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Commit 9f8fd33

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vivaxytrekhleb
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feat(algorithms): ✨Add Floyd-Warshall (trekhleb#97)
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‎README.md‎

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

‎README.zh-CN.md‎

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* [归并排序](src/algorithms/sorting/merge-sort)
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* [快速排序](src/algorithms/sorting/quick-sort)
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* [希尔排序](src/algorithms/sorting/shell-sort)
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* **树**
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* **树**
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* [深度优先搜索](src/algorithms/tree/depth-first-search) (DFS)
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* [广度优先搜索](src/algorithms/tree/breadth-first-search) (BFS)
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* **图**
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* [哈密顿图](src/algorithms/graph/hamiltonian-cycle) - 恰好访问每个顶点一次
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* [强连通分量](src/algorithms/graph/strongly-connected-components) - Kosaraju算法
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* [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
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* **未分类**
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* [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
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* **未分类**
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* [汉诺塔](src/algorithms/uncategorized/hanoi-tower)
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* [八皇后问题](src/algorithms/uncategorized/n-queens)
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* [骑士巡逻](src/algorithms/uncategorized/knight-tour)

‎README.zh-TW.md‎

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* [合併排序](src/algorithms/sorting/merge-sort)
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* [快速排序](src/algorithms/sorting/quick-sort)
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* [希爾排序](src/algorithms/sorting/shell-sort)
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* **樹**
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* **樹**
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* [深度優先搜尋](src/algorithms/tree/depth-first-search) (DFS)
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* [廣度優先搜尋](src/algorithms/tree/breadth-first-search) (BFS)
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* **圖**
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* [漢彌爾頓環](src/algorithms/graph/hamiltonian-cycle) - Visit every vertex exactly once
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* [強連通組件](src/algorithms/graph/strongly-connected-components) - Kosaraju's algorithm
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* [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
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* **未分類**
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* [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
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* **未分類**
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* [河內塔](src/algorithms/uncategorized/hanoi-tower)
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* [N-皇后問題](src/algorithms/uncategorized/n-queens)
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* [騎士走棋盤](src/algorithms/uncategorized/knight-tour)
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# Floyd–Warshall algorithm
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## References
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- [Wikipedia](https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm)
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import GraphVertex from '../../../../data-structures/graph/GraphVertex';
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import GraphEdge from '../../../../data-structures/graph/GraphEdge';
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import Graph from '../../../../data-structures/graph/Graph';
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import floydWarshall from '../floydWarshall';
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describe('floydWarshall', () => {
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it('should find minimum paths to all vertices for undirected graph', () => {
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const vertexA = new GraphVertex('A');
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const vertexB = new GraphVertex('B');
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const vertexC = new GraphVertex('C');
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const vertexD = new GraphVertex('D');
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const vertexE = new GraphVertex('E');
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const vertexF = new GraphVertex('F');
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const vertexG = new GraphVertex('G');
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const vertexH = new GraphVertex('H');
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const edgeAB = new GraphEdge(vertexA, vertexB, 4);
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const edgeAE = new GraphEdge(vertexA, vertexE, 7);
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const edgeAC = new GraphEdge(vertexA, vertexC, 3);
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const edgeBC = new GraphEdge(vertexB, vertexC, 6);
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const edgeBD = new GraphEdge(vertexB, vertexD, 5);
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const edgeEC = new GraphEdge(vertexE, vertexC, 8);
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const edgeED = new GraphEdge(vertexE, vertexD, 2);
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const edgeDC = new GraphEdge(vertexD, vertexC, 11);
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const edgeDG = new GraphEdge(vertexD, vertexG, 10);
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const edgeDF = new GraphEdge(vertexD, vertexF, 2);
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const edgeFG = new GraphEdge(vertexF, vertexG, 3);
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const edgeEG = new GraphEdge(vertexE, vertexG, 5);
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const graph = new Graph();
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graph
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.addVertex(vertexH)
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.addEdge(edgeAB)
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.addEdge(edgeAE)
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.addEdge(edgeAC)
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.addEdge(edgeBC)
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.addEdge(edgeBD)
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.addEdge(edgeEC)
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.addEdge(edgeED)
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.addEdge(edgeDC)
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.addEdge(edgeDG)
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.addEdge(edgeDF)
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.addEdge(edgeFG)
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.addEdge(edgeEG);
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const { distances, previousVertices } = floydWarshall(graph);
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const vertices = graph.getAllVertices();
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const vertexAIndex = vertices.indexOf(vertexA);
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const vl = vertices.length;
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expect(distances[vertexAIndex][vertices.indexOf(vertexH)][vl]).toBe(Infinity);
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expect(distances[vertexAIndex][vertexAIndex][vl]).toBe(0);
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expect(distances[vertexAIndex][vertices.indexOf(vertexB)][vl]).toBe(4);
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expect(distances[vertexAIndex][vertices.indexOf(vertexE)][vl]).toBe(7);
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expect(distances[vertexAIndex][vertices.indexOf(vertexC)][vl]).toBe(3);
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expect(distances[vertexAIndex][vertices.indexOf(vertexD)][vl]).toBe(9);
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expect(distances[vertexAIndex][vertices.indexOf(vertexG)][vl]).toBe(12);
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expect(distances[vertexAIndex][vertices.indexOf(vertexF)][vl]).toBe(11);
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expect(previousVertices[vertexAIndex][vertices.indexOf(vertexF)][vl]).toBe(vertexD);
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expect(previousVertices[vertexAIndex][vertices.indexOf(vertexD)][vl]).toBe(vertexB);
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expect(previousVertices[vertexAIndex][vertices.indexOf(vertexB)][vl]).toBe(vertexA);
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expect(previousVertices[vertexAIndex][vertices.indexOf(vertexG)][vl]).toBe(vertexE);
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expect(previousVertices[vertexAIndex][vertices.indexOf(vertexC)][vl]).toBe(vertexA);
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expect(previousVertices[vertexAIndex][vertexAIndex][vl]).toBe(null);
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expect(previousVertices[vertexAIndex][vertices.indexOf(vertexH)][vl]).toBe(null);
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});
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it('should find minimum paths to all vertices for directed graph with negative edge weights', () => {
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const vertexS = new GraphVertex('S');
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const vertexE = new GraphVertex('E');
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const vertexA = new GraphVertex('A');
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const vertexD = new GraphVertex('D');
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const vertexB = new GraphVertex('B');
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const vertexC = new GraphVertex('C');
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const vertexH = new GraphVertex('H');
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const edgeSE = new GraphEdge(vertexS, vertexE, 8);
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const edgeSA = new GraphEdge(vertexS, vertexA, 10);
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const edgeED = new GraphEdge(vertexE, vertexD, 1);
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const edgeDA = new GraphEdge(vertexD, vertexA, -4);
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const edgeDC = new GraphEdge(vertexD, vertexC, -1);
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const edgeAC = new GraphEdge(vertexA, vertexC, 2);
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const edgeCB = new GraphEdge(vertexC, vertexB, -2);
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const edgeBA = new GraphEdge(vertexB, vertexA, 1);
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const graph = new Graph(true);
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graph
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.addVertex(vertexH)
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.addEdge(edgeSE)
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.addEdge(edgeSA)
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.addEdge(edgeED)
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.addEdge(edgeDA)
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.addEdge(edgeDC)
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.addEdge(edgeAC)
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.addEdge(edgeCB)
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.addEdge(edgeBA);
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const { distances, previousVertices } = floydWarshall(graph);
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const vertices = graph.getAllVertices();
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const vertexSIndex = vertices.indexOf(vertexS);
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const vl = vertices.length;
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expect(distances[vertexSIndex][vertices.indexOf(vertexH)][vl]).toBe(Infinity);
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expect(distances[vertexSIndex][vertexSIndex][vl]).toBe(0);
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expect(distances[vertexSIndex][vertices.indexOf(vertexA)][vl]).toBe(5);
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expect(distances[vertexSIndex][vertices.indexOf(vertexB)][vl]).toBe(5);
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expect(distances[vertexSIndex][vertices.indexOf(vertexC)][vl]).toBe(7);
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expect(distances[vertexSIndex][vertices.indexOf(vertexD)][vl]).toBe(9);
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expect(distances[vertexSIndex][vertices.indexOf(vertexE)][vl]).toBe(8);
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expect(previousVertices[vertexSIndex][vertices.indexOf(vertexH)][vl]).toBe(null);
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expect(previousVertices[vertexSIndex][vertexSIndex][vl]).toBe(null);
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expect(previousVertices[vertexSIndex][vertices.indexOf(vertexB)][vl]).toBe(vertexC);
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expect(previousVertices[vertexSIndex][vertices.indexOf(vertexC)][vl]).toBe(vertexA);
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expect(previousVertices[vertexSIndex][vertices.indexOf(vertexA)][vl]).toBe(vertexD);
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expect(previousVertices[vertexSIndex][vertices.indexOf(vertexD)][vl]).toBe(vertexE);
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});
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});
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export default function floydWarshall(graph) {
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const vertices = graph.getAllVertices();
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// Three dimension matrices.
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const distances = [];
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const previousVertices = [];
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// There are k vertices, loop from 0 to k.
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for (let k = 0; k <= vertices.length; k += 1) {
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// Path starts from vertex i.
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vertices.forEach((vertex, i) => {
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if (k === 0) {
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distances[i] = [];
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previousVertices[i] = [];
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}
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// Path ends to vertex j.
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vertices.forEach((endVertex, j) => {
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if (k === 0) {
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// Initialize distance and previousVertices array
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distances[i][j] = [];
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previousVertices[i][j] = [];
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if (vertex === endVertex) {
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// Distance to self as 0
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distances[i][j][k] = 0;
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// Previous vertex to self as null
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previousVertices[i][j][k] = null;
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} else {
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const edge = graph.findEdge(vertex, endVertex);
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if (edge) {
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// There is an edge from vertex i to vertex j.
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// Save distance and previous vertex.
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distances[i][j][k] = edge.weight;
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previousVertices[i][j][k] = vertex;
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} else {
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distances[i][j][k] = Infinity;
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previousVertices[i][j][k] = null;
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}
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}
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} else {
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// Compare distance from i to j, with distance from i to k - 1 and then from k - 1 to j.
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// Save the shortest distance and previous vertex
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// distance[i][j][k] = min( distance[i][k - 1][k - 1], distance[k - 1][j][k - 1] )
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if (distances[i][j][k - 1] > distances[i][k - 1][k - 1] + distances[k - 1][j][k - 1]) {
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distances[i][j][k] = distances[i][k - 1][k - 1] + distances[k - 1][j][k - 1];
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previousVertices[i][j][k] = previousVertices[k - 1][j][k - 1];
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} else {
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distances[i][j][k] = distances[i][j][k - 1];
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previousVertices[i][j][k] = previousVertices[i][j][k - 1];
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}
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}
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});
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});
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}
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// Shortest distance from x to y: distance[x][y][k]
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// Previous vertex when shortest distance from x to y: previousVertices[x][y][k]
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return { distances, previousVertices };
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}

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