回溯法求解tsp问题python代码
时间: 2024-06-30 11:01:11 浏览: 8
回溯法是一种常见的搜索算法,常用于解决旅行商问题(Traveling Salesman Problem, TSP)等组合优化问题。在Python中,我们可以使用递归的方式来实现回溯法求解TSP。以下是一个简单的例子:
```python
import itertools
def tsp(cities, start):
def is_valid(permutation):
return sum(city_distances[permutation[i-1]][permutation[i]] for i in range(1, len(permutation))) == 0
def find_min_distance(permutation, last_city):
nonlocal best_distance
if last_city == len(permutation) - 1:
return city_distances[permutation][last_city]
else:
min_distance = float('inf')
for next_city in range(last_city + 1, len(cities)):
new_permutation = permutation.copy()
new_permutation.append(next_city)
if is_valid(new_permutation):
min_distance = min(min_distance, find_min_distance(new_permutation, next_city))
return min_distance
# 城市之间的距离矩阵
city_distances = [[cities[i][j] for j in cities] for i in cities]
best_distance = float('inf')
best_path = None
for permutation in itertools.permutations(range(len(cities)), len(cities)):
if is_valid(permutation):
distance = find_min_distance(permutation, 0)
if distance < best_distance:
best_distance = distance
best_path = permutation
return best_distance, [cities[i][j] for i, j in zip(best_path[:-1], best_path[1:])]
# 示例用法
cities = [
[(0, 0), (1, 0)],
[(1, 0), (2, 0)],
[(2, 0), (3, 0)]
] # 假设这是三个城市的位置
start_city = 0
best_distance, optimal_path = tsp(cities, start_city)
print(f"最优路径总距离: {best_distance}")
print(f"最优路径: {optimal_path}")
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