mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-26 20:26:29 +08:00
55 lines
1.7 KiB
Python
55 lines
1.7 KiB
Python
"""
|
|
File: unbounded_knapsack.py
|
|
Created Time: 2023-07-10
|
|
Author: Krahets (krahets@163.com)
|
|
"""
|
|
|
|
|
|
def unbounded_knapsack_dp(wgt: list[int], val: list[int], cap: int) -> int:
|
|
"""完全背包：动态规划"""
|
|
n = len(wgt)
|
|
# 初始化 dp 表
|
|
dp = [[0] * (cap + 1) for _ in range(n + 1)]
|
|
# 状态转移
|
|
for i in range(1, n + 1):
|
|
for c in range(1, cap + 1):
|
|
if wgt[i - 1] > c:
|
|
# 若超过背包容量，则不选物品 i
|
|
dp[i][c] = dp[i - 1][c]
|
|
else:
|
|
# 不选和选物品 i 这两种方案的较大值
|
|
dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1])
|
|
return dp[n][cap]
|
|
|
|
|
|
def unbounded_knapsack_dp_comp(wgt: list[int], val: list[int], cap: int) -> int:
|
|
"""完全背包：空间优化后的动态规划"""
|
|
n = len(wgt)
|
|
# 初始化 dp 表
|
|
dp = [0] * (cap + 1)
|
|
# 状态转移
|
|
for i in range(1, n + 1):
|
|
# 正序遍历
|
|
for c in range(1, cap + 1):
|
|
if wgt[i - 1] > c:
|
|
# 若超过背包容量，则不选物品 i
|
|
dp[c] = dp[c]
|
|
else:
|
|
# 不选和选物品 i 这两种方案的较大值
|
|
dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])
|
|
return dp[cap]
|
|
|
|
|
|
"""Driver Code"""
|
|
if __name__ == "__main__":
|
|
wgt = [1, 2, 3]
|
|
val = [5, 11, 15]
|
|
cap = 4
|
|
|
|
# 动态规划
|
|
res = unbounded_knapsack_dp(wgt, val, cap)
|
|
print(f"不超过背包容量的最大物品价值为 {res}")
|
|
|
|
# 空间优化后的动态规划
|
|
res = unbounded_knapsack_dp_comp(wgt, val, cap)
|
|
print(f"不超过背包容量的最大物品价值为 {res}")
|