Add exercise 2 solution

notes-and-examples/2026.08.11/exercise2_solution.py

@@ -0,0 +1,55 @@
+# note: I added Anaheim to the sample graph here. The solution should work
+# appropriately with either graph.
+
+sample_graph = {
+    'Santa Ana': {
+        'Los Angeles': 5,
+        'Anaheim': 3,
+        'Palm Springs': 50
+    },
+    'Anaheim': {
+        'Los Angeles': 2,
+        'Santa Ana': 3
+    },
+    'Los Angeles': {
+        'Anaheim': 2,
+        'San Francisco': 25,
+        'Santa Ana': 5
+    },
+    'Palm Springs': {
+        'San Francisco': 30,
+        'Santa Ana': 50
+    },
+    'San Francisco': {
+        'Los Angeles': 25,
+        'Palm Springs': 30
+    }
+}
+
+
+def possible_paths(graph: dict[str, dict[str, int]],
+                   start: str,
+                   end: str):
+    # (path, total distance represented by path)
+    queue = [([start], 0)]
+    valid_paths = []
+
+    # appending to queue:
+    # append the new vertex to the path, add the distance to the total distance
+    # do not append to queue if in visited
+
+    while queue:
+        path, distance = queue.pop(0)
+        if path[-1] == end:
+            valid_paths.append((path, distance))
+        else:
+            for vertex, weight in graph[path[-1]].items():
+                # question: what can we do to improve time efficiency here?
+                if vertex not in path:
+                    new_path = path.copy()
+                    new_path.append(vertex)
+                    queue.append((new_path, distance + weight))
+
+    return valid_paths
+
+print(possible_paths(sample_graph, 'Santa Ana', 'San Francisco'))