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Prim algorithm using numpy array functions
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import numpy as np | |
def prim_np(weights, node1, node2): | |
"""Prim's algorithm is a greedy algorithm that | |
finds a minimum spanning tree for a weighted undirected graph. | |
1. Initialize a tree with a single vertex, | |
chosen arbitrarily from the graph. | |
2. Grow the tree by one edge: of the edges that connect the tree to | |
vertices not yet in the tree, find the minimum-weight edge, | |
and transfer it to the tree. | |
3. Repeat step 2 (until all vertices are in the tree). | |
Inputs: | |
weights, heads, tails: list of numbers (not np arrays) | |
""" | |
w_indexes = np.array([i for i in range(len(weights))]) | |
edges_in = [False] * len(weights) | |
# Using sets for storing the vectors of the tree | |
rem_nodes = set(list(node1)+list(node2)) | |
has_nodes = set([node1[0]]) | |
rem_nodes.remove(node1[0]) | |
while len(rem_nodes)>0: | |
# Selecting the edges between the tree and the remaining vertices. | |
has_node1 = np.isin(node1, list(has_nodes)) | |
has_node2 = np.isin(node2, list(has_nodes)) | |
between_edges = np.not_equal(has_node1,has_node2) | |
# Selecting the minimum weight edge. | |
w = weights[between_edges] | |
w_i = w_indexes[between_edges] | |
n_edge = w_i[np.argmin(w)] | |
# Select the new node and add it to the tree vertices. | |
n_node = node2[n_edge] if node1[n_edge] in has_nodes else node1[n_edge] | |
has_nodes.add(n_node) | |
rem_nodes.remove(n_node) | |
edges_in[n_edge] = True | |
return edges_in | |
def build_arrays(V, G): | |
"""Build arrays for np array prim from graph: | |
Input: | |
V: Number of nodes | |
G: edges [h,t,w]: head - tail, weight | |
Output: | |
weights: list of weights | |
heads: list of first nodes | |
tails: list of last nodes""" | |
Gn = np.array(G) | |
return Gn[:,2], Gn[:,0], Gn[:,1] |
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