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: 2023-12-25 09:04:15 浏览: 73
好的,那么我们可以先定义一个背包问题的解决函数,使用回溯法进行求解:
```python
def knapsack_backtracking(capacity, weights, values):
n = len(weights)
max_value = float('-inf') # 初始化最大价值为负无穷
current_weight, current_value = 0, 0 # 初始化当前重量和当前价值为0
def backtrack(i):
nonlocal max_value, current_weight, current_value
# 如果已经遍历过所有物品,更新最大价值
if i == n:
max_value = max(max_value, current_value)
return
# 如果当前物品的重量加上背包中已有物品的重量小于等于背包容量,可以选择放入背包
if current_weight + weights[i] <= capacity:
current_weight += weights[i]
current_value += values[i]
backtrack(i+1)
# 回溯,不放入当前物品
current_weight -= weights[i]
current_value -= values[i]
# 回溯,不放入当前物品
backtrack(i+1)
# 从第一个物品开始遍历
backtrack(0)
return max_value
```
使用给定的数据进行测试:
```python
weights = [2, 2, 6, 4]
values = [6, 3, 5, 6]
capacity = 10
max_value = knapsack_backtracking(capacity, weights, values)
print(max_value) # 输出最大价值
```
输出结果为:
```
15
```
因此,在背包容量为10的情况下,最大价值为15。
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