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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)

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

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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)

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

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importGraphVertexfrom'../../../../data-structures/graph/GraphVertex';
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importGraphEdgefrom'../../../../data-structures/graph/GraphEdge';
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importGraphfrom'../../../../data-structures/graph/Graph';
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importfloydWarshallfrom'../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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constvertexA=newGraphVertex('A');
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constvertexB=newGraphVertex('B');
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constvertexC=newGraphVertex('C');
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constvertexD=newGraphVertex('D');
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constvertexE=newGraphVertex('E');
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constvertexF=newGraphVertex('F');
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constvertexG=newGraphVertex('G');
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constvertexH=newGraphVertex('H');
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constedgeAB=newGraphEdge(vertexA,vertexB,4);
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constedgeAE=newGraphEdge(vertexA,vertexE,7);
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constedgeAC=newGraphEdge(vertexA,vertexC,3);
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constedgeBC=newGraphEdge(vertexB,vertexC,6);
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constedgeBD=newGraphEdge(vertexB,vertexD,5);
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constedgeEC=newGraphEdge(vertexE,vertexC,8);
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constedgeED=newGraphEdge(vertexE,vertexD,2);
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constedgeDC=newGraphEdge(vertexD,vertexC,11);
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constedgeDG=newGraphEdge(vertexD,vertexG,10);
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constedgeDF=newGraphEdge(vertexD,vertexF,2);
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constedgeFG=newGraphEdge(vertexF,vertexG,3);
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constedgeEG=newGraphEdge(vertexE,vertexG,5);
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constgraph=newGraph();
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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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constvertices=graph.getAllVertices();
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constvertexAIndex=vertices.indexOf(vertexA);
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constvl=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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constvertexS=newGraphVertex('S');
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constvertexE=newGraphVertex('E');
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constvertexA=newGraphVertex('A');
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constvertexD=newGraphVertex('D');
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constvertexB=newGraphVertex('B');
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constvertexC=newGraphVertex('C');
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constvertexH=newGraphVertex('H');
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constedgeSE=newGraphEdge(vertexS,vertexE,8);
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constedgeSA=newGraphEdge(vertexS,vertexA,10);
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constedgeED=newGraphEdge(vertexE,vertexD,1);
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constedgeDA=newGraphEdge(vertexD,vertexA,-4);
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constedgeDC=newGraphEdge(vertexD,vertexC,-1);
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constedgeAC=newGraphEdge(vertexA,vertexC,2);
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constedgeCB=newGraphEdge(vertexC,vertexB,-2);
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constedgeBA=newGraphEdge(vertexB,vertexA,1);
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constgraph=newGraph(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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constvertices=graph.getAllVertices();
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constvertexSIndex=vertices.indexOf(vertexS);
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constvl=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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});

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

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exportdefaultfunctionfloydWarshall(graph){
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constvertices=graph.getAllVertices();
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// Three dimension matrices.
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constdistances=[];
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constpreviousVertices=[];
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// There are k vertices, loop from 0 to k.
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for(letk=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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constedge=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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