reorg and add code for second edition

09_dijkstras_algorithm/dart/01_djikstra_algorithm.dart

@@ -0,0 +1,72 @@
+void main(List<String> args) {
+  final graph = <String, Map<String, double>>{}..addAll(
+      {
+        'start': {
+          'a': 6,
+          'b': 2,
+        },
+        'a': {
+          'end': 1,
+        },
+        'b': {
+          'a': 3,
+          'end': 5,
+        },
+        'end': {},
+      },
+    );
+
+  final costs = <String, double>{
+    'a': 6,
+    'b': 2,
+    'end': double.infinity,
+  };
+
+  final parents = <String, String?>{
+    'a': 'start',
+    'b': 'start',
+    'end': null,
+  };
+
+  djikstra(graph, costs, parents);
+  print(graph);
+  print(costs);
+  print(parents);
+}
+
+void djikstra(
+  Map<String, Map<String, double>> graph,
+  Map<String, double> costs,
+  Map<String, String?> parents,
+) {
+  final processeds = <String>[];
+  String? node = findTheCheapestOne(costs, processeds);
+
+  while (node != null) {
+    final cost = costs[node];
+    final neighbors = graph[node];
+    for (String neighbor in neighbors!.keys) {
+      final double newCost = cost! + neighbors[neighbor]!;
+      if (costs[neighbor]! > newCost) {
+        costs[neighbor] = newCost;
+        parents[neighbor] = node;
+      }
+    }
+    processeds.add(node);
+    node = findTheCheapestOne(costs, processeds);
+  }
+}
+
+String? findTheCheapestOne(Map<String, double> costs, List<String> processed) {
+  double cheapestCost = double.infinity;
+  String? cheapestNode;
+
+  for (String node in costs.keys) {
+    final double cost = costs[node]!;
+    if (cost < cheapestCost && !processed.contains(node)) {
+      cheapestCost = cost;
+      cheapestNode = node;
+    }
+  }
+  return cheapestNode;
+}