76 lines
3.0 KiB
Python
76 lines
3.0 KiB
Python
#!/usr/bin/env python3
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# -*- coding: utf-8 -*-
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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# IMPORTS
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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from src.thirdparty.types import *;
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from src.thirdparty.maths import *;
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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# EXPORTS
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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__all__ = [
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'tsp_algorithm',
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];
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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# METHOD tsp_algorithm
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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def tsp_algorithm(
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dist: np.ndarray, # NDArray[(Any, Any), float],
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optimise = min,
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verbose: bool = False,
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) -> tuple[float, list[list[int]]]:
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m, n = dist.shape[:2];
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assert m == n;
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memory: Dict[tuple[int, tuple], tuple[float, list[list[int]]]] = dict();
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def g(i: int, S: list[int]) -> tuple[float, list[list[int]]]:
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# wenn g bereits für den Input definiert ist, gib diesen Wert zurück:
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if (i, tuple(S)) not in memory.keys():
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if len(S) == 0:
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paths = [[i]] if i == 0 else [[i, 0]];
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memory[(i, tuple(S))] = (dist[i,0], paths);
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else:
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values_and_paths = [ (j, *g(j, (*S[:index], *S[(index+1):]))) for index, j in enumerate(S) ];
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# berechne d(i,j) + g(j, S \ {i}) for each j in S:
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values_and_paths = [ (j, dist[i,j] + value, paths) for j, value, paths in values_and_paths];
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value = optimise([value for _, value, _ in values_and_paths]);
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paths = [];
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for j, value_, paths_ in values_and_paths:
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if value_ == value:
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paths += [ [i, *path] for path in paths_ ];
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memory[(i, tuple(S))] = (value, paths);
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return memory[(i, tuple(S))];
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# berechne g(0, {1,2,...,n-1}):
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optimal_wert = g(0, [i for i in range(1,n)]);
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if verbose:
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display_computation(n, memory);
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return optimal_wert, [];
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def display_computation(n: int, memory: Dict[tuple[int, tuple], tuple[float, list[list[int]]]]):
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keys = sorted(memory.keys(), key=lambda key: (len(key[1]), key[0], key[1]));
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addone = lambda x: x + 1;
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for k in range(0,n):
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print(f'\x1b[4;1m|S| = {k}:\x1b[0m');
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for (i, S) in keys:
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if len(S) != k:
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continue;
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value, paths = memory[(i, S)];
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print(f'g({addone(i)}, {list(map(addone, S))}) = {value}');
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if len(paths) == 1:
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print(f'optimal way: {" -> ".join(map(str, map(addone, paths[0])))}');
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else:
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print('optimal ways:');
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for path in paths:
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print(f'* {" -> ".join(map(str, map(addone, path)))}');
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print('');
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return;
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