Created DijkstraSmallestPath.js in Graphs (#185)

* Created DijkstraSmallestPath.js in Graphs

* Deleted DijkstraSmallestPath.js from Maths

Graphs/DijkstraSmallestPath.js

@@ -0,0 +1,111 @@
+// starting at s
+function solve (graph, s) {
+  var solutions = {}
+  solutions[s] = []
+  solutions[s].dist = 0
+
+  while (true) {
+    var p = null
+    var neighbor = null
+    var dist = Infinity
+
+    for (var n in solutions) {
+      if (!solutions[n]) { continue }
+      var ndist = solutions[n].dist
+      var adj = graph[n]
+
+      for (var a in adj) {
+        if (solutions[a]) { continue }
+
+        var d = adj[a] + ndist
+        if (d < dist) {
+          p = solutions[n]
+          neighbor = a
+          dist = d
+        }
+      }
+    }
+
+    // no more solutions
+    if (dist === Infinity) {
+      break
+    }
+
+    // extend parent's solution path
+    solutions[neighbor] = p.concat(neighbor)
+    // extend parent's cost
+    solutions[neighbor].dist = dist
+  }
+
+  return solutions
+}
+// create graph
+var graph = {}
+
+var layout = {
+  R: ['2'],
+  2: ['3', '4'],
+  3: ['4', '6', '13'],
+  4: ['5', '8'],
+  5: ['7', '11'],
+  6: ['13', '15'],
+  7: ['10'],
+  8: ['11', '13'],
+  9: ['14'],
+  10: [],
+  11: ['12'],
+  12: [],
+  13: ['14'],
+  14: [],
+  15: []
+}
+
+// convert uni-directional to bi-directional graph
+// var graph = {
+//     a: {e:1, b:1, g:3},
+//     b: {a:1, c:1},
+//     c: {b:1, d:1},
+//     d: {c:1, e:1},
+//     e: {d:1, a:1},
+//     f: {g:1, h:1},
+//     g: {a:3, f:1},
+//     h: {f:1}
+// };
+
+for (var id in layout) {
+  if (!graph[id]) { graph[id] = {} }
+  layout[id].forEach(function (aid) {
+    graph[id][aid] = 1
+    if (!graph[aid]) { graph[aid] = {} }
+    graph[aid][id] = 1
+  })
+}
+
+// choose start node
+var start = '10'
+// get all solutions
+var solutions = solve(graph, start)
+
+console.log("From '" + start + "' to")
+// display solutions
+for (var s in solutions) {
+  if (!solutions[s]) continue
+  console.log(' -> ' + s + ': [' + solutions[s].join(', ') + ']   (dist:' + solutions[s].dist + ')')
+}
+
+// From '10' to
+//  -> 2: [7, 5, 4, 2]   (dist:4)
+//  -> 3: [7, 5, 4, 3]   (dist:4)
+//  -> 4: [7, 5, 4]   (dist:3)
+//  -> 5: [7, 5]   (dist:2)
+//  -> 6: [7, 5, 4, 3, 6]   (dist:5)
+//  -> 7: [7]   (dist:1)
+//  -> 8: [7, 5, 4, 8]   (dist:4)
+//  -> 9: [7, 5, 4, 3, 13, 14, 9]   (dist:7)
+//  -> 10: []   (dist:0)
+//  -> 11: [7, 5, 11]   (dist:3)
+//  -> 12: [7, 5, 11, 12]   (dist:4)
+//  -> 13: [7, 5, 4, 3, 13]   (dist:5)
+//  -> 14: [7, 5, 4, 3, 13, 14]   (dist:6)
+//  -> 15: [7, 5, 4, 3, 6, 15]   (dist:6)
+//  -> R: [7, 5, 4, 2, R]   (dist:5)