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110 lines
3.4 KiB
Python
110 lines
3.4 KiB
Python
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from __future__ import annotations
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class DisjointSetTreeNode:
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# Disjoint Set Node to store the parent and rank
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def __init__(self, key: int) -> None:
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self.key = key
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self.parent = self
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self.rank = 0
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class DisjointSetTree:
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# Disjoint Set DataStructure
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def __init__(self):
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# map from node name to the node object
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self.map = {}
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def make_set(self, x: int) -> None:
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# create a new set with x as its member
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self.map[x] = DisjointSetTreeNode(x)
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def find_set(self, x: int) -> DisjointSetTreeNode:
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# find the set x belongs to (with path-compression)
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elem_ref = self.map[x]
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if elem_ref != elem_ref.parent:
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elem_ref.parent = self.find_set(elem_ref.parent.key)
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return elem_ref.parent
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def link(self, x: int, y: int) -> None:
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# helper function for union operation
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if x.rank > y.rank:
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y.parent = x
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else:
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x.parent = y
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if x.rank == y.rank:
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y.rank += 1
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def union(self, x: int, y: int) -> None:
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# merge 2 disjoint sets
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self.link(self.find_set(x), self.find_set(y))
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class GraphUndirectedWeighted:
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def __init__(self):
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# connections: map from the node to the neighbouring nodes (with weights)
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self.connections = {}
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def add_node(self, node: int) -> None:
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# add a node ONLY if its not present in the graph
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if node not in self.connections:
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self.connections[node] = {}
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def add_edge(self, node1: int, node2: int, weight: int) -> None:
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# add an edge with the given weight
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self.add_node(node1)
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self.add_node(node2)
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self.connections[node1][node2] = weight
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self.connections[node2][node1] = weight
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def kruskal(self) -> GraphUndirectedWeighted:
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# Kruskal's Algorithm to generate a Minimum Spanning Tree (MST) of a graph
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"""
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Details: https://en.wikipedia.org/wiki/Kruskal%27s_algorithm
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Example:
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>>> graph = GraphUndirectedWeighted()
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>>> graph.add_edge(1, 2, 1)
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>>> graph.add_edge(2, 3, 2)
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>>> graph.add_edge(3, 4, 1)
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>>> graph.add_edge(3, 5, 100) # Removed in MST
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>>> graph.add_edge(4, 5, 5)
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>>> assert 5 in graph.connections[3]
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>>> mst = graph.kruskal()
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>>> assert 5 not in mst.connections[3]
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"""
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# getting the edges in ascending order of weights
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edges = []
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seen = set()
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for start in self.connections:
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for end in self.connections[start]:
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if (start, end) not in seen:
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seen.add((end, start))
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edges.append((start, end, self.connections[start][end]))
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edges.sort(key=lambda x: x[2])
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# creating the disjoint set
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disjoint_set = DisjointSetTree()
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[disjoint_set.make_set(node) for node in self.connections]
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# MST generation
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num_edges = 0
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index = 0
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graph = GraphUndirectedWeighted()
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while num_edges < len(self.connections) - 1:
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u, v, w = edges[index]
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index += 1
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parentu = disjoint_set.find_set(u)
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parentv = disjoint_set.find_set(v)
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if parentu != parentv:
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num_edges += 1
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graph.add_edge(u, v, w)
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disjoint_set.union(u, v)
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return graph
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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