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| 1 | +class DisjointSetTreeNode { |
| 2 | + // Disjoint Set Node to store the parent and rank |
| 3 | + constructor (key) { |
| 4 | + this.key = key |
| 5 | + this.parent = this |
| 6 | + this.rank = 0 |
| 7 | + } |
| 8 | +} |
| 9 | + |
| 10 | +class DisjointSetTree { |
| 11 | + // Disjoint Set DataStructure |
| 12 | + constructor () { |
| 13 | + // map to from node name to the node object |
| 14 | + this.map = {} |
| 15 | + } |
| 16 | + |
| 17 | + makeSet (x) { |
| 18 | + // Function to create a new set with x as its member |
| 19 | + this.map[x] = new DisjointSetTreeNode(x) |
| 20 | + } |
| 21 | + |
| 22 | + findSet (x) { |
| 23 | + // Function to find the set x belongs to (with path-compression) |
| 24 | + if (this.map[x] !== this.map[x].parent) { |
| 25 | + this.map[x].parent = this.findSet(this.map[x].parent.key) |
| 26 | + } |
| 27 | + return this.map[x].parent |
| 28 | + } |
| 29 | + |
| 30 | + union (x, y) { |
| 31 | + // Function to merge 2 disjoint sets |
| 32 | + this.link(this.findSet(x), this.findSet(y)) |
| 33 | + } |
| 34 | + |
| 35 | + link (x, y) { |
| 36 | + // Helper function for union operation |
| 37 | + if (x.rank > y.rank) { |
| 38 | + y.parent = x |
| 39 | + } else { |
| 40 | + x.parent = y |
| 41 | + if (x.rank === y.rank) { |
| 42 | + y.rank += 1 |
| 43 | + } |
| 44 | + } |
| 45 | + } |
| 46 | +} |
| 47 | + |
| 48 | +class GraphWeightedUndirectedAdjacencyList { |
| 49 | + // Weighted Undirected Graph class |
| 50 | + constructor () { |
| 51 | + this.connections = {} |
| 52 | + this.nodes = 0 |
| 53 | + } |
| 54 | + |
| 55 | + addNode (node) { |
| 56 | + // Function to add a node to the graph (connection represented by set) |
| 57 | + this.connections[node] = {} |
| 58 | + this.nodes += 1 |
| 59 | + } |
| 60 | + |
| 61 | + addEdge (node1, node2, weight) { |
| 62 | + // Function to add an edge (adds the node too if they are not present in the graph) |
| 63 | + if (!(node1 in this.connections)) { this.addNode(node1) } |
| 64 | + if (!(node2 in this.connections)) { this.addNode(node2) } |
| 65 | + this.connections[node1][node2] = weight |
| 66 | + this.connections[node2][node1] = weight |
| 67 | + } |
| 68 | + |
| 69 | + KruskalMST () { |
| 70 | + // Kruskal's Algorithm to generate a Minimum Spanning Tree (MST) of a graph |
| 71 | + // Details: https://en.wikipedia.org/wiki/Kruskal%27s_algorithm |
| 72 | + // getting the edges in ascending order of weights |
| 73 | + const edges = [] |
| 74 | + const seen = new Set() |
| 75 | + for (const start of Object.keys(this.connections)) { |
| 76 | + for (const end of Object.keys(this.connections[start])) { |
| 77 | + if (!seen.has(`${start} ${end}`)) { |
| 78 | + seen.add(`${end} ${start}`) |
| 79 | + edges.push([start, end, this.connections[start][end]]) |
| 80 | + } |
| 81 | + } |
| 82 | + } |
| 83 | + edges.sort((a, b) => a[2] - b[2]) |
| 84 | + // creating the disjoint set |
| 85 | + const disjointSet = new DisjointSetTree() |
| 86 | + Object.keys(this.connections).forEach(node => disjointSet.makeSet(node)) |
| 87 | + // MST generation |
| 88 | + const graph = new GraphWeightedUndirectedAdjacencyList() |
| 89 | + let numEdges = 0 |
| 90 | + let index = 0 |
| 91 | + while (numEdges < this.nodes - 1) { |
| 92 | + const [u, v, w] = edges[index] |
| 93 | + index += 1 |
| 94 | + if (disjointSet.findSet(u) !== disjointSet.findSet(v)) { |
| 95 | + numEdges += 1 |
| 96 | + graph.addEdge(u, v, w) |
| 97 | + disjointSet.union(u, v) |
| 98 | + } |
| 99 | + } |
| 100 | + return graph |
| 101 | + } |
| 102 | +} |
| 103 | + |
| 104 | +function main () { |
| 105 | + const graph = new GraphWeightedUndirectedAdjacencyList() |
| 106 | + graph.addEdge(1, 2, 1) |
| 107 | + graph.addEdge(2, 3, 2) |
| 108 | + graph.addEdge(3, 4, 1) |
| 109 | + graph.addEdge(3, 5, 100) // Removed in MST |
| 110 | + graph.addEdge(4, 5, 5) |
| 111 | + console.log(graph) |
| 112 | + console.log(graph.KruskalMST()) |
| 113 | +} |
| 114 | + |
| 115 | +main() |
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