72 lines
2.4 KiB
Python
72 lines
2.4 KiB
Python
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# Implementation of the count-and-label
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# connected component counting algorithm.
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#
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# Author: John Bowers
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# Version: Mar 17, 2021
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# March 2022 -- molloykp
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# Changed code to label components starting a 0 (instead of 1)
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# October 2023 -- molloykp
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# Change code to accept new adj list/hash map structure
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# Version of the iterative dfs that takes as input
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# a list of labels, one per vertex, and a starting
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# vertex v and uses iterative depth-first-search
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# to label each vertex with a given currentLabel
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#
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# Parameters:
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# * graph is an adjaceny list where vertices name/keys are stored
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# in a dictionary. Each vertex has its own dictionary
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# where the key is the edge endpoint and the value is the
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# weight of the edge.
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# * v is the vertex to DFS from
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# * labels is an array of length V which is -1 if the vertex is unvisited
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# * currentLabel is the label to set on every visited vertex
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#
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# labels is an out-parameter and will be modified destructively during the
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# run of this operation.
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#
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def dfs_label(graph, v, labels, currentLabel):
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bag = [v]
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while bag: # while bag is not empty
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u = bag.pop()
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if labels[u] == -1:
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labels[u] = currentLabel
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for w in graph[u]:
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bag.append(w)
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# Counts the number of connected components in the graph
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# and labels each vertex with its connected component index
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#
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# Parameters:
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# * graph given as an adjaceny list/set structure with vertices 0..(n-1)
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#
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# Returns:
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# count, labels
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# where count is the number of connected components in the graph
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# and labels is the labeling of each vertex's connected component
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# starting from index 0
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def count_and_label(graph):
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labels = [-1 for _ in range(len(graph))] # Initially all labels are -1
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count = -1
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for v in range(len(graph)): # for each vertex
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if labels[v] == -1: # if v is not visited
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count += 1
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dfs_label(graph, v, labels, count)
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return count+1, labels
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if __name__ == "__main__":
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graph = {
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0: {1:2}, # 0's neighbors
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1: {0:2, 2:4, 3:1}, # 1's neighbors
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2: {1:4, 3:5}, # 2's neighbors
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3: {1:1, 2:5}, # 3's neighbors
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4: {5:8}, # 4's neighbors
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5: {4:8} # 5's neighbors
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}
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count, labels = count_and_label(graph)
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print(f"Number of connected components: {count}")
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print(f"Vertex labels: {labels}")
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