prim算法python:实现Prim算法求解最小生成树

Prim算法是一种用于求解最小生成树(MST)的贪心算法。它的基本思想是:从一个顶点出发,每次找到最近的顶点,并将其加入到最小生成树中,直到所有的顶点都被加入到最小生成树中。

Prim算法是一种用于求解最小生成树(MST)的贪心算法。它的基本思想是:从一个顶点出发,每次找到最近的顶点,并将其加入到最小生成树中,直到所有的顶点都被加入到最小生成树中。

是使用Python实现Prim算法的代码:

# Python program for Prim's Minimum Spanning Tree (MST) algorithm.

# The program is for adjacency matrix representation of the graph

import sys # Library for INT_MAX

class Graph():

def __init__(self, vertices):

self.V = vertices

self.graph = [[0 for column in range(vertices)]

for row in range(vertices)]

# A utility function to print the constructed MST stored in parent[]

def printMST(self, parent):

print("Edge \tWeight")

for i in range(1, self.V):

print(parent[i], "-", i, "\t", self.graph[i][ parent[i] ] )

# A utility function to find the vertex with

# minimum distance value, from the set of vertices

# not yet included in shortest path tree

def minKey(self, key, mstSet):

# Initilaize min value

min = sys.maxsize

for v in range(self.V):

if key[v] < min and mstSet[v] == False:

min = key[v]

min_index = v

return min_index

# Function to construct and print MST for a graph

# represented using adjacency matrix representation

def primMST(self):

# Key values used to pick minimum weight edge in cut

key = [sys.maxsize] * self.V

parent = [None] * self.V # Array to store constructed MST

# Make key 0 so that this vertex is picked as first vertex

key[0] = 0

mstSet = [False] * self.V

parent[0] = -1 # First node is always the root of

for cout in range(self.V):

# Pick the minimum distance vertex from

# the set of vertices not yet processed.

# u is always equal to src in first iteration

u = self.minKey(key, mstSet)

# Put the minimum distance vertex in

# the shortest path tree

mstSet[u] = True

# Update dist value of the adjacent vertices

# of the picked vertex only if the current

# distance is greater than new distance and

# the vertex in not in the shotest path tree

for v in range(self.V):

# graph[u][v] is non zero only for adjacent vertices of m

# mstSet[v] is false for vertices not yet included in MST

# Update the key only if graph[u][v] is smaller than key[v]

if self.graph[u][v] > 0 and mstSet[v] == False and key[v] > self.graph[u][v]:

key[v] = self.graph[u][v]

parent[v] = u

self.printMST(parent)

g = Graph(5)

g.graph = [ [0, 2, 0, 6, 0],

[2, 0, 3,

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