Add Prim's algorithm implementation (using Priority Queue)

Implement Prim's algorithm to find the minimum spanning tree of a graph using a priority queue.

Author: laiba-Ashfaq

data_structures/Prim’s-Algorithm.py

@@ -0,0 +1,37 @@
+import heapq
+
+def prim_mst(graph, start=0):
+    visited = set()
+    mst = []
+    total_cost = 0
+
+    # Min-heap (cost, current_node, next_node)
+    edges = [(0, start, start)]
+
+    while edges:
+        cost, u, v = heapq.heappop(edges)
+        if v in visited:
+            continue
+        visited.add(v)
+        total_cost += cost
+        if u != v:
+            mst.append((u, v, cost))
+        for neighbor, weight in graph[v]:
+            if neighbor not in visited:
+                heapq.heappush(edges, (weight, v, neighbor))
+
+    return mst, total_cost
+
+
+# Example Graph as adjacency list
+graph = {
+    0: [(1, 2), (3, 6)],
+    1: [(0, 2), (2, 3), (3, 8), (4, 5)],
+    2: [(1, 3), (4, 7)],
+    3: [(0, 6), (1, 8)],
+    4: [(1, 5), (2, 7)]
+}
+
+mst, cost = prim_mst(graph)
+print("Edges in MST:", mst)
+print("Total Cost:", cost)