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Prims Algorithm - Greedy Method
Explanation
Prim's algorithm is a greedy algorithm that finds the minimum spanning tree of a weighted,
undirected graph
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Prim's algorithm works by starting with a single vertex and then growing the tree by adding the
edge with the minimum weight that connects the tree to a new vertex
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Algorithm

1
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2
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 Add the edge to the minimum spanning tree
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3
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Code
Here is an implementation of Prim's algorithm in Python:
Python
def prims(graph):
mst = set([graph[0]])
visited = set([graph[0]])

while len(visited) < len(graph):
current = min(

(v for v in visited if v not in mst),
key=lambda v: min(weight for u, weight in graph[v]
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add(current)
visited
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items():
if neighbor not in visited and weight < min(
edge[1] for edge in mst if edge[0] == current):
mst
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The algorithm starts with the vertex A and then adds the edge with the minimum weight, which
is the edge from A to B with weight 2
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The minimum spanning tree of
this graph is the tree with edges AB, BC, and CD
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This is because the algorithm needs to sort
the edges in the graph at each step, which takes O(E log V) time
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 It is also a greedy algorithm, which means that it always finds a feasible solution to the
problem
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This is because the
algorithm needs to sort the edges in the graph at each step
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If the graph is not connected, then the algorithm will not terminate
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 Finding the minimum cost of connecting a set of cities with flights
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Prim's algorithm is also used in a variety of other applications, such as:
 Natural language processing
 Robotics
 Operations research



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