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update (#1)
* Graph Theory * Delete Graphs * Graph * Dijkstra Smallest Path * DijkstraSmallestPath after fixing some errors. * Topological Sort directed graphs * correcting name of file * updating DIRECTORY.md * doublylinkedlist * add-doublylinkedlist * add-doublylinkedlist * change in Directory.md * updating DIRECTORY.md Co-authored-by: Nur69 <60115902+Nur69@users.noreply.github.com> Co-authored-by: Stepfen Shawn <m18824909883@163.com> Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Co-authored-by: hmizz <hamza.chabchoub@medtech.tn>
This commit is contained in:
vinayak
118
maths/DijkstraSmallestPath.js
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118
maths/DijkstraSmallestPath.js
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// starting at s
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function solve(graph, s) {
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var solutions = {};
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solutions[s] = [];
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solutions[s].dist = 0;
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while(true) {
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var p = null;
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var neighbor = null;
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var dist = Infinity;
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for(var n in solutions) {
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if(!solutions[n])
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continue
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var ndist = solutions[n].dist;
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var adj = graph[n];
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for(var a in adj) {
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if(solutions[a])
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continue;
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var d = adj[a] + ndist;
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if(d < dist) {
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p = solutions[n];
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neighbor = a;
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dist = d;
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}
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}
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}
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//no more solutions
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if(dist === Infinity) {
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break;
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}
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//extend parent's solution path
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solutions[neighbor] = p.concat(neighbor);
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//extend parent's cost
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solutions[neighbor].dist = dist;
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}
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return solutions;
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}
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//create graph
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var graph = {};
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var layout = {
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'R': ['2'],
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'2': ['3','4'],
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'3': ['4','6','13'],
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'4': ['5','8'],
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'5': ['7','11'],
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'6': ['13','15'],
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'7': ['10'],
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'8': ['11','13'],
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'9': ['14'],
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'10': [],
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'11': ['12'],
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'12': [],
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'13': ['14'],
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'14': [],
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'15': []
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}
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//convert uni-directional to bi-directional graph
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// var graph = {
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// a: {e:1, b:1, g:3},
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// b: {a:1, c:1},
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// c: {b:1, d:1},
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// d: {c:1, e:1},
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// e: {d:1, a:1},
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// f: {g:1, h:1},
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// g: {a:3, f:1},
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// h: {f:1}
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// };
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for(var id in layout) {
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if(!graph[id])
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graph[id] = {};
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layout[id].forEach(function(aid) {
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graph[id][aid] = 1;
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if(!graph[aid])
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graph[aid] = {};
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graph[aid][id] = 1;
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});
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}
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//choose start node
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var start = '10';
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//get all solutions
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var solutions = solve(graph, start);
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console.log("From '"+start+"' to");
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//display solutions
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for(var s in solutions) {
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if(!solutions[s]) continue;
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console.log(" -> " + s + ": [" + solutions[s].join(", ") + "] (dist:" + solutions[s].dist + ")");
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}
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// From '10' to
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// -> 2: [7, 5, 4, 2] (dist:4)
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// -> 3: [7, 5, 4, 3] (dist:4)
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// -> 4: [7, 5, 4] (dist:3)
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// -> 5: [7, 5] (dist:2)
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// -> 6: [7, 5, 4, 3, 6] (dist:5)
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// -> 7: [7] (dist:1)
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// -> 8: [7, 5, 4, 8] (dist:4)
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// -> 9: [7, 5, 4, 3, 13, 14, 9] (dist:7)
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// -> 10: [] (dist:0)
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// -> 11: [7, 5, 11] (dist:3)
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// -> 12: [7, 5, 11, 12] (dist:4)
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// -> 13: [7, 5, 4, 3, 13] (dist:5)
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// -> 14: [7, 5, 4, 3, 13, 14] (dist:6)
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// -> 15: [7, 5, 4, 3, 6, 15] (dist:6)
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// -> R: [7, 5, 4, 2, R] (dist:5)
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94
maths/graph.js
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94
maths/graph.js
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// create a graph class
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class Graph {
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// defining vertex array and
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// adjacent list
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constructor(noOfVertices)
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{
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this.noOfVertices = noOfVertices;
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this.AdjList = new Map();
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}
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// functions to be implemented
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// addVertex(v)
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// addEdge(v, w)
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// printGraph()
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// bfs(v)
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// dfs(v)
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}
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// add vertex to the graph
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addVertex(v)
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{
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// initialize the adjacent list with a
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// null array
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this.AdjList.set(v, []);
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}
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// add edge to the graph
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addEdge(v, w)
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{
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// get the list for vertex v and put the
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// vertex w denoting edge between v and w
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this.AdjList.get(v).push(w);
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// Since graph is undirected,
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// add an edge from w to v also
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this.AdjList.get(w).push(v);
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}
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// Prints the vertex and adjacency list
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printGraph()
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{
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// get all the vertices
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var get_keys = this.AdjList.keys();
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// iterate over the vertices
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for (var i of get_keys)
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{
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// great the corresponding adjacency list
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// for the vertex
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var get_values = this.AdjList.get(i);
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var conc = "";
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// iterate over the adjacency list
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// concatenate the values into a string
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for (var j of get_values)
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conc += j + " ";
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// print the vertex and its adjacency list
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console.log(i + " -> " + conc);
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}
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}
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// Example
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var graph = new Graph(6);
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var vertices = [ 'A', 'B', 'C', 'D', 'E', 'F' ];
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// adding vertices
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for (var i = 0; i < vertices.length; i++) {
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g.addVertex(vertices[i]);
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}
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// adding edges
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g.addEdge('A', 'B');
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g.addEdge('A', 'D');
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g.addEdge('A', 'E');
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g.addEdge('B', 'C');
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g.addEdge('D', 'E');
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g.addEdge('E', 'F');
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g.addEdge('E', 'C');
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g.addEdge('C', 'F');
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// prints all vertex and
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// its adjacency list
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// A -> B D E
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// B -> A C
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// C -> B E F
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// D -> A E
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// E -> A D F C
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// F -> E C
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g.printGraph();
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