There are two different sources for specifying an input graph: Draw Graph: You can draw any connected undirected weighted graph as the input graph. Example Graphs: You can select from the list of example connected undirected weighted graphs to get you started. Discussion: Is this the only possible sort criteria? Drop an email to visualgo. Go through this animated example first before continuing.
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Given a connected and undirected graph, a spanning tree of that graph is a subgraph that is a tree and connects all the vertices together. A single graph can have many different spanning trees.
A minimum spanning tree MST or minimum weight spanning tree for a weighted, connected and undirected graph is a spanning tree with weight less than or equal to the weight of every other spanning tree. The weight of a spanning tree is the sum of weights given to each edge of the spanning tree. How many edges does a minimum spanning tree has? A minimum spanning tree has V — 1 edges where V is the number of vertices in the given graph.
What are the applications of Minimum Spanning Tree? See this for applications of MST. Sort all the edges in non-decreasing order of their weight. Pick the smallest edge. Check if it forms a cycle with the spanning tree formed so far. If cycle is not formed, include this edge. Else, discard it. Repeat step 2 until there are V-1 edges in the spanning tree. The step 2 uses Union-Find algorithm to detect cycle.
So we recommend to read following post as a prerequisite. The Greedy Choice is to pick the smallest weight edge that does not cause a cycle in the MST constructed so far. Let us understand it with an example: Consider the below input graph.
The graph contains 9 vertices and 14 edges. Pick edge No cycle is formed, include it. Pick edge Since including this edge results in cycle, discard it. Since the number of edges included equals V — 1 , the algorithm stops here.
Algoritmo de Kruskal
We can achieve this bound as follows: first sort the edges by weight using a comparison sort in O E log E time; this allows the step "remove an edge with minimum weight from S" to operate in constant time. Next, we use a disjoint-set data structure to keep track of which vertices are in which components. Even a simple disjoint-set data structure such as disjoint-set forests with union by rank can perform O V operations in O V log V time. CE is now the shortest edge that does not form a cycle, with length 5, so it is highlighted as the second edge. The next edge, DF with length 6, is highlighted using much the same method.
13. Algorithmes sur les graphes
Kruskal’s Minimum Spanning Tree Algorithm | Greedy Algo-2