Add Prim.

Author: trekhleb

README.md

@@ -69,7 +69,7 @@
   * [Dijkstra Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/dijkstra) - finding shortest path to all graph vertices
   * [Bellman-Ford Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/bellman-ford) - finding shortest path to all graph vertices
   * [Detect Cycle](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/detect-cycle) - for both directed and undirected graphs (DFS and Disjoint Set based versions)
-  * [Prim’s Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST)
+  * [Prim’s Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST) for weighted undirected graph
   * Kruskal’s Algorithm - finding Minimum Spanning Tree (MST)
   * Topological Sorting
   * Eulerian path, Eulerian circuit

src/algorithms/graph/prim/README.md

@@ -44,3 +44,4 @@ are two possibilities of minimum spanning tree of the given graph.
 - [Minimum Spanning Tree on Wikipedia](https://en.wikipedia.org/wiki/Minimum_spanning_tree)
 - [Prim's Algorithm on Wikipedia](https://en.wikipedia.org/wiki/Prim%27s_algorithm)
 - [Prim's Algorithm on YouTube by Tushar Roy](https://www.youtube.com/watch?v=oP2-8ysT3QQ)
+- [Prim's Algorithm on YouTube by Michael Sambol](https://www.youtube.com/watch?v=cplfcGZmX7I)

src/algorithms/graph/prim/__test__/prim.test.js

@@ -0,0 +1,91 @@
+import GraphVertex from '../../../../data-structures/graph/GraphVertex';
+import GraphEdge from '../../../../data-structures/graph/GraphEdge';
+import Graph from '../../../../data-structures/graph/Graph';
+import prim from '../prim';
+
+describe('prim', () => {
+  it('should fire an error for directed graph', () => {
+    function applyPrimToDirectedGraph() {
+      const graph = new Graph(true);
+
+      prim(graph);
+    }
+
+    expect(applyPrimToDirectedGraph).toThrowError();
+  });
+
+  it('should find minimum spanning tree', () => {
+    const vertexA = new GraphVertex('A');
+    const vertexB = new GraphVertex('B');
+    const vertexC = new GraphVertex('C');
+    const vertexD = new GraphVertex('D');
+    const vertexE = new GraphVertex('E');
+    const vertexF = new GraphVertex('F');
+    const vertexG = new GraphVertex('G');
+
+    const edgeAB = new GraphEdge(vertexA, vertexB, 2);
+    const edgeAD = new GraphEdge(vertexA, vertexD, 3);
+    const edgeAC = new GraphEdge(vertexA, vertexC, 3);
+    const edgeBC = new GraphEdge(vertexB, vertexC, 4);
+    const edgeBE = new GraphEdge(vertexB, vertexE, 3);
+    const edgeDF = new GraphEdge(vertexD, vertexF, 7);
+    const edgeEC = new GraphEdge(vertexE, vertexC, 1);
+    const edgeEF = new GraphEdge(vertexE, vertexF, 8);
+    const edgeFG = new GraphEdge(vertexF, vertexG, 9);
+    const edgeFC = new GraphEdge(vertexF, vertexC, 6);
+
+    const graph = new Graph();
+
+    graph
+      .addEdge(edgeAB)
+      .addEdge(edgeAD)
+      .addEdge(edgeAC)
+      .addEdge(edgeBC)
+      .addEdge(edgeBE)
+      .addEdge(edgeDF)
+      .addEdge(edgeEC)
+      .addEdge(edgeEF)
+      .addEdge(edgeFC)
+      .addEdge(edgeFG);
+
+    expect(graph.getWeight()).toEqual(46);
+
+    const minimumSpanningTree = prim(graph);
+
+    expect(minimumSpanningTree.getWeight()).toBe(24);
+    expect(minimumSpanningTree.getAllVertices().length).toBe(graph.getAllVertices().length);
+    expect(minimumSpanningTree.getAllEdges().length).toBe(graph.getAllVertices().length - 1);
+    expect(minimumSpanningTree.toString()).toBe('A,B,D,C,E,F,G');
+  });
+
+  it('should find minimum spanning tree for simple graph', () => {
+    const vertexA = new GraphVertex('A');
+    const vertexB = new GraphVertex('B');
+    const vertexC = new GraphVertex('C');
+    const vertexD = new GraphVertex('D');
+
+    const edgeAB = new GraphEdge(vertexA, vertexB, 1);
+    const edgeAD = new GraphEdge(vertexA, vertexD, 3);
+    const edgeBC = new GraphEdge(vertexB, vertexC, 1);
+    const edgeBD = new GraphEdge(vertexB, vertexD, 3);
+    const edgeCD = new GraphEdge(vertexC, vertexD, 1);
+
+    const graph = new Graph();
+
+    graph
+      .addEdge(edgeAB)
+      .addEdge(edgeAD)
+      .addEdge(edgeBC)
+      .addEdge(edgeBD)
+      .addEdge(edgeCD);
+
+    expect(graph.getWeight()).toEqual(9);
+
+    const minimumSpanningTree = prim(graph);
+
+    expect(minimumSpanningTree.getWeight()).toBe(3);
+    expect(minimumSpanningTree.getAllVertices().length).toBe(graph.getAllVertices().length);
+    expect(minimumSpanningTree.getAllEdges().length).toBe(graph.getAllVertices().length - 1);
+    expect(minimumSpanningTree.toString()).toBe('A,B,C,D');
+  });
+});

src/algorithms/graph/prim/prim.js

@@ -0,0 +1,73 @@
+import Graph from '../../../data-structures/graph/Graph';
+import PriorityQueue from '../../../data-structures/priority-queue/PriorityQueue';
+
+/**
+ * @param {Graph} graph
+ * @return {Graph}
+ */
+export default function prim(graph) {
+  // It should fire error if graph is directed since the algorithm works only
+  // for undirected graphs.
+  if (graph.isDirected) {
+    throw new Error('Prim\'s algorithms works only for undirected graphs');
+  }
+
+  // Init new graph that will contain minimum spanning tree of original graph.
+  const minimumSpanningTree = new Graph();
+
+  // This priority queue will contain all the edges that are starting from
+  // visited nodes and they will be ranked by edge weight - so that on each step
+  // we would always pick the edge with minimal edge weight.
+  const edgesQueue = new PriorityQueue();
+
+  // Set of vertices that has been already visited.
+  const visitedVertices = {};
+
+  // Vertex from which we will start graph traversal.
+  const startVertex = graph.getAllVertices()[0];
+
+  // Add start vertex to the set of visited ones.
+  visitedVertices[startVertex.getKey()] = startVertex;
+
+  // Add all edges of start vertex to the queue.
+  startVertex.getEdges().forEach((graphEdge) => {
+    edgesQueue.add(graphEdge, graphEdge.weight);
+  });
+
+  // Now let's explore all queued edges.
+  while (!edgesQueue.isEmpty()) {
+    // Fetch next queued edge with minimal weight.
+    /** @var {GraphEdge} currentEdge */
+    const currentMinEdge = edgesQueue.poll();
+
+    // Find out the next unvisited minimal vertex to traverse.
+    let nextMinVertex = null;
+    if (!visitedVertices[currentMinEdge.startVertex.getKey()]) {
+      nextMinVertex = currentMinEdge.startVertex;
+    } else if (!visitedVertices[currentMinEdge.endVertex.getKey()]) {
+      nextMinVertex = currentMinEdge.endVertex;
+    }
+
+    // If all vertices of current edge has been already visited then skip this round.
+    if (nextMinVertex) {
+      // Add current min edge to MST.
+      minimumSpanningTree.addEdge(currentMinEdge);
+
+      // Add vertex to the set of visited ones.
+      visitedVertices[nextMinVertex.getKey()] = nextMinVertex;
+
+      // Add all current vertex's edges to the queue.
+      nextMinVertex.getEdges().forEach((graphEdge) => {
+        // Add only vertices that link to unvisited nodes.
+        if (
+          !visitedVertices[graphEdge.startVertex.getKey()] ||
+          !visitedVertices[graphEdge.endVertex.getKey()]
+        ) {
+          edgesQueue.add(graphEdge, graphEdge.weight);
+        }
+      });
+    }
+  }
+
+  return minimumSpanningTree;
+}

src/data-structures/graph/Graph.js

@@ -110,12 +110,18 @@ export default class Graph {
     return null;
   }
 
+  /**
+   * @return {number}
+   */
   getWeight() {
     return this.getAllEdges().reduce((weight, graphEdge) => {
       return weight + graphEdge.weight;
     }, 0);
   }
 
+  /**
+   * @return {string}
+   */
   toString() {
     return Object.keys(this.vertices).toString();
   }

src/data-structures/graph/GraphEdge.js

@@ -19,4 +19,11 @@ export default class GraphEdge {
 
     return `${startVertexKey}_${endVertexKey}`;
   }
+
+  /**
+   * @return {string}
+   */
+  toString() {
+    return this.getKey();
+  }
 }

src/data-structures/graph/GraphVertex.js

@@ -1,6 +1,9 @@
 import LinkedList from '../linked-list/LinkedList';
 
 export default class GraphVertex {
+  /**
+   * @param {*} value
+   */
   constructor(value) {
     if (value === undefined) {
       throw new Error('Graph vertex must have a value');
@@ -37,6 +40,13 @@ export default class GraphVertex {
     return edges.map(neighborsConverter);
   }
 
+  /**
+   * @return {GraphEdge[]}
+   */
+  getEdges() {
+    return this.edges.toArray().map(linkedListNode => linkedListNode.value);
+  }
+
   /**
    * @param {GraphEdge} requiredEdge
    * @returns {boolean}

src/data-structures/graph/__test__/GraphEdge.test.js

@@ -8,6 +8,7 @@ describe('GraphEdge', () => {
     const edge = new GraphEdge(startVertex, endVertex);
 
     expect(edge.getKey()).toBe('A_B');
+    expect(edge.toString()).toBe('A_B');
     expect(edge.startVertex).toEqual(startVertex);
     expect(edge.endVertex).toEqual(endVertex);
     expect(edge.weight).toEqual(0);

src/data-structures/graph/__test__/GraphVertex.test.js

@@ -21,17 +21,20 @@ describe('GraphVertex', () => {
     expect(vertex.toString()).toBe('A');
     expect(vertex.getKey()).toBe('A');
     expect(vertex.edges.toString()).toBe('');
+    expect(vertex.getEdges()).toEqual([]);
   });
 
   it('should add edges to vertex and check if it exists', () => {
     const vertexA = new GraphVertex('A');
-    const vertexB = new GraphVertex('A');
+    const vertexB = new GraphVertex('B');
 
     const edgeAB = new GraphEdge(vertexA, vertexB);
     vertexA.addEdge(edgeAB);
 
     expect(vertexA.hasEdge(edgeAB)).toBeTruthy();
     expect(vertexB.hasEdge(edgeAB)).toBeFalsy();
+    expect(vertexA.getEdges().length).toBe(1);
+    expect(vertexA.getEdges()[0].toString()).toBe('A_B');
   });
 
   it('should return vertex neighbors in case if current node is start one', () => {