Railroad Construction: Added initial boilerplate

Railroad-Construction/connected_components.py

@@ -0,0 +1,71 @@
+# Implementation of the count-and-label 
+# connected component counting algorithm.
+#
+# Author: John Bowers
+# Version: Mar 17, 2021
+
+# March 2022 -- molloykp
+#  Changed code to label components starting a 0 (instead of 1)
+# October 2023 -- molloykp
+#  Change code to accept new adj list/hash map structure
+
+# Version of the iterative dfs that takes as input
+# a list of labels, one per vertex, and a starting 
+# vertex v and uses iterative depth-first-search
+# to label each vertex with a given currentLabel
+# 
+# Parameters: 
+#   * graph is an adjaceny list where vertices name/keys are stored
+#     in a dictionary.  Each vertex has its own dictionary
+#     where the key is the edge endpoint and the value is the
+#     weight of the edge.
+#   * v is the vertex to DFS from
+#   * labels is an array of length V which is -1 if the vertex is unvisited
+#   * currentLabel is the label to set on every visited vertex
+#
+# labels is an out-parameter and will be modified destructively during the 
+# run of this operation. 
+#
+
+def dfs_label(graph, v, labels, currentLabel):
+    bag = [v]
+    while bag: # while bag is not empty
+        u = bag.pop()
+        if labels[u] == -1:
+            labels[u] = currentLabel
+            for w in graph[u]:
+                bag.append(w)
+
+# Counts the number of connected components in the graph
+# and labels each vertex with its connected component index
+#
+# Parameters:
+#   * graph given as an adjaceny list/set structure with vertices 0..(n-1)
+#
+# Returns: 
+#   count, labels
+#   where count is the number of connected components in the graph
+#   and labels is the labeling of each vertex's connected component
+#   starting from index 0 
+def count_and_label(graph):
+    labels = [-1 for _ in range(len(graph))] # Initially all labels are -1
+    count = -1
+    for v in range(len(graph)): # for each vertex
+        if labels[v] == -1: # if v is not visited
+            count += 1
+            dfs_label(graph, v, labels, count)
+    return count+1, labels
+
+if __name__ == "__main__":
+    graph = {
+        0: {1:2},           # 0's neighbors
+        1: {0:2, 2:4, 3:1}, # 1's neighbors
+        2: {1:4, 3:5},      # 2's neighbors
+        3: {1:1, 2:5},      # 3's neighbors
+        4: {5:8},           # 4's neighbors
+        5: {4:8}            # 5's neighbors
+    }
+
+    count, labels = count_and_label(graph)
+    print(f"Number of connected components: {count}")
+    print(f"Vertex labels: {labels}")