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public/map/dijkstra.js

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+'use strict';
+
+/******************************************************************************
+ * Created 2008-08-19.
+ *
+ * Dijkstra path-finding functions. Adapted from the Dijkstar Python project.
+ *
+ * Copyright (C) 2008
+ *   Wyatt Baldwin <self@wyattbaldwin.com>
+ *   All rights reserved
+ *
+ * Licensed under the MIT license.
+ *
+ *   http://www.opensource.org/licenses/mit-license.php
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+ * THE SOFTWARE.
+ *****************************************************************************/
+window.dijkstra = {
+  single_source_shortest_paths: function(graph, s, d) {
+    // Predecessor map for each node that has been encountered.
+    // node ID => predecessor node ID
+    var predecessors = {};
+
+    // Costs of shortest paths from s to all nodes encountered.
+    // node ID => cost
+    var costs = {};
+    costs[s] = 0;
+
+    // Costs of shortest paths from s to all nodes encountered; differs from
+    // `costs` in that it provides easy access to the node that currently has
+    // the known shortest path from s.
+    // XXX: Do we actually need both `costs` and `open`?
+    var open = dijkstra.PriorityQueue.make();
+    open.push(s, 0);
+
+    var closest,
+        u, v,
+        cost_of_s_to_u,
+        adjacent_nodes,
+        cost_of_e,
+        cost_of_s_to_u_plus_cost_of_e,
+        cost_of_s_to_v,
+        first_visit;
+    while (!open.empty()) {
+      // In the nodes remaining in graph that have a known cost from s,
+      // find the node, u, that currently has the shortest path from s.
+      closest = open.pop();
+      u = closest.value;
+      cost_of_s_to_u = closest.cost;
+
+      // Get nodes adjacent to u...
+      adjacent_nodes = graph[u] || {};
+
+      // ...and explore the edges that connect u to those nodes, updating
+      // the cost of the shortest paths to any or all of those nodes as
+      // necessary. v is the node across the current edge from u.
+      for (v in adjacent_nodes) {
+        if (adjacent_nodes.hasOwnProperty(v)) {
+          // Get the cost of the edge running from u to v.
+          cost_of_e = adjacent_nodes[v];
+
+          // Cost of s to u plus the cost of u to v across e--this is *a*
+          // cost from s to v that may or may not be less than the current
+          // known cost to v.
+          cost_of_s_to_u_plus_cost_of_e = cost_of_s_to_u + cost_of_e;
+
+          // If we haven't visited v yet OR if the current known cost from s to
+          // v is greater than the new cost we just found (cost of s to u plus
+          // cost of u to v across e), update v's cost in the cost list and
+          // update v's predecessor in the predecessor list (it's now u).
+          cost_of_s_to_v = costs[v];
+          first_visit = (typeof costs[v] === 'undefined');
+          if (first_visit || cost_of_s_to_v > cost_of_s_to_u_plus_cost_of_e) {
+            costs[v] = cost_of_s_to_u_plus_cost_of_e;
+            open.push(v, cost_of_s_to_u_plus_cost_of_e);
+            predecessors[v] = u;
+          }
+        }
+      }
+    }
+
+    if (typeof d !== 'undefined' && typeof costs[d] === 'undefined') {
+      var msg = ['Could not find a path from ', s, ' to ', d, '.'].join('');
+      throw new Error(msg);
+    }
+
+    return predecessors;
+  },
+
+  extract_shortest_path_from_predecessor_list: function(predecessors, d) {
+    var nodes = [];
+    var u = d;
+    var predecessor;
+    while (u) {
+      nodes.push(u);
+      predecessor = predecessors[u];
+      u = predecessors[u];
+    }
+    nodes.reverse();
+    return nodes;
+  },
+
+  find_path: function(graph, s, d) {
+    var predecessors = dijkstra.single_source_shortest_paths(graph, s, d);
+    return dijkstra.extract_shortest_path_from_predecessor_list(
+      predecessors, d);
+  },
+
+  /**
+   * A very naive priority queue implementation.
+   */
+  PriorityQueue: {
+    make: function (opts) {
+      var T = dijkstra.PriorityQueue,
+          t = {},
+          key;
+      opts = opts || {};
+      for (key in T) {
+        if (T.hasOwnProperty(key)) {
+          t[key] = T[key];
+        }
+      }
+      t.queue = [];
+      t.sorter = opts.sorter || T.default_sorter;
+      return t;
+    },
+
+    default_sorter: function (a, b) {
+      return a.cost - b.cost;
+    },
+
+    /**
+     * Add a new item to the queue and ensure the highest priority element
+     * is at the front of the queue.
+     */
+    push: function (value, cost) {
+      var item = {value: value, cost: cost};
+      this.queue.push(item);
+      this.queue.sort(this.sorter);
+    },
+
+    /**
+     * Return the highest priority element in the queue.
+     */
+    pop: function () {
+      return this.queue.shift();
+    },
+
+    empty: function () {
+      return this.queue.length === 0;
+    }
+  }
+};
+
+
+// node.js module exports
+if (typeof module !== 'undefined') {
+  module.exports = dijkstra;
+}