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https://github.com/TheAlgorithms/Python.git
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122 lines
4.0 KiB
Python
122 lines
4.0 KiB
Python
from __future__ import annotations
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from typing import Generic, TypeVar
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T = TypeVar("T")
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class DisjointSetTreeNode(Generic[T]):
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# Disjoint Set Node to store the parent and rank
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def __init__(self, data: T) -> None:
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self.data = data
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self.parent = self
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self.rank = 0
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class DisjointSetTree(Generic[T]):
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# Disjoint Set DataStructure
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def __init__(self) -> None:
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# map from node name to the node object
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self.map: dict[T, DisjointSetTreeNode[T]] = {}
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def make_set(self, data: T) -> None:
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# create a new set with x as its member
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self.map[data] = DisjointSetTreeNode(data)
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def find_set(self, data: T) -> DisjointSetTreeNode[T]:
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# find the set x belongs to (with path-compression)
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elem_ref = self.map[data]
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if elem_ref != elem_ref.parent:
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elem_ref.parent = self.find_set(elem_ref.parent.data)
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return elem_ref.parent
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def link(
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self, node1: DisjointSetTreeNode[T], node2: DisjointSetTreeNode[T]
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) -> None:
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# helper function for union operation
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if node1.rank > node2.rank:
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node2.parent = node1
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else:
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node1.parent = node2
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if node1.rank == node2.rank:
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node2.rank += 1
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def union(self, data1: T, data2: T) -> None:
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# merge 2 disjoint sets
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self.link(self.find_set(data1), self.find_set(data2))
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class GraphUndirectedWeighted(Generic[T]):
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def __init__(self) -> None:
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# connections: map from the node to the neighbouring nodes (with weights)
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self.connections: dict[T, dict[T, int]] = {}
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def add_node(self, node: T) -> 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: T, node2: T, 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[T]:
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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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>>> g1 = GraphUndirectedWeighted[int]()
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>>> g1.add_edge(1, 2, 1)
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>>> g1.add_edge(2, 3, 2)
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>>> g1.add_edge(3, 4, 1)
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>>> g1.add_edge(3, 5, 100) # Removed in MST
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>>> g1.add_edge(4, 5, 5)
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>>> assert 5 in g1.connections[3]
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>>> mst = g1.kruskal()
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>>> assert 5 not in mst.connections[3]
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>>> g2 = GraphUndirectedWeighted[str]()
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>>> g2.add_edge('A', 'B', 1)
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>>> g2.add_edge('B', 'C', 2)
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>>> g2.add_edge('C', 'D', 1)
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>>> g2.add_edge('C', 'E', 100) # Removed in MST
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>>> g2.add_edge('D', 'E', 5)
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>>> assert 'E' in g2.connections["C"]
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>>> mst = g2.kruskal()
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>>> assert 'E' not in mst.connections['C']
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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[T]()
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for node in self.connections:
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disjoint_set.make_set(node)
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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[T]()
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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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parent_u = disjoint_set.find_set(u)
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parent_v = disjoint_set.find_set(v)
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if parent_u != parent_v:
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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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