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Add Prim's algorithm implementation (using Priority Queue) #13414

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Add Prim's algorithm implementation (using Priority Queue)
laiba-Ashfaq Oct 10, 2025
8317b78
[pre-commit.ci] auto fixes from pre-commit.com hooks
pre-commit-ci[bot] Oct 10, 2025
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37 changes: 37 additions & 0 deletions data_structures/Prim’s-Algorithm.py
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import heapq

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data_structures/Prim’s-Algorithm.py:1:1: I001 Import block is un-sorted or un-formatted

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data_structures/Prim’s-Algorithm.py:1:1: N999 Invalid module name: 'Prim’s-Algorithm'

def prim_mst(graph, start=0):
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@algorithms-keeper algorithms-keeper bot Oct 10, 2025

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As there is no test file in this pull request nor any test function or class in the file data_structures/Prim’s-Algorithm.py, please provide doctest for the function prim_mst

Please provide return type hint for the function: prim_mst. If the function does not return a value, please provide the type hint as: def function() -> None:

Please provide type hint for the parameter: graph

Please provide type hint for the parameter: start

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)
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