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49 lines
1.4 KiB
49 lines
1.4 KiB
import numpy as np
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def tsp_dp(distances):
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n = len(distances)
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dp = np.full((1 << n, n), np.inf)
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path = np.zeros((1 << n, n), dtype=int)
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for i in range(n):
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dp[1 << i][i] = 0
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for S in range(1, 1 << n):
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for j in range(n):
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if not (S & (1 << j)):
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continue
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for k in range(n):
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if k == j or not (S & (1 << k)):
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continue
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if dp[S][j] > dp[S - (1 << j)][k] + distances[k][j]:
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dp[S][j] = dp[S - (1 << j)][k] + distances[k][j]
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path[S][j] = k
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final_path = []
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S = (1 << n) - 1
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j = 0
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while S:
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final_path.append(j)
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k = path[S][j]
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S -= 1 << j
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j = k
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final_path.append(0)
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ans = float('inf')
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for j in range(n): # 枚举所有结束点
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if distances[j][0] != np.inf: # 如果结束点j与起点0相连
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ans = min(ans, dp[(1 << n) - 1][j] + distances[j][0])
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return ans, final_path
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# 示例使用
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distances = np.array([
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[np.inf, 50, 99, np.inf, 64, np.inf],
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[50, np.inf, 12, 45, 74, 13],
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[99, 12, np.inf, 25, np.inf, 61],
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[np.inf, 45, 25, np.inf, 45, 47],
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[64, 74, np.inf, 45, np.inf, np.inf],
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[np.inf, 13, 61, 47, np.inf, np.inf]
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])
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min_cost, min_path = tsp_dp(distances)
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print("Minimum cost:", min_cost)
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print("Minimum path:", min_path) |