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We can use the ValueGraph data structure in Google Guava to represent an edge-weighted graph. Finally, the edge (2, 4) satisfies our condition, and we can include it for the minimum spanning tree. Therefore, we discard this edge and continue to check the next one. When we check the next edge (1, 2), we can see that both nodes of this edge are in the same set. We can repeat the above steps until we construct the whole spanning tree.įor example, in the above minimum spanning tree construction, we first have 5 node sets. Otherwise, we merge the two disjoint sets into one set and include the edge for the spanning tree. If the answer is yes, then it will create a cycle. Then, each time we introduce an edge, we check whether its two nodes are in the same set. Cycle Detection with a Disjoint Setįirstly, we treat each node of the graph as an individual set that contains only one node. The following figure shows the step-by-step construction of a maximum spanning tree on our sample graph. To calculate the maximum spanning tree, we can change the sorting order to descending order. Finally, the algorithm finishes by adding the edge (2, 4) of weight 10. Therefore, we discard this edge and continue to choose the next smallest one. However, if we include this edge, we'll produce a cycle (0, 1, 2).
Now the next candidate is edge (1, 2) with weight 9. Then, we can add edges (3, 4) and (0, 1) as they do not create any cycles.
Let's run Kruskal’s algorithm for a minimum spanning tree on our sample graph step-by-step:įirstly, we choose the edge (0, 2) because it has the smallest weight. How to make a matrix in Excel Check this guide for making matrix in Excel and even easier way.
If the edge doesn't introduce any cycles, add it into T. Sort all graph edges by the ascending order of their weight values.Ĭheck whether it will create a cycle with the edges inside T.