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added kruskal #104

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62 changes: 62 additions & 0 deletions Javascript/graph/kruskal.js
Original file line number Diff line number Diff line change
@@ -0,0 +1,62 @@
import Graph from '../../../data-structures/graph/Graph';
import QuickSort from '../../sorting/quick-sort/QuickSort';
import DisjointSet from '../../../data-structures/disjoint-set/DisjointSet';

/**
* @param {Graph} graph
* @return {Graph}
*/
export default function kruskal(graph) {
// It should fire error if graph is directed since the algorithm works only
// for undirected graphs.
if (graph.isDirected) {
throw new Error('Kruskal\'s algorithms works only for undirected graphs');
}

// Init new graph that will contain minimum spanning tree of original graph.
const minimumSpanningTree = new Graph();

// Sort all graph edges in increasing order.
const sortingCallbacks = {
/**
* @param {GraphEdge} graphEdgeA
* @param {GraphEdge} graphEdgeB
*/
compareCallback: (graphEdgeA, graphEdgeB) => {
if (graphEdgeA.weight === graphEdgeB.weight) {
return 1;
}

return graphEdgeA.weight <= graphEdgeB.weight ? -1 : 1;
},
};
const sortedEdges = new QuickSort(sortingCallbacks).sort(graph.getAllEdges());

// Create disjoint sets for all graph vertices.
const keyCallback = (graphVertex) => graphVertex.getKey();
const disjointSet = new DisjointSet(keyCallback);

graph.getAllVertices().forEach((graphVertex) => {
disjointSet.makeSet(graphVertex);
});

// Go through all edges started from the minimum one and try to add them
// to minimum spanning tree. The criteria of adding the edge would be whether
// it is forms the cycle or not (if it connects two vertices from one disjoint
// set or not).
for (let edgeIndex = 0; edgeIndex < sortedEdges.length; edgeIndex += 1) {
/** @var {GraphEdge} currentEdge */
const currentEdge = sortedEdges[edgeIndex];

// Check if edge forms the cycle. If it does then skip it.
if (!disjointSet.inSameSet(currentEdge.startVertex, currentEdge.endVertex)) {
// Unite two subsets into one.
disjointSet.union(currentEdge.startVertex, currentEdge.endVertex);

// Add this edge to spanning tree.
minimumSpanningTree.addEdge(currentEdge);
}
}

return minimumSpanningTree;
}