Add Bellman-Ford.

Author: trekhleb

README.md

@@ -65,8 +65,8 @@
 * **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
+  * [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
   * Topological Sorting
   * Eulerian path, Eulerian circuit
@@ -84,7 +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
+  * [Dijkstra Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/dijkstra) - finding shortest path to all graph vertices
 * **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)
@@ -103,6 +103,7 @@
   * [0/1 Knapsack Problem](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem)
   * [Integer Partition](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/integer-partition)
   * [Maximum Subarray](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/maximum-subarray)
+  * [Bellman-Ford Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/bellman-ford) - finding shortest path to all graph vertices
 * **Backtracking**
 * **Branch & Bound**
 

src/algorithms/graph/bellman-ford/README.md

@@ -0,0 +1,21 @@
+# Bellman–Ford Algorithm
+
+The Bellman–Ford algorithm is an algorithm that computes shortest 
+paths from a single source vertex to all of the other vertices 
+in a weighted digraph. It is slower than Dijkstra's algorithm 
+for the same problem, but more versatile, as it is capable of 
+handling graphs in which some of the edge weights are negative 
+numbers.
+
+![Bellman-Ford](https://upload.wikimedia.org/wikipedia/commons/2/2e/Shortest_path_Dijkstra_vs_BellmanFord.gif)
+
+## Complexity
+
+Worst-case performance `O(|V||E|)`
+Best-case performance	`O(|E|)`
+Worst-case space complexity `O(|V|)`
+
+## References
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm)
+- [On YouTube by Michael Sambol](https://www.youtube.com/watch?v=obWXjtg0L64)

src/algorithms/graph/bellman-ford/__test__/bellmanFord.test.js

@@ -0,0 +1,56 @@
+import GraphVertex from '../../../../data-structures/graph/GraphVertex';
+import GraphEdge from '../../../../data-structures/graph/GraphEdge';
+import Graph from '../../../../data-structures/graph/Graph';
+import bellmanFord from '../bellmanFord';
+
+describe('bellmanFord', () => {
+  it('should find minimum paths to all vertices', () => {
+    const vertexS = new GraphVertex('S');
+    const vertexE = new GraphVertex('E');
+    const vertexA = new GraphVertex('A');
+    const vertexD = new GraphVertex('D');
+    const vertexB = new GraphVertex('B');
+    const vertexC = new GraphVertex('C');
+    const vertexH = new GraphVertex('H');
+
+    const edgeSE = new GraphEdge(vertexS, vertexE, 8);
+    const edgeSA = new GraphEdge(vertexS, vertexA, 10);
+    const edgeED = new GraphEdge(vertexE, vertexD, 1);
+    const edgeDA = new GraphEdge(vertexD, vertexA, -4);
+    const edgeDC = new GraphEdge(vertexD, vertexC, -1);
+    const edgeAC = new GraphEdge(vertexA, vertexC, 2);
+    const edgeCB = new GraphEdge(vertexC, vertexB, -2);
+    const edgeBA = new GraphEdge(vertexB, vertexA, 1);
+
+    const graph = new Graph(true);
+    graph
+      .addVertex(vertexH)
+      .addEdge(edgeSE)
+      .addEdge(edgeSA)
+      .addEdge(edgeED)
+      .addEdge(edgeDA)
+      .addEdge(edgeDC)
+      .addEdge(edgeAC)
+      .addEdge(edgeCB)
+      .addEdge(edgeBA);
+
+    const { distances, previousVertices } = bellmanFord(graph, vertexS);
+
+    expect(distances).toEqual({
+      H: Infinity,
+      S: 0,
+      A: 5,
+      B: 5,
+      C: 7,
+      D: 9,
+      E: 8,
+    });
+
+    expect(previousVertices.H).toBeNull();
+    expect(previousVertices.S).toBeNull();
+    expect(previousVertices.B.getKey()).toBe('C');
+    expect(previousVertices.C.getKey()).toBe('A');
+    expect(previousVertices.A.getKey()).toBe('D');
+    expect(previousVertices.D.getKey()).toBe('E');
+  });
+});

src/algorithms/graph/bellman-ford/bellmanFord.js

@@ -0,0 +1,45 @@
+/**
+ * @param {Graph} graph
+ * @param {GraphVertex} startVertex
+ * @return {{distances, previousVertices}}
+ */
+export default function bellmanFord(graph, startVertex) {
+  const distances = {};
+  const previousVertices = {};
+
+  // Init all distances with infinity assuming that currently we can't reach
+  // any of the vertices except start one.
+  distances[startVertex.getKey()] = 0;
+  graph.getAllVertices().forEach((vertex) => {
+    previousVertices[vertex.getKey()] = null;
+    if (vertex.getKey() !== startVertex.getKey()) {
+      distances[vertex.getKey()] = Infinity;
+    }
+  });
+
+  // We need (|V| - 1) iterations.
+  for (let iteration = 0; iteration < (graph.getAllVertices().length - 1); iteration += 1) {
+    // During each iteration go through all vertices.
+    Object.keys(distances).forEach((vertexKey) => {
+      const vertex = graph.getVertexByKey(vertexKey);
+
+      // Go through all vertex edges.
+      graph.getNeighbors(vertex).forEach((neighbor) => {
+        const edge = graph.findEdge(vertex, neighbor);
+        // Find out if the distance to the neighbor is shorter in this iteration
+        // then in previous one.
+        const distanceToVertex = distances[vertex.getKey()];
+        const distanceToNeighbor = distanceToVertex + edge.weight;
+        if (distanceToNeighbor < distances[neighbor.getKey()]) {
+          distances[neighbor.getKey()] = distanceToNeighbor;
+          previousVertices[neighbor.getKey()] = vertex;
+        }
+      });
+    });
+  }
+
+  return {
+    distances,
+    previousVertices,
+  };
+}

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

@@ -61,5 +61,7 @@ describe('dijkstra', () => {
     expect(previousVertices.B.getKey()).toBe('A');
     expect(previousVertices.G.getKey()).toBe('E');
     expect(previousVertices.C.getKey()).toBe('A');
+    expect(previousVertices.A).toBeNull();
+    expect(previousVertices.H).toBeNull();
   });
 });

src/algorithms/graph/dijkstra/dijkstra.js

@@ -12,8 +12,9 @@ export default function dijkstra(graph, startVertex) {
 
   // 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;
+  graph.getAllVertices().forEach((vertex) => {
+    distances[vertex.getKey()] = Infinity;
+    previousVertices[vertex.getKey()] = null;
   });
   distances[startVertex.getKey()] = 0;
 

src/data-structures/graph/Graph.js

@@ -32,6 +32,13 @@ export default class Graph {
     return vertex.getNeighbors();
   }
 
+  /**
+   * @return {GraphVertex[]}
+   */
+  getAllVertices() {
+    return Object.values(this.vertices);
+  }
+
   /**
    * @param {GraphEdge} edge
    * @returns {Graph}

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

@@ -28,6 +28,10 @@ describe('Graph', () => {
 
     graph.addEdge(edgeAB);
 
+    expect(graph.getAllVertices().length).toBe(2);
+    expect(graph.getAllVertices()[0]).toEqual(vertexA);
+    expect(graph.getAllVertices()[1]).toEqual(vertexB);
+
     const graphVertexA = graph.findVertexByKey(vertexA.getKey());
     const graphVertexB = graph.findVertexByKey(vertexB.getKey());