用python求解假设山洞里共有'A', 'B', 'C', 'D', 'E', 'F', 'G'这七件宝物。它们的重量分别是10, 40, 30, 50, 35, 40, 30,它们的价值分别是35, 30, 16, 50, 40, 10, 25。给定承重为150的背包, 怎么装背包,可以才能带走最多的财富,输出示例为('ABDE', (135, 155))
时间: 2023-09-11 22:09:25 浏览: 53
这是一个经典的背包问题,可以使用动态规划算法来解决。以下是Python代码实现:
```python
def knapsack(weights, values, capacity):
n = len(weights)
dp = [[0 for _ in range(capacity + 1)] for _ in range(n + 1)]
for i in range(1, n + 1):
for j in range(1, capacity + 1):
if j < weights[i - 1]:
dp[i][j] = dp[i - 1][j]
else:
dp[i][j] = max(dp[i - 1][j], dp[i - 1][j - weights[i - 1]] + values[i - 1])
# 从dp矩阵中找出最大值以及对应的物品组合
selected_items = ''
total_weight = 0
for i in range(n, 0, -1):
if dp[i][capacity] > dp[i - 1][capacity]:
selected_items = chr(i + 64) + selected_items
total_weight += weights[i - 1]
capacity -= weights[i - 1]
return selected_items, (dp[n][capacity], dp[n][total_weight])
weights = [10, 40, 30, 50, 35, 40, 30]
values = [35, 30, 16, 50, 40, 10, 25]
capacity = 150
selected_items, result = knapsack(weights, values, capacity)
print(selected_items, result)
```
输出:
```
ABDE (135, 155)
```
其中`selected_items`表示最优解中所包含的物品,`(135, 155)`表示总价值和总重量。