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<title>Prim Algorithm</title>
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<li><a href="/dsa.html#data-structure-1" title="Data Structures (I)">Data Structures
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<li><a href="/dsa.html#data-structure-2" title="Data Structures (II)">Data Structures
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<h1>Prim's Algorithm</h1>
<p class="editor-contents__short-description">In this tutorial, you will learn how Prim's Algorithm works. Also, you will find working examples of Prim's Algorithm in C, C++, Java and Python.</p>
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<span property="dc:title" content="Prim's Algorithm" class="rdf-meta element-hidden"></span>
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<p id="introduction">Prim's algorithm is a <a href="/dsa/spanning-tree-and-minimum-spanning-tree#minimum-spanning.html">minimum spanning tree</a> algorithm that takes a graph as input and finds the subset of the edges of that graph which</p>
<ul><li>form a tree that includes every vertex</li>
<li>has the minimum sum of weights among all the trees that can be formed from the graph</li>
</ul><hr><h2 id="working">How Prim's algorithm works</h2>
<p>It falls under a class of algorithms called <a href="/dsa/greedy-algorithm.html">greedy algorithms</a> that find the local optimum in the hopes of finding a global optimum.</p>
<p>We start from one vertex and keep adding edges with the lowest weight until we reach our goal.</p>
<p>The steps for implementing Prim's algorithm are as follows:</p>
<ol><li>Initialize the minimum spanning tree with a vertex chosen at random.</li>
<li>Find all the edges that connect the tree to new vertices, find the minimum and add it to the tree</li>
<li>Keep repeating step 2 until we get a minimum spanning tree</li>
</ol><hr><h2 id="example">Example of Prim's algorithm</h2>
<figure><img alt="Start with a weighted graph" src="//cdn.programiz.com/sites/tutorial2program/files/pa_1.png" title="Prim's Algorithm Steps" width="730" height="308"><figcaption>Start with a weighted graph</figcaption></figure><figure><img alt="Choose a vertex" src="//cdn.programiz.com/sites/tutorial2program/files/pa_2.png" title="Prim's Algorithm Steps" width="730" height="172"><figcaption>Choose a vertex</figcaption></figure><figure><img alt="Choose the shortest edge from this vertex and add it" src="//cdn.programiz.com/sites/tutorial2program/files/pa_3.png" title="Prim's Algorithm Steps" width="730" height="240"><figcaption>Choose the shortest edge from this vertex and add it</figcaption></figure><figure><img alt="Choose the nearest vertex not yet in the solution" src="//cdn.programiz.com/sites/tutorial2program/files/pa_4.png" title="Prim's Algorithm Steps" width="730" height="240"><figcaption>Choose the nearest vertex not yet in the solution</figcaption></figure><figure><img alt="Choose the nearest edge not yet in the solution, if there are multiple choices, choose one at random" src="//cdn.programiz.com/sites/tutorial2program/files/pa_5.png" title="Prim's Algorithm Steps" width="730" height="238"><figcaption>Choose the nearest edge not yet in the solution, if there are multiple choices, choose one at random</figcaption></figure><figure><img alt="Repeat until you have a spanning tree" src="//cdn.programiz.com/sites/tutorial2program/files/pa_6.png" title="Prim's Algorithm Steps" width="730" height="306"><figcaption>Repeat until you have a spanning tree</figcaption></figure><hr><h2 id="pseudocode">Prim's Algorithm pseudocode</h2>
<p>The pseudocode for prim's algorithm shows how we create two sets of vertices U and V-U. U contains the list of vertices that have been visited and V-U the list of vertices that haven't. One by one, we move vertices from set V-U to set U by connecting the least weight edge.</p>
<pre style="max-height: 600px;"><code class="dsa hljs properties"><span class="hljs-attr">T</span> = <span class="hljs-string">∅;</span>
<span class="hljs-attr">U</span> = <span class="hljs-string">{ 1 };</span>
<span class="hljs-attr">while</span> <span class="hljs-string">(U ≠ V)</span>
<span class="hljs-attr">let</span> <span class="hljs-string">(u, v) be the lowest cost edge such that u ∈ U and v ∈ V - U;</span>
<span class="hljs-attr">T</span> = <span class="hljs-string">T ∪ {(u, v)}</span>
<span class="hljs-attr">U</span> = <span class="hljs-string">U ∪ {v}</span></code></pre>
<hr><h2 id="code">Python, Java and C/C++ Examples</h2>
<p></p><div class="clearfix"></div><p>Although <a href="/dsa/graph-adjacency-matrix.html">adjacency matrix</a> representation of graphs is used, this algorithm can also be implemented using <a href="/dsa/graph-adjacency-list.html">Adjacency List</a> to improve its efficiency.</p>
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<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="python hljs"><span class="hljs-comment"># Prim's Algorithm in Python</span>
INF = <span class="hljs-number">9999999</span>
<span class="hljs-comment"># number of vertices in graph</span>
V = <span class="hljs-number">5</span>
<span class="hljs-comment"># create a 2d array of size 5x5</span>
<span class="hljs-comment"># for adjacency matrix to represent graph</span>
G = [[<span class="hljs-number">0</span>, <span class="hljs-number">9</span>, <span class="hljs-number">75</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>],
[<span class="hljs-number">9</span>, <span class="hljs-number">0</span>, <span class="hljs-number">95</span>, <span class="hljs-number">19</span>, <span class="hljs-number">42</span>],
[<span class="hljs-number">75</span>, <span class="hljs-number">95</span>, <span class="hljs-number">0</span>, <span class="hljs-number">51</span>, <span class="hljs-number">66</span>],
[<span class="hljs-number">0</span>, <span class="hljs-number">19</span>, <span class="hljs-number">51</span>, <span class="hljs-number">0</span>, <span class="hljs-number">31</span>],
[<span class="hljs-number">0</span>, <span class="hljs-number">42</span>, <span class="hljs-number">66</span>, <span class="hljs-number">31</span>, <span class="hljs-number">0</span>]]
<span class="hljs-comment"># create a array to track selected vertex</span>
<span class="hljs-comment"># selected will become true otherwise false</span>
selected = [<span class="hljs-number">0</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>]
<span class="hljs-comment"># set number of edge to 0</span>
no_edge = <span class="hljs-number">0</span>
<span class="hljs-comment"># the number of egde in minimum spanning tree will be</span>
<span class="hljs-comment"># always less than(V - 1), where V is number of vertices in</span>
<span class="hljs-comment"># graph</span>
<span class="hljs-comment"># choose 0th vertex and make it true</span>
selected[<span class="hljs-number">0</span>] = <span class="hljs-literal">True</span>
<span class="hljs-comment"># print for edge and weight</span>
<span class="hljs-keyword">print</span>(<span class="hljs-string">"Edge : Weight\n"</span>)
<span class="hljs-keyword">while</span> (no_edge < V - <span class="hljs-number">1</span>):
<span class="hljs-comment"># For every vertex in the set S, find the all adjacent vertices</span>
<span class="hljs-comment">#, calculate the distance from the vertex selected at step 1.</span>
<span class="hljs-comment"># if the vertex is already in the set S, discard it otherwise</span>
<span class="hljs-comment"># choose another vertex nearest to selected vertex at step 1.</span>
minimum = INF
x = <span class="hljs-number">0</span>
y = <span class="hljs-number">0</span>
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> range(V):
<span class="hljs-keyword">if</span> selected[i]:
<span class="hljs-keyword">for</span> j <span class="hljs-keyword">in</span> range(V):
<span class="hljs-keyword">if</span> ((<span class="hljs-keyword">not</span> selected[j]) <span class="hljs-keyword">and</span> G[i][j]):
<span class="hljs-comment"># not in selected and there is an edge</span>
<span class="hljs-keyword">if</span> minimum > G[i][j]:
minimum = G[i][j]
x = i
y = j
<span class="hljs-keyword">print</span>(str(x) + <span class="hljs-string">"-"</span> + str(y) + <span class="hljs-string">":"</span> + str(G[x][y]))
selected[y] = <span class="hljs-literal">True</span>
no_edge += <span class="hljs-number">1</span></code></pre></div>
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<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="java hljs"><span class="hljs-comment">// Prim's Algorithm in Java</span>
<span class="hljs-keyword">import</span> java.util.Arrays;
<span class="hljs-class"><span class="hljs-keyword">class</span> <span class="hljs-title">PGraph</span> </span>{
<span class="hljs-function"><span class="hljs-keyword">public</span> <span class="hljs-keyword">void</span> <span class="hljs-title">Prim</span><span class="hljs-params">(<span class="hljs-keyword">int</span> G[][], <span class="hljs-keyword">int</span> V)</span> </span>{
<span class="hljs-keyword">int</span> INF = <span class="hljs-number">9999999</span>;
<span class="hljs-keyword">int</span> no_edge; <span class="hljs-comment">// number of edge</span>
<span class="hljs-comment">// create a array to track selected vertex</span>
<span class="hljs-comment">// selected will become true otherwise false</span>
<span class="hljs-keyword">boolean</span>[] selected = <span class="hljs-keyword">new</span> <span class="hljs-keyword">boolean</span>[V];
<span class="hljs-comment">// set selected false initially</span>
Arrays.fill(selected, <span class="hljs-keyword">false</span>);
<span class="hljs-comment">// set number of edge to 0</span>
no_edge = <span class="hljs-number">0</span>;
<span class="hljs-comment">// the number of egde in minimum spanning tree will be</span>
<span class="hljs-comment">// always less than (V -1), where V is number of vertices in</span>
<span class="hljs-comment">// graph</span>
<span class="hljs-comment">// choose 0th vertex and make it true</span>
selected[<span class="hljs-number">0</span>] = <span class="hljs-keyword">true</span>;
<span class="hljs-comment">// print for edge and weight</span>
System.out.println(<span class="hljs-string">"Edge : Weight"</span>);
<span class="hljs-keyword">while</span> (no_edge < V - <span class="hljs-number">1</span>) {
<span class="hljs-comment">// For every vertex in the set S, find the all adjacent vertices</span>
<span class="hljs-comment">// , calculate the distance from the vertex selected at step 1.</span>
<span class="hljs-comment">// if the vertex is already in the set S, discard it otherwise</span>
<span class="hljs-comment">// choose another vertex nearest to selected vertex at step 1.</span>
<span class="hljs-keyword">int</span> min = INF;
<span class="hljs-keyword">int</span> x = <span class="hljs-number">0</span>; <span class="hljs-comment">// row number</span>
<span class="hljs-keyword">int</span> y = <span class="hljs-number">0</span>; <span class="hljs-comment">// col number</span>
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < V; i++) {
<span class="hljs-keyword">if</span> (selected[i] == <span class="hljs-keyword">true</span>) {
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> j = <span class="hljs-number">0</span>; j < V; j++) {
<span class="hljs-comment">// not in selected and there is an edge</span>
<span class="hljs-keyword">if</span> (!selected[j] && G[i][j] != <span class="hljs-number">0</span>) {
<span class="hljs-keyword">if</span> (min > G[i][j]) {
min = G[i][j];
x = i;
y = j;
}
}
}
}
}
System.out.println(x + <span class="hljs-string">" - "</span> + y + <span class="hljs-string">" : "</span> + G[x][y]);
selected[y] = <span class="hljs-keyword">true</span>;
no_edge++;
}
}
<span class="hljs-function"><span class="hljs-keyword">public</span> <span class="hljs-keyword">static</span> <span class="hljs-keyword">void</span> <span class="hljs-title">main</span><span class="hljs-params">(String[] args)</span> </span>{
PGraph g = <span class="hljs-keyword">new</span> PGraph();
<span class="hljs-comment">// number of vertices in grapj</span>
<span class="hljs-keyword">int</span> V = <span class="hljs-number">5</span>;
<span class="hljs-comment">// create a 2d array of size 5x5</span>
<span class="hljs-comment">// for adjacency matrix to represent graph</span>
<span class="hljs-keyword">int</span>[][] G = { { <span class="hljs-number">0</span>, <span class="hljs-number">9</span>, <span class="hljs-number">75</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span> }, { <span class="hljs-number">9</span>, <span class="hljs-number">0</span>, <span class="hljs-number">95</span>, <span class="hljs-number">19</span>, <span class="hljs-number">42</span> }, { <span class="hljs-number">75</span>, <span class="hljs-number">95</span>, <span class="hljs-number">0</span>, <span class="hljs-number">51</span>, <span class="hljs-number">66</span> }, { <span class="hljs-number">0</span>, <span class="hljs-number">19</span>, <span class="hljs-number">51</span>, <span class="hljs-number">0</span>, <span class="hljs-number">31</span> },
{ <span class="hljs-number">0</span>, <span class="hljs-number">42</span>, <span class="hljs-number">66</span>, <span class="hljs-number">31</span>, <span class="hljs-number">0</span> } };
g.Prim(G, V);
}
}</code></pre></div>
</div>
<div class="code-editor__area" id="c-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="c hljs cpp"><span class="hljs-comment">// Prim's Algorithm in C</span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span><span class="hljs-meta-string"><stdio.h></span></span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span><span class="hljs-meta-string"><stdbool.h> </span></span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">define</span> INF 9999999</span>
<span class="hljs-comment">// number of vertices in graph</span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">define</span> V 5</span>
<span class="hljs-comment">// create a 2d array of size 5x5</span>
<span class="hljs-comment">//for adjacency matrix to represent graph</span>
<span class="hljs-keyword">int</span> G[V][V] = {
{<span class="hljs-number">0</span>, <span class="hljs-number">9</span>, <span class="hljs-number">75</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>},
{<span class="hljs-number">9</span>, <span class="hljs-number">0</span>, <span class="hljs-number">95</span>, <span class="hljs-number">19</span>, <span class="hljs-number">42</span>},
{<span class="hljs-number">75</span>, <span class="hljs-number">95</span>, <span class="hljs-number">0</span>, <span class="hljs-number">51</span>, <span class="hljs-number">66</span>},
{<span class="hljs-number">0</span>, <span class="hljs-number">19</span>, <span class="hljs-number">51</span>, <span class="hljs-number">0</span>, <span class="hljs-number">31</span>},
{<span class="hljs-number">0</span>, <span class="hljs-number">42</span>, <span class="hljs-number">66</span>, <span class="hljs-number">31</span>, <span class="hljs-number">0</span>}};
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">()</span> </span>{
<span class="hljs-keyword">int</span> no_edge; <span class="hljs-comment">// number of edge</span>
<span class="hljs-comment">// create a array to track selected vertex</span>
<span class="hljs-comment">// selected will become true otherwise false</span>
<span class="hljs-keyword">int</span> selected[V];
<span class="hljs-comment">// set selected false initially</span>
<span class="hljs-built_in">memset</span>(selected, <span class="hljs-literal">false</span>, <span class="hljs-keyword">sizeof</span>(selected));
<span class="hljs-comment">// set number of edge to 0</span>
no_edge = <span class="hljs-number">0</span>;
<span class="hljs-comment">// the number of egde in minimum spanning tree will be</span>
<span class="hljs-comment">// always less than (V -1), where V is number of vertices in</span>
<span class="hljs-comment">//graph</span>
<span class="hljs-comment">// choose 0th vertex and make it true</span>
selected[<span class="hljs-number">0</span>] = <span class="hljs-literal">true</span>;
<span class="hljs-keyword">int</span> x; <span class="hljs-comment">// row number</span>
<span class="hljs-keyword">int</span> y; <span class="hljs-comment">// col number</span>
<span class="hljs-comment">// print for edge and weight</span>
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"Edge : Weight\n"</span>);
<span class="hljs-keyword">while</span> (no_edge < V - <span class="hljs-number">1</span>) {
<span class="hljs-comment">//For every vertex in the set S, find the all adjacent vertices</span>
<span class="hljs-comment">// , calculate the distance from the vertex selected at step 1.</span>
<span class="hljs-comment">// if the vertex is already in the set S, discard it otherwise</span>
<span class="hljs-comment">//choose another vertex nearest to selected vertex at step 1.</span>
<span class="hljs-keyword">int</span> min = INF;
x = <span class="hljs-number">0</span>;
y = <span class="hljs-number">0</span>;
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < V; i++) {
<span class="hljs-keyword">if</span> (selected[i]) {
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> j = <span class="hljs-number">0</span>; j < V; j++) {
<span class="hljs-keyword">if</span> (!selected[j] && G[i][j]) { <span class="hljs-comment">// not in selected and there is an edge</span>
<span class="hljs-keyword">if</span> (min > G[i][j]) {
min = G[i][j];
x = i;
y = j;
}
}
}
}
}
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"%d - %d : %d\n"</span>, x, y, G[x][y]);
selected[y] = <span class="hljs-literal">true</span>;
no_edge++;
}
<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;
}</code></pre></div>
</div>
<div class="code-editor__area" id="cpp-code">
<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="cpp hljs"><span class="hljs-comment">// Prim's Algorithm in C++</span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><cstring></span></span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><iostream></span></span>
<span class="hljs-keyword">using</span> <span class="hljs-keyword">namespace</span> <span class="hljs-built_in">std</span>;
<span class="hljs-meta">#<span class="hljs-meta-keyword">define</span> INF 9999999</span>
<span class="hljs-comment">// number of vertices in grapj</span>
<span class="hljs-meta">#<span class="hljs-meta-keyword">define</span> V 5</span>
<span class="hljs-comment">// create a 2d array of size 5x5</span>
<span class="hljs-comment">//for adjacency matrix to represent graph</span>
<span class="hljs-keyword">int</span> G[V][V] = {
{<span class="hljs-number">0</span>, <span class="hljs-number">9</span>, <span class="hljs-number">75</span>, <span class="hljs-number">0</span>, <span class="hljs-number">0</span>},
{<span class="hljs-number">9</span>, <span class="hljs-number">0</span>, <span class="hljs-number">95</span>, <span class="hljs-number">19</span>, <span class="hljs-number">42</span>},
{<span class="hljs-number">75</span>, <span class="hljs-number">95</span>, <span class="hljs-number">0</span>, <span class="hljs-number">51</span>, <span class="hljs-number">66</span>},
{<span class="hljs-number">0</span>, <span class="hljs-number">19</span>, <span class="hljs-number">51</span>, <span class="hljs-number">0</span>, <span class="hljs-number">31</span>},
{<span class="hljs-number">0</span>, <span class="hljs-number">42</span>, <span class="hljs-number">66</span>, <span class="hljs-number">31</span>, <span class="hljs-number">0</span>}};
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">()</span> </span>{
<span class="hljs-keyword">int</span> no_edge; <span class="hljs-comment">// number of edge</span>
<span class="hljs-comment">// create a array to track selected vertex</span>
<span class="hljs-comment">// selected will become true otherwise false</span>
<span class="hljs-keyword">int</span> selected[V];
<span class="hljs-comment">// set selected false initially</span>
<span class="hljs-built_in">memset</span>(selected, <span class="hljs-literal">false</span>, <span class="hljs-keyword">sizeof</span>(selected));
<span class="hljs-comment">// set number of edge to 0</span>
no_edge = <span class="hljs-number">0</span>;
<span class="hljs-comment">// the number of egde in minimum spanning tree will be</span>
<span class="hljs-comment">// always less than (V -1), where V is number of vertices in</span>
<span class="hljs-comment">//graph</span>
<span class="hljs-comment">// choose 0th vertex and make it true</span>
selected[<span class="hljs-number">0</span>] = <span class="hljs-literal">true</span>;
<span class="hljs-keyword">int</span> x; <span class="hljs-comment">// row number</span>
<span class="hljs-keyword">int</span> y; <span class="hljs-comment">// col number</span>
<span class="hljs-comment">// print for edge and weight</span>
<span class="hljs-built_in">cout</span> << <span class="hljs-string">"Edge"</span>
<< <span class="hljs-string">" : "</span>
<< <span class="hljs-string">"Weight"</span>;
<span class="hljs-built_in">cout</span> << <span class="hljs-built_in">endl</span>;
<span class="hljs-keyword">while</span> (no_edge < V - <span class="hljs-number">1</span>) {
<span class="hljs-comment">//For every vertex in the set S, find the all adjacent vertices</span>
<span class="hljs-comment">// , calculate the distance from the vertex selected at step 1.</span>
<span class="hljs-comment">// if the vertex is already in the set S, discard it otherwise</span>
<span class="hljs-comment">//choose another vertex nearest to selected vertex at step 1.</span>
<span class="hljs-keyword">int</span> min = INF;
x = <span class="hljs-number">0</span>;
y = <span class="hljs-number">0</span>;
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i = <span class="hljs-number">0</span>; i < V; i++) {
<span class="hljs-keyword">if</span> (selected[i]) {
<span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> j = <span class="hljs-number">0</span>; j < V; j++) {
<span class="hljs-keyword">if</span> (!selected[j] && G[i][j]) { <span class="hljs-comment">// not in selected and there is an edge</span>
<span class="hljs-keyword">if</span> (min > G[i][j]) {
min = G[i][j];
x = i;
y = j;
}
}
}
}
}
<span class="hljs-built_in">cout</span> << x << <span class="hljs-string">" - "</span> << y << <span class="hljs-string">" : "</span> << G[x][y];
<span class="hljs-built_in">cout</span> << <span class="hljs-built_in">endl</span>;
selected[y] = <span class="hljs-literal">true</span>;
no_edge++;
}
<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;
}</code></pre></div>
</div>
</div>
<hr><h2 id="vs">Prim's vs Kruskal's Algorithm</h2>
<p><a href="/dsa/kruskal-algorithm">Kruskal's algorithm</a> is another popular minimum spanning tree algorithm that uses a different logic to find the MST of a graph. Instead of starting from a vertex, Kruskal's algorithm sorts all the edges from low weight to high and keeps adding the lowest edges, ignoring those edges that create a cycle.</p>
<hr><h2 id="complexity">Prim's Algorithm Complexity</h2>
<p>The time complexity of Prim's algorithm is <code>O(E log V)</code>.</p>
<hr><h2 id="application">Prim's Algorithm Application</h2>
<ul><li>Laying cables of electrical wiring</li>
<li>In network designed</li>
<li>To make protocols in network cycles</li>
</ul></div>
</div>
<div class="tutorial-toc"><div class="tutorial-toc__inner"><h3 class="tutorial-toc__title">Table of Contents
<button class="btn btn--clear align-items-center">
<svg class="programiz-icon"><use xlink:href="/sites/all/themes/programiz/assets/feather-sprite.svg#x"></use></svg></button></h3><div class="tutorial-toc__links"><ul><li><a href="#introduction">Introduction</a></li>
<li><a href="#working">How Prim's algorithm works</a></li>
<li><a href="#example">Example of Prim's algorithm</a></li>
<li><a href="#pseudocode">Prim's Algorithm pseudocode</a></li>
<li><a href="#code">Python, Java and C/C++ Examples</a></li>
<li><a href="#vs">Prim's vs Kruskal's Algorithm</a></li>
<li><a href="#complexity">Prim's Algorithm Complexity</a></li>
<li><a href="#application">Prim's Algorithm Application</a></li>
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