From bdedd2df0f256b3b5d2c489fb558e92563822ce6 Mon Sep 17 00:00:00 2001 From: jianghongcheng <35664721+jianghongcheng@users.noreply.github.com> Date: Mon, 5 Jun 2023 07:46:22 -0500 Subject: [PATCH] =?UTF-8?q?Update=20=E8=83=8C=E5=8C=85=E9=97=AE=E9=A2=98?= =?UTF-8?q?=E7=90=86=E8=AE=BA=E5=9F=BA=E7=A1=80=E5=A4=9A=E9=87=8D=E8=83=8C?= =?UTF-8?q?=E5=8C=85.md?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../背包问题理论基础多重背包.md | 134 ++++++++++++++---- 1 file changed, 103 insertions(+), 31 deletions(-) diff --git a/problems/背包问题理论基础多重背包.md b/problems/背包问题理论基础多重背包.md index af10dab7..1a856bf5 100644 --- a/problems/背包问题理论基础多重背包.md +++ b/problems/背包问题理论基础多重背包.md @@ -194,55 +194,127 @@ public void testMultiPack2(){ Python: +改变物品数量为01背包格式(无参版) ```python -def test_multi_pack1(): - '''版本一:改变物品数量为01背包格式''' +def test_multi_pack(): weight = [1, 3, 4] value = [15, 20, 30] nums = [2, 3, 2] - bag_weight = 10 + bagWeight = 10 + + # 将数量大于1的物品展开 for i in range(len(nums)): - # 将物品展开数量为1 while nums[i] > 1: weight.append(weight[i]) value.append(value[i]) nums[i] -= 1 - - dp = [0]*(bag_weight + 1) - # 遍历物品 - for i in range(len(weight)): - # 遍历背包 - for j in range(bag_weight, weight[i] - 1, -1): + + dp = [0] * (bagWeight + 1) + for i in range(len(weight)): # 遍历物品 + for j in range(bagWeight, weight[i] - 1, -1): # 遍历背包容量 dp[j] = max(dp[j], dp[j - weight[i]] + value[i]) - - print(" ".join(map(str, dp))) + for j in range(bagWeight + 1): + print(dp[j], end=" ") + print() -def test_multi_pack2(): - '''版本:改变遍历个数''' - weight = [1, 3, 4] - value = [15, 20, 30] - nums = [2, 3, 2] - bag_weight = 10 - - dp = [0]*(bag_weight + 1) - for i in range(len(weight)): - for j in range(bag_weight, weight[i] - 1, -1): - # 以上是01背包,加上遍历个数 - for k in range(1, nums[i] + 1): - if j - k*weight[i] >= 0: - dp[j] = max(dp[j], dp[j - k*weight[i]] + k*value[i]) - - print(" ".join(map(str, dp))) + print(dp[bagWeight]) -if __name__ == '__main__': - test_multi_pack1() - test_multi_pack2() +test_multi_pack() + ``` +改变遍历个数(无参版) +```python +def test_multi_pack(): + weight = [1, 3, 4] + value = [15, 20, 30] + nums = [2, 3, 2] + bagWeight = 10 + dp = [0] * (bagWeight + 1) + + for i in range(len(weight)): # 遍历物品 + for j in range(bagWeight, weight[i] - 1, -1): # 遍历背包容量 + # 以上为01背包,然后加一个遍历个数 + for k in range(1, nums[i] + 1): # 遍历个数 + if j - k * weight[i] >= 0: + dp[j] = max(dp[j], dp[j - k * weight[i]] + k * value[i]) + + # 打印一下dp数组 + for j in range(bagWeight + 1): + print(dp[j], end=" ") + print() + + print(dp[bagWeight]) +test_multi_pack() + +``` + + +改变物品数量为01背包格式(有参版) +```python +def test_multi_pack(weight, value, nums, bagWeight): + # 将数量大于1的物品展开 + for i in range(len(nums)): + while nums[i] > 1: + weight.append(weight[i]) + value.append(value[i]) + nums[i] -= 1 + + dp = [0] * (bagWeight + 1) + for i in range(len(weight)): # 遍历物品 + for j in range(bagWeight, weight[i] - 1, -1): # 遍历背包容量 + dp[j] = max(dp[j], dp[j - weight[i]] + value[i]) + for j in range(bagWeight + 1): + print(dp[j], end=" ") + print() + + print(dp[bagWeight]) + + + + +if __name__ == "__main__": + weight = [1, 3, 4] + value = [15, 20, 30] + nums = [2, 3, 2] + bagWeight = 10 + test_multi_pack(weight, value, nums, bagWeight) +``` + + +改变遍历个数(有参版) +```python +def test_multi_pack(weight, value, nums, bagWeight): + dp = [0] * (bagWeight + 1) + + for i in range(len(weight)): # 遍历物品 + for j in range(bagWeight, weight[i] - 1, -1): # 遍历背包容量 + # 以上为01背包,然后加一个遍历个数 + for k in range(1, nums[i] + 1): # 遍历个数 + if j - k * weight[i] >= 0: + dp[j] = max(dp[j], dp[j - k * weight[i]] + k * value[i]) + + # 使用 join 函数打印 dp 数组 + print(' '.join(str(dp[j]) for j in range(bagWeight + 1))) + + print(dp[bagWeight]) + + + + + +if __name__ == "__main__": + weight = [1, 3, 4] + value = [15, 20, 30] + nums = [2, 3, 2] + bagWeight = 10 + test_multi_pack(weight, value, nums, bagWeight) + +``` Go: ```go