From 0bafb2d775466d18eec6b142163657ffe3a66b05 Mon Sep 17 00:00:00 2001 From: Kelvin Date: Tue, 15 Jun 2021 21:05:09 -0400 Subject: [PATCH 1/4] =?UTF-8?q?=E6=9B=B4=E6=94=B9=20=E8=83=8C=E5=8C=85?= =?UTF-8?q?=E7=90=86=E8=AE=BA=E5=9F=BA=E7=A1=8001=E8=83=8C=E5=8C=85-2.md?= =?UTF-8?q?=20Java=20=E4=BB=A3=E7=A0=81=E6=A0=BC=E5=BC=8F.?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- problems/背包理论基础01背包-2.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/problems/背包理论基础01背包-2.md b/problems/背包理论基础01背包-2.md index e85d31b4..075bb5b1 100644 --- a/problems/背包理论基础01背包-2.md +++ b/problems/背包理论基础01背包-2.md @@ -214,7 +214,7 @@ int main() { Java： ```java - public static void main(String[] args) { + public static void main(String[] args) { int[] weight = {1, 3, 4}; int[] value = {15, 20, 30}; int bagWight = 4; From ecd98c9a79e1e3efbde2dc140d9adc7b2af93c3b Mon Sep 17 00:00:00 2001 From: Kelvin Date: Tue, 15 Jun 2021 21:06:42 -0400 Subject: [PATCH 2/4] =?UTF-8?q?=E5=A2=9E=E5=8A=A0=20=E8=83=8C=E5=8C=85?= =?UTF-8?q?=E7=90=86=E8=AE=BA=E5=9F=BA=E7=A1=8001=E8=83=8C=E5=8C=85-2.md?= =?UTF-8?q?=20Python3=20=E5=AE=9E=E7=8E=B0=E4=BB=A3=E7=A0=81?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- problems/背包理论基础01背包-2.md | 17 +++++++++++++++++ 1 file changed, 17 insertions(+) diff --git a/problems/背包理论基础01背包-2.md b/problems/背包理论基础01背包-2.md index 075bb5b1..aee1a929 100644 --- a/problems/背包理论基础01背包-2.md +++ b/problems/背包理论基础01背包-2.md @@ -242,7 +242,24 @@ Java： Python： +```python +def test_1_wei_bag_problem(): + weight = [1, 3, 4] + value = [15, 20, 30] + bag_weight = 4 + # 初始化: 全为0 + dp = [0] * (bag_weight + 1) + # 先遍历物品, 再遍历背包容量 + for i in range(len(weight)): + for j in range(bag_weight, weight[i] - 1, -1): + # 递归公式 + dp[j] = max(dp[j], dp[j - weight[i]] + value[i]) + + print(dp) + +test_1_wei_bag_problem() +``` Go： ```go From 5dc2a0b745086c026e75cde53d898a67f9e98eb1 Mon Sep 17 00:00:00 2001 From: Kelvin Date: Tue, 15 Jun 2021 21:09:06 -0400 Subject: [PATCH 3/4] =?UTF-8?q?=E6=9B=B4=E6=94=B9=20=E8=83=8C=E5=8C=85?= =?UTF-8?q?=E7=90=86=E8=AE=BA=E5=9F=BA=E7=A1=8001=E8=83=8C=E5=8C=85-2.md?= =?UTF-8?q?=20=E6=A0=BC=E5=BC=8F?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 增加一个空行, 因为如果没有空行浏览器render文字就会有问题. --- problems/背包理论基础01背包-2.md | 1 + 1 file changed, 1 insertion(+) diff --git a/problems/背包理论基础01背包-2.md b/problems/背包理论基础01背包-2.md index aee1a929..c8b80655 100644 --- a/problems/背包理论基础01背包-2.md +++ b/problems/背包理论基础01背包-2.md @@ -5,6 +5,7 @@

欢迎大家参与本项目，贡献其他语言版本的代码，拥抱开源，让更多学习算法的小伙伴们收益！

+ # 动态规划：关于01背包问题，你该了解这些！（滚动数组） 昨天[动态规划：关于01背包问题，你该了解这些！](https://mp.weixin.qq.com/s/FwIiPPmR18_AJO5eiidT6w)中是用二维dp数组来讲解01背包。 From 3746acd22b02e94945a20d9c2a69de788a0f016c Mon Sep 17 00:00:00 2001 From: Kelvin Date: Tue, 15 Jun 2021 21:10:08 -0400 Subject: [PATCH 4/4] =?UTF-8?q?=E6=9B=B4=E6=96=B0=20=E8=83=8C=E5=8C=85?= =?UTF-8?q?=E7=90=86=E8=AE=BA=E5=9F=BA=E7=A1=8001=E8=83=8C=E5=8C=85-2.md?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 小typo. --- problems/背包理论基础01背包-2.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/problems/背包理论基础01背包-2.md b/problems/背包理论基础01背包-2.md index c8b80655..48275908 100644 --- a/problems/背包理论基础01背包-2.md +++ b/problems/背包理论基础01背包-2.md @@ -36,7 +36,7 @@ **其实可以发现如果把dp[i - 1]那一层拷贝到dp[i]上，表达式完全可以是：dp[i][j] = max(dp[i][j], dp[i][j - weight[i]] + value[i]);** -**于其把dp[i - 1]这一层拷贝到dp[i]上，不如只用一个一维数组了**，只用dp[j]（一维数组，也可以理解是一个滚动数组）。 +**与其把dp[i - 1]这一层拷贝到dp[i]上，不如只用一个一维数组了**，只用dp[j]（一维数组，也可以理解是一个滚动数组）。 这就是滚动数组的由来，需要满足的条件是上一层可以重复利用，直接拷贝到当前层。