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83 lines
1.8 KiB
Python
83 lines
1.8 KiB
Python
"""
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Prim's Algorithm.
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Determines the minimum spanning tree(MST) of a graph using the Prim's Algorithm
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Create a list to store x the vertices.
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G = [vertex(n) for n in range(x)]
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For each vertex in G, add the neighbors:
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G[x].addNeighbor(G[y])
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G[y].addNeighbor(G[x])
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For each vertex in G, add the edges:
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G[x].addEdge(G[y], w)
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G[y].addEdge(G[x], w)
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To solve run:
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MST = prim(G, G[0])
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"""
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import math
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class vertex():
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"""Class Vertex."""
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def __init__(self, id):
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"""
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Arguments:
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id - input an id to identify the vertex
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Attributes:
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neighbors - a list of the vertices it is linked to
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edges - a dict to store the edges's weight
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"""
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self.id = str(id)
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self.key = None
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self.pi = None
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self.neighbors = []
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self.edges = {} # [vertex:distance]
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def __lt__(self, other):
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"""Comparison rule to < operator."""
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return (self.key < other.key)
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def __repr__(self):
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"""Return the vertex id."""
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return self.id
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def addNeighbor(self, vertex):
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"""Add a pointer to a vertex at neighbor's list."""
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self.neighbors.append(vertex)
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def addEdge(self, vertex, weight):
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"""Destination vertex and weight."""
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self.edges[vertex.id] = weight
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def prim(graph, root):
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"""
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Prim's Algorithm.
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Return a list with the edges of a Minimum Spanning Tree
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prim(graph, graph[0])
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"""
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A = []
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for u in graph:
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u.key = math.inf
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u.pi = None
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root.key = 0
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Q = graph[:]
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while Q:
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u = min(Q)
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Q.remove(u)
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for v in u.neighbors:
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if (v in Q) and (u.edges[v.id] < v.key):
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v.pi = u
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v.key = u.edges[v.id]
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for i in range(1, len(graph)):
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A.append([graph[i].id, graph[i].pi.id])
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return(A)
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