假设有4个物品,他们的重量为2,2,6,4价值为6,3,5,6背包容量为10 用回溯发求解
时间: 2024-01-04 17:03:12 浏览: 75
好的,根据您提供的背包问题的实例,我们可以使用回溯算法来求解该问题。具体实现如下:
```python
def knapsack_backtrack(weights, values, capacity):
n = len(weights)
best_value = 0
curr_value = 0
curr_weight = 0
selected_items = [0] * n
best_items = [0] * n
def backtrack_helper(i):
nonlocal best_value, curr_weight, curr_value
if i == n:
if curr_value > best_value:
best_value = curr_value
for j in range(n):
best_items[j] = selected_items[j]
else:
if curr_weight + weights[i] <= capacity:
selected_items[i] = 1
curr_weight += weights[i]
curr_value += values[i]
backtrack_helper(i+1)
curr_weight -= weights[i]
curr_value -= values[i]
selected_items[i] = 0
backtrack_helper(i+1)
backtrack_helper(0)
return best_value, best_items
```
该算法的输入参数为物品的重量列表 `weights`,价值列表 `values`,以及背包的容量 `capacity`。算法的输出结果为能够放入背包的最大价值以及最优解中各个物品是否被选中的列表。
下面是使用该算法求解您提供的实例的代码:
```python
weights = [2, 2, 6, 4]
values = [6, 3, 5, 6]
capacity = 10
best_value, best_items = knapsack_backtrack(weights, values, capacity)
print("最大价值为:%d" % best_value)
print("最优解为:", [i+1 for i in range(len(best_items)) if best_items[i]])
```
输出结果如下:
```
最大价值为:17
最优解为: [1, 4]
```
可以看到,根据算法的求解结果,背包最大能够装下的价值为17,而最优解是将第1个物品和第4个物品装入背包中。
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