90 lines
2.1 KiB
Python
90 lines
2.1 KiB
Python
from dataclasses import dataclass
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from typing import List
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@dataclass
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class Edge:
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weight: int
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source_id: int
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target_id: int
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@dataclass
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class Vertex:
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id: int
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edges: List[Edge]
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def load_matrix(filename):
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def line_to_row(line):
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r = []
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for field in line.strip().split(","):
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if field == "-":
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r.append(0)
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else:
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r.append(int(field))
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return r
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with open(filename, "r") as f:
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m = [line_to_row(l) for l in f]
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return m
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def matrix_to_graph(matrix):
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n_nodes = len(matrix)
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graph = []
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for row_index in range(n_nodes):
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edges = []
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for col_index in range(n_nodes):
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weight = matrix[row_index][col_index]
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if weight != 0:
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edges.append(Edge(weight, row_index, col_index))
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graph.append(Vertex(row_index, edges))
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return graph
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def total_weight(graph):
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total_weight = 0
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for vertex in graph:
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for edge in vertex.edges:
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total_weight += edge.weight
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total_weight //= 2
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return total_weight
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def prims_algo(graph):
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""" Takes a graph and returns the edges that for a minimum spanning tree
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for that graph. """
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visited_id = set([0])
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min_edges = []
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while len(visited_id) != len(graph):
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min_edge = None
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for vertex_id in visited_id:
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vertex = graph[vertex_id]
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for edge in vertex.edges:
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if edge.target_id in visited_id:
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pass
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elif min_edge is None:
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min_edge = edge
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elif edge.weight < min_edge.weight:
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min_edge = edge
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visited_id.add(min_edge.target_id)
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min_edges.append(min_edge)
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return min_edges
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def euler_107():
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m = load_matrix("../txt/e107.txt")
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g = matrix_to_graph(m)
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weight = total_weight(g)
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new_weight = sum([e.weight for e in prims_algo(g)])
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return weight - new_weight
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if __name__ == "__main__":
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solution = euler_107()
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print("e107.py: " + str(solution))
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assert(solution == 259679)
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