feat(algorithms): ✨Add Floyd-Warshall (trekhleb#97)

Author: vivaxy

README.md

@@ -113,7 +113,8 @@ a set of rules that precisely define a sequence of operations.
   * `A` [Hamiltonian Cycle](src/algorithms/graph/hamiltonian-cycle) - Visit every vertex exactly once
   * `A` [Strongly Connected Components](src/algorithms/graph/strongly-connected-components) - Kosaraju's algorithm
   * `A` [Travelling Salesman Problem](src/algorithms/graph/travelling-salesman) - shortest possible route that visits each city and returns to the origin city
-* **Uncategorized**  
+  * `A` [Floyd-Warshall algorithm](src/algorithms/graph/floyd-warshall) - a single execution of the algorithm will find the lengths (summed weights) of shortest paths between all pairs of vertices
+* **Uncategorized**
   * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower)
   * `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - in-place algorithm
   * `B` [Jump Game](src/algorithms/uncategorized/jump-game) - backtracking, dynamic programming (top-down + bottom-up) and greedy examples 

README.zh-CN.md

@@ -69,7 +69,7 @@ _Read this in other languages:_
   * [归并排序](src/algorithms/sorting/merge-sort)
   * [快速排序](src/algorithms/sorting/quick-sort)
   * [希尔排序](src/algorithms/sorting/shell-sort)
-* **树**  
+* **树**
   * [深度优先搜索](src/algorithms/tree/depth-first-search) (DFS)
   * [广度优先搜索](src/algorithms/tree/breadth-first-search) (BFS)
 * **图**
@@ -87,7 +87,8 @@ _Read this in other languages:_
   * [哈密顿图](src/algorithms/graph/hamiltonian-cycle) - 恰好访问每个顶点一次
   * [强连通分量](src/algorithms/graph/strongly-connected-components) - Kosaraju算法
   * [旅行推销员问题](src/algorithms/graph/travelling-salesman) - 尽可能以最短的路线访问每个城市并返回原始城市
-* **未分类**  
+  * [Floyd-Warshall algorithm](src/algorithms/graph/floyd-warshall) - 一次循环可以找出所有顶点之间的最短路径
+* **未分类**
   * [汉诺塔](src/algorithms/uncategorized/hanoi-tower)
   * [八皇后问题](src/algorithms/uncategorized/n-queens)
   * [骑士巡逻](src/algorithms/uncategorized/knight-tour)

README.zh-TW.md

@@ -68,7 +68,7 @@ _Read this in other languages:_
   * [合併排序](src/algorithms/sorting/merge-sort)
   * [快速排序](src/algorithms/sorting/quick-sort)
   * [希爾排序](src/algorithms/sorting/shell-sort)
-* **樹**  
+* **樹**
   * [深度優先搜尋](src/algorithms/tree/depth-first-search) (DFS)
   * [廣度優先搜尋](src/algorithms/tree/breadth-first-search) (BFS)
 * **圖**
@@ -86,7 +86,8 @@ _Read this in other languages:_
   * [漢彌爾頓環](src/algorithms/graph/hamiltonian-cycle) - Visit every vertex exactly once
   * [強連通組件](src/algorithms/graph/strongly-connected-components) - Kosaraju's algorithm
   * [旅行推銷員問題](src/algorithms/graph/travelling-salesman) - shortest possible route that visits each city and returns to the origin city
-* **未分類**  
+  * [Floyd-Warshall algorithm](src/algorithms/graph/floyd-warshall) - 一次循环可以找出所有頂點之间的最短路徑
+* **未分類**
   * [河內塔](src/algorithms/uncategorized/hanoi-tower)
   * [N-皇后問題](src/algorithms/uncategorized/n-queens)
   * [騎士走棋盤](src/algorithms/uncategorized/knight-tour)

src/algorithms/graph/floyd-warshall/README.md

@@ -0,0 +1,5 @@
+# Floyd–Warshall algorithm
+
+## References
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm)

src/algorithms/graph/floyd-warshall/__test__/floydWarshall.test.js

@@ -0,0 +1,121 @@
+import GraphVertex from '../../../../data-structures/graph/GraphVertex';
+import GraphEdge from '../../../../data-structures/graph/GraphEdge';
+import Graph from '../../../../data-structures/graph/Graph';
+import floydWarshall from '../floydWarshall';
+
+describe('floydWarshall', () => {
+  it('should find minimum paths to all vertices for undirected graph', () => {
+    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, previousVertices } = floydWarshall(graph);
+
+    const vertices = graph.getAllVertices();
+    const vertexAIndex = vertices.indexOf(vertexA);
+    const vl = vertices.length;
+
+    expect(distances[vertexAIndex][vertices.indexOf(vertexH)][vl]).toBe(Infinity);
+    expect(distances[vertexAIndex][vertexAIndex][vl]).toBe(0);
+    expect(distances[vertexAIndex][vertices.indexOf(vertexB)][vl]).toBe(4);
+    expect(distances[vertexAIndex][vertices.indexOf(vertexE)][vl]).toBe(7);
+    expect(distances[vertexAIndex][vertices.indexOf(vertexC)][vl]).toBe(3);
+    expect(distances[vertexAIndex][vertices.indexOf(vertexD)][vl]).toBe(9);
+    expect(distances[vertexAIndex][vertices.indexOf(vertexG)][vl]).toBe(12);
+    expect(distances[vertexAIndex][vertices.indexOf(vertexF)][vl]).toBe(11);
+
+    expect(previousVertices[vertexAIndex][vertices.indexOf(vertexF)][vl]).toBe(vertexD);
+    expect(previousVertices[vertexAIndex][vertices.indexOf(vertexD)][vl]).toBe(vertexB);
+    expect(previousVertices[vertexAIndex][vertices.indexOf(vertexB)][vl]).toBe(vertexA);
+    expect(previousVertices[vertexAIndex][vertices.indexOf(vertexG)][vl]).toBe(vertexE);
+    expect(previousVertices[vertexAIndex][vertices.indexOf(vertexC)][vl]).toBe(vertexA);
+    expect(previousVertices[vertexAIndex][vertexAIndex][vl]).toBe(null);
+    expect(previousVertices[vertexAIndex][vertices.indexOf(vertexH)][vl]).toBe(null);
+  });
+
+  it('should find minimum paths to all vertices for directed graph with negative edge weights', () => {
+    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 } = floydWarshall(graph);
+
+    const vertices = graph.getAllVertices();
+    const vertexSIndex = vertices.indexOf(vertexS);
+    const vl = vertices.length;
+
+    expect(distances[vertexSIndex][vertices.indexOf(vertexH)][vl]).toBe(Infinity);
+    expect(distances[vertexSIndex][vertexSIndex][vl]).toBe(0);
+    expect(distances[vertexSIndex][vertices.indexOf(vertexA)][vl]).toBe(5);
+    expect(distances[vertexSIndex][vertices.indexOf(vertexB)][vl]).toBe(5);
+    expect(distances[vertexSIndex][vertices.indexOf(vertexC)][vl]).toBe(7);
+    expect(distances[vertexSIndex][vertices.indexOf(vertexD)][vl]).toBe(9);
+    expect(distances[vertexSIndex][vertices.indexOf(vertexE)][vl]).toBe(8);
+
+    expect(previousVertices[vertexSIndex][vertices.indexOf(vertexH)][vl]).toBe(null);
+    expect(previousVertices[vertexSIndex][vertexSIndex][vl]).toBe(null);
+    expect(previousVertices[vertexSIndex][vertices.indexOf(vertexB)][vl]).toBe(vertexC);
+    expect(previousVertices[vertexSIndex][vertices.indexOf(vertexC)][vl]).toBe(vertexA);
+    expect(previousVertices[vertexSIndex][vertices.indexOf(vertexA)][vl]).toBe(vertexD);
+    expect(previousVertices[vertexSIndex][vertices.indexOf(vertexD)][vl]).toBe(vertexE);
+  });
+});

src/algorithms/graph/floyd-warshall/floydWarshall.js

@@ -0,0 +1,60 @@
+export default function floydWarshall(graph) {
+  const vertices = graph.getAllVertices();
+
+  // Three dimension matrices.
+  const distances = [];
+  const previousVertices = [];
+
+  // There are k vertices, loop from 0 to k.
+  for (let k = 0; k <= vertices.length; k += 1) {
+    // Path starts from vertex i.
+    vertices.forEach((vertex, i) => {
+      if (k === 0) {
+        distances[i] = [];
+        previousVertices[i] = [];
+      }
+
+      // Path ends to vertex j.
+      vertices.forEach((endVertex, j) => {
+        if (k === 0) {
+          // Initialize distance and previousVertices array
+          distances[i][j] = [];
+          previousVertices[i][j] = [];
+
+          if (vertex === endVertex) {
+            // Distance to self as 0
+            distances[i][j][k] = 0;
+            // Previous vertex to self as null
+            previousVertices[i][j][k] = null;
+          } else {
+            const edge = graph.findEdge(vertex, endVertex);
+            if (edge) {
+              // There is an edge from vertex i to vertex j.
+              // Save distance and previous vertex.
+              distances[i][j][k] = edge.weight;
+              previousVertices[i][j][k] = vertex;
+            } else {
+              distances[i][j][k] = Infinity;
+              previousVertices[i][j][k] = null;
+            }
+          }
+        } else {
+          // Compare distance from i to j, with distance from i to k - 1 and then from k - 1 to j.
+          // Save the shortest distance and previous vertex
+          // distance[i][j][k] = min( distance[i][k - 1][k - 1], distance[k - 1][j][k - 1] )
+          if (distances[i][j][k - 1] > distances[i][k - 1][k - 1] + distances[k - 1][j][k - 1]) {
+            distances[i][j][k] = distances[i][k - 1][k - 1] + distances[k - 1][j][k - 1];
+            previousVertices[i][j][k] = previousVertices[k - 1][j][k - 1];
+          } else {
+            distances[i][j][k] = distances[i][j][k - 1];
+            previousVertices[i][j][k] = previousVertices[i][j][k - 1];
+          }
+        }
+      });
+    });
+  }
+
+  // Shortest distance from x to y: distance[x][y][k]
+  // Previous vertex when shortest distance from x to y: previousVertices[x][y][k]
+  return { distances, previousVertices };
+}