Add dijkstra.

Author: trekhleb

Diff for: README.md

@@ -65,11 +65,11 @@
 * **Graph**
   * [Depth-First Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/depth-first-search) (DFS)
   * [Breadth-First Search](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/breadth-first-search) (BFS)
+  * [Dijkstra Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/dijkstra) - finding shortest path
+  * Bellman Ford
   * Detect Cycle
   * Topological Sorting
-  * Dijkstra Algorithm to Find Shortest Path
   * Eulerian path, Eulerian circuit
-  * Bellman Ford
   * Strongly Connected Component algorithm
   * Shortest Path Faster Algorithm (SPFA)
 * **Minimum Spanning Tree**
@@ -84,6 +84,7 @@
 
 * **Greedy**
   * [Unbound Knapsack Problem](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem)
+  * [Dijkstra Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/dijkstra) - finding shortest path
 * **Divide and Conquer**
   * [Euclidean Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD)
   * [Permutations](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/permutations) (with and without repetitions)

Diff for: src/algorithms/graph/dijkstra/README.md

@@ -0,0 +1,25 @@
+# Dijkstra's Algorithm
+
+Dijkstra's algorithm is an algorithm for finding the shortest 
+paths between nodes in a graph, which may represent, for example, 
+road networks. 
+
+The algorithm exists in many variants; Dijkstra's original variant 
+found the shortest path between two nodes, but a more common 
+variant fixes a single node as the "source" node and finds 
+shortest paths from the source to all other nodes in the graph, 
+producing a shortest-path tree.
+
+![Dijkstra](https://upload.wikimedia.org/wikipedia/commons/5/57/Dijkstra_Animation.gif)
+
+Dijkstra's algorithm to find the shortest path between `a` and `b`.
+It picks the unvisited vertex with the lowest distance, 
+calculates the distance through it to each unvisited neighbor, 
+and updates the neighbor's distance if smaller. Mark visited
+(set to red) when done with neighbors.
+
+## References
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm)
+- [On YouTube by Nathaniel Fan](https://www.youtube.com/watch?v=gdmfOwyQlcI)
+- [On YouTube by Tushar Roy](https://www.youtube.com/watch?v=lAXZGERcDf4)

Diff for: src/algorithms/graph/dijkstra/__test__/dijkstra.test.js

@@ -0,0 +1,59 @@
+import GraphVertex from '../../../../data-structures/graph/GraphVertex';
+import GraphEdge from '../../../../data-structures/graph/GraphEdge';
+import Graph from '../../../../data-structures/graph/Graph';
+import dijkstra from '../dijkstra';
+
+describe('dijkstra', () => {
+  it('should find minimum paths to all vertices', () => {
+    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 vertexH = new GraphVertex('H');
+
+    const edgeAB = new GraphEdge(vertexA, vertexB, 4);
+    const edgeAE = new GraphEdge(vertexA, vertexE, 7);
+    const edgeAC = new GraphEdge(vertexA, vertexC, 3);
+    const edgeBC = new GraphEdge(vertexB, vertexC, 6);
+    const edgeBD = new GraphEdge(vertexB, vertexD, 5);
+    const edgeEC = new GraphEdge(vertexE, vertexC, 8);
+    const edgeED = new GraphEdge(vertexE, vertexD, 2);
+    const edgeDC = new GraphEdge(vertexD, vertexC, 11);
+    const edgeDG = new GraphEdge(vertexD, vertexG, 10);
+    const edgeDF = new GraphEdge(vertexD, vertexF, 2);
+    const edgeFG = new GraphEdge(vertexF, vertexG, 3);
+    const edgeEG = new GraphEdge(vertexE, vertexG, 5);
+
+    const graph = new Graph();
+    graph
+      .addVertex(vertexH)
+      .addEdge(edgeAB)
+      .addEdge(edgeAE)
+      .addEdge(edgeAC)
+      .addEdge(edgeBC)
+      .addEdge(edgeBD)
+      .addEdge(edgeEC)
+      .addEdge(edgeED)
+      .addEdge(edgeDC)
+      .addEdge(edgeDG)
+      .addEdge(edgeDF)
+      .addEdge(edgeFG)
+      .addEdge(edgeEG);
+
+    const distances = dijkstra(graph, vertexA);
+
+    expect(distances).toEqual({
+      H: Infinity,
+      A: 0,
+      B: 4,
+      E: 7,
+      C: 3,
+      D: 9,
+      G: 12,
+      F: 11,
+    });
+  });
+});

Diff for: src/algorithms/graph/dijkstra/dijkstra.js

@@ -0,0 +1,48 @@
+import PriorityQueue from '../../../data-structures/priority-queue/PriorityQueue';
+
+/**
+ * @param {Graph} graph
+ * @param {GraphVertex} startVertex
+ */
+export default function dijkstra(graph, startVertex) {
+  const distances = {};
+  const visitedVertices = {};
+  const queue = new PriorityQueue();
+
+  // Init all distances with infinity assuming that currently we can't reach
+  // any of the vertices except start one.
+  Object.keys(graph.vertices).forEach((vertexKey) => {
+    distances[vertexKey] = Infinity;
+  });
+  distances[startVertex.getKey()] = 0;
+
+  // Init vertices queue.
+  queue.add(startVertex, distances[startVertex.getKey()]);
+
+  while (!queue.isEmpty()) {
+    const currentVertex = queue.poll();
+
+    graph.getNeighbors(currentVertex).forEach((neighbor) => {
+      // Don't visit already visited vertices.
+      if (!visitedVertices[neighbor.getKey()]) {
+        // Update distances to every neighbor from current vertex.
+        const edge = graph.findEdge(currentVertex, neighbor);
+
+        const existingDistanceToNeighbor = distances[neighbor.getKey()];
+        const distanceToNeighborFromCurrent = distances[currentVertex.getKey()] + edge.weight;
+
+        if (distanceToNeighborFromCurrent < existingDistanceToNeighbor) {
+          distances[neighbor.getKey()] = distanceToNeighborFromCurrent;
+        }
+
+        // Add neighbor to the queue for further visiting.
+        queue.add(neighbor, distances[neighbor.getKey()]);
+      }
+    });
+
+    // Add current vertex to visited ones.
+    visitedVertices[currentVertex.getKey()] = currentVertex;
+  }
+
+  return distances;
+}

Diff for: src/data-structures/graph/Graph.js

@@ -71,6 +71,7 @@ export default class Graph {
   /**
    * @param {GraphVertex} startVertex
    * @param {GraphVertex} endVertex
+   * @return {(GraphEdge|null)}
    */
   findEdge(startVertex, endVertex) {
     const vertex = this.getVertexByKey(startVertex.getKey());