diff --git a/Javascript/graph/floyd-warshall b/Javascript/graph/floyd-warshall new file mode 100644 index 0000000..870d78a --- /dev/null +++ b/Javascript/graph/floyd-warshall @@ -0,0 +1,72 @@ +/** + * @param {Graph} graph + * @return {{distances: number[][], nextVertices: GraphVertex[][]}} + */ +export default function floydWarshall(graph) { + // Get all graph vertices. + const vertices = graph.getAllVertices(); + + // Init previous vertices matrix with nulls meaning that there are no + // previous vertices exist that will give us shortest path. + const nextVertices = Array(vertices.length).fill(null).map(() => { + return Array(vertices.length).fill(null); + }); + + // Init distances matrix with Infinities meaning there are no paths + // between vertices exist so far. + const distances = Array(vertices.length).fill(null).map(() => { + return Array(vertices.length).fill(Infinity); + }); + + // Init distance matrix with the distance we already now (from existing edges). + // And also init previous vertices from the edges. + vertices.forEach((startVertex, startIndex) => { + vertices.forEach((endVertex, endIndex) => { + if (startVertex === endVertex) { + // Distance to the vertex itself is 0. + distances[startIndex][endIndex] = 0; + } else { + // Find edge between the start and end vertices. + const edge = graph.findEdge(startVertex, endVertex); + + if (edge) { + // There is an edge from vertex with startIndex to vertex with endIndex. + // Save distance and previous vertex. + distances[startIndex][endIndex] = edge.weight; + nextVertices[startIndex][endIndex] = startVertex; + } else { + distances[startIndex][endIndex] = Infinity; + } + } + }); + }); + + // Now let's go to the core of the algorithm. + // Let's all pair of vertices (from start to end ones) and try to check if there + // is a shorter path exists between them via middle vertex. Middle vertex may also + // be one of the graph vertices. As you may see now we're going to have three + // loops over all graph vertices: for start, end and middle vertices. + vertices.forEach((middleVertex, middleIndex) => { + // Path starts from startVertex with startIndex. + vertices.forEach((startVertex, startIndex) => { + // Path ends to endVertex with endIndex. + vertices.forEach((endVertex, endIndex) => { + // Compare existing distance from startVertex to endVertex, with distance + // from startVertex to endVertex but via middleVertex. + // Save the shortest distance and previous vertex that allows + // us to have this shortest distance. + const distViaMiddle = distances[startIndex][middleIndex] + distances[middleIndex][endIndex]; + + if (distances[startIndex][endIndex] > distViaMiddle) { + // We've found a shortest pass via middle vertex. + distances[startIndex][endIndex] = distViaMiddle; + nextVertices[startIndex][endIndex] = middleVertex; + } + }); + }); + }); + + // Shortest distance from x to y: distance[x][y]. + // Next vertex after x one in path from x to y: nextVertices[x][y]. + return { distances, nextVertices }; +}