Add lab/quiz 5 work

Labs/5/5.py

@@ -0,0 +1,53 @@
+import heapq
+
+def dijkstra_verbose(graph, start):
+    distances = {node: float('inf') for node in graph}
+    distances[start] = 0
+    pq = [(0, start)]
+    step = 0
+
+    print(f"\n--- Dijkstra's Algorithm from Node {start} ---\n")
+    print(f"Initial distances: {distances}")
+
+    while pq:
+        current_distance, current_node = heapq.heappop(pq)
+        print(f"\nStep {step}: Visiting node {current_node} with current distance {current_distance}")
+
+        if current_distance > distances[current_node]:
+            print("\tSkipping since a shorter path is already found.")
+            continue
+
+        for neighbor, weight in graph[current_node].items():
+            distance = current_distance + weight
+            if distance < distances[neighbor]:
+                old_distance = distances[neighbor]
+                distances[neighbor] = distance
+                heapq.heappush(pq, (distance, neighbor))
+                print(f"\tUpdating distance to node {neighbor}: {old_distance} -> {distance}")
+            else:
+                print(f"\tNo update required for node {neighbor} (current: {distances[neighbor]}, new: {distance})")
+
+        print(f"Distances after step {step}: {distances}")
+        step += 1
+
+    print(f"\nFinal shortest distances from node {start}: {distances}")
+    return distances
+
+# Compute SSSPT for each node and print the steps
+graph = {
+    0: {1: 3, 2: 1},
+    1: {3: 2},
+    2: {1: 1, 4: 5, 5: 5},
+    3: {2: 4, 4: 3},
+    4: {5: 1, 6: 3},
+    5: {6: 1, 7: 4},
+    6: {7: 1},
+    7: {}
+}
+
+#Compute SSSPT for each node and print the steps
+#for node in graph:
+#    dijkstra_verbose(graph, node)
+
+# Compute SSSPT for a specific node and print the steps
+dijkstra_verbose(graph, 0)