tr>
<td><a href="https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm">Dijkstra's algorithm</a></td>
<td><code class="orange">O(|E| log |V|)</code></td>
<td><code class="red">O(|V|^2)</code></td>
<td><code class="yellow">O(|V| + |E|)</code></td>
</tr>
<tr>
<td><a href="https://en.wikipedia.org/wiki/A*_search_algorithm">A* search algorithm</a></td>
<td><code class="yellow">O(|E|)</code></td>
<td><code class="red">O(b^d)</code></td>
<td><code class="red">O(b^d)</code></td>
</tr>
<tr>
<td><a href="https://en.wikipedia.org/wiki/Prim%27s_algorithm">Prim's algorithm</a></td>
<td><code class="orange">O(|E| log |V|)</code></td>
<td><code class="red">O(|V|^2)</code></td>
<td><code class="yellow">O(|V| + |E|)</code></td>
</tr>
<tr>
<td><a href="https://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm">Bellman–Ford algorithm</a></td>
<td><code class="red">O(|E| &sdot; |V|)</code></td>
<td><code class="red">O(|E| &sdot; |V|)</code></td>
<td><code class="yellow">O(|V|)</code></td>
</tr>
<tr>
<td><a href="https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm">Floyd-Warshall algorithm</a></td>
<td><code class="red">O(|V|^3)</code></td>
<td><code class="red">O(|V|^3)</code></td>
<td><code class="red">O(|V|^2)</code></td>
</tr>
<tr>
<td><a href="https://en.wikipedia.org/wiki/Topological_sorting">Topological sort</a></td>
<td><code class="yellow">O(|V| + |E|)</code></td>
<td><code class="yellow">O(|V| + |E|)</code></td>
<td><code class="yellow">O(|V| + |E|)</code></td>
</tr>

</table>