From 3193d16f53372a6bd9d294538a83ef3e5d92a87f Mon Sep 17 00:00:00 2001
From: matthew <1123957599@qq.com>
Date: Tue, 2 Apr 2024 14:53:01 +0800
Subject: [PATCH 1/4] =?UTF-8?q?=E6=B7=BB=E5=8A=A00279.=E5=AE=8C=E5=85=A8?=
 =?UTF-8?q?=E5=B9=B3=E6=96=B9=E6=95=B0=20Python=E7=89=88=E6=9C=AC?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 problems/0279.完全平方数.md | 20 ++++++++++++++++++++
 1 file changed, 20 insertions(+)

diff --git a/problems/0279.完全平方数.md b/problems/0279.完全平方数.md
index f7c06dbd..1b29626f 100644
--- a/problems/0279.完全平方数.md
+++ b/problems/0279.完全平方数.md
@@ -271,7 +271,27 @@ class Solution:
         # 返回结果
         return dp[n]
 
+```
+```python
+class Solution(object):
+    def numSquares(self, n):
+        # 先把可以选的数准备好，更好理解
+        nums, num = [], 1
+        while num ** 2 <= n:
+            nums.append(num ** 2)
+            num += 1
+        # dp数组初始化
+        dp = [float('inf')] * (n + 1)
+        dp[0] = 0
 
+        # 遍历准备好的完全平方数
+        for i in range(len(nums)):
+            # 遍历背包容量
+            for j in range(nums[i], n+1):
+                dp[j] = min(dp[j], dp[j-nums[i]]+1)
+        # 返回结果
+        return dp[-1]
+        
 
 ```
 ### Go：

From 6dd9d117ffc60cb6854f26814b05aa5be2033e84 Mon Sep 17 00:00:00 2001
From: matthew <1123957599@qq.com>
Date: Tue, 2 Apr 2024 23:58:58 +0800
Subject: [PATCH 2/4] =?UTF-8?q?=E6=B7=BB=E5=8A=A00139.=E5=8D=95=E8=AF=8D?=
 =?UTF-8?q?=E6=8B=86=E5=88=86=20Python=20DP=E5=89=AA=E6=9E=9D=E6=96=B9?=
 =?UTF-8?q?=E6=B3=95?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 problems/0139.单词拆分.md | 21 +++++++++++++++++++++
 1 file changed, 21 insertions(+)

diff --git a/problems/0139.单词拆分.md b/problems/0139.单词拆分.md
index a3d59ec7..5ad0fcb0 100644
--- a/problems/0139.单词拆分.md
+++ b/problems/0139.单词拆分.md
@@ -394,7 +394,28 @@ class Solution:
                     dp[j] = dp[j] or (dp[j - len(word)] and word == s[j - len(word):j])
         return dp[len(s)]
 ```
+DP（剪枝）
 
+```python
+class Solution(object):
+    def wordBreak(self, s, wordDict):
+
+        # 先对单词按长度排序
+        wordDict.sort(key=lambda x: len(x))
+        n = len(s)
+        dp = [False] * (n + 1)
+        dp[0] = True
+        # 遍历背包
+        for i in range(1, n + 1):
+            # 遍历单词
+            for word in wordDict:
+                # 简单的 “剪枝”
+                if len(word) > i:
+                    break
+                dp[i] = dp[i] or (dp[i - len(word)] and s[i - len(word): i] == word)
+        return dp[-1]
+
+```
 
 
 ### Go：

From fda18c06b7221b1c7bddd6b4115de5549e4fd5a4 Mon Sep 17 00:00:00 2001
From: matthew <1123957599@qq.com>
Date: Wed, 3 Apr 2024 22:23:48 +0800
Subject: [PATCH 3/4] =?UTF-8?q?=E6=B7=BB=E5=8A=A0=20=E8=83=8C=E5=8C=85?=
 =?UTF-8?q?=E9=97=AE=E9=A2=98=E7=90=86=E8=AE=BA=E5=9F=BA=E7=A1=80=E5=A4=9A?=
 =?UTF-8?q?=E9=87=8D=E8=83=8C=E5=8C=85=20Python=E8=A7=A3=E6=B3=95?=
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   | 23 +++++++++++++++++++
 1 file changed, 23 insertions(+)

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 5d6440e3..29f157fb 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
@@ -204,6 +204,29 @@ class multi_pack{
 ```
 ### Python：
 
+```python
+
+C, N = input().split(" ")
+C, N = int(C), int(N)
+
+# value数组需要判断一下非空不然过不了
+weights = [int(x) for x in input().split(" ")]
+values = [int(x) for x in input().split(" ") if x]
+nums = [int(x) for x in input().split(" ")]
+
+dp = [0] * (C + 1)
+# 遍历背包容量
+for i in range(N):
+    for j in range(C, weights[i] - 1, -1):
+        for k in range(1, nums[i] + 1):
+            # 遍历 k，如果已经大于背包容量直接跳出循环
+            if k * weights[i] > j:
+                break
+            dp[j] = max(dp[j], dp[j - weights[i] * k] + values[i] * k) 
+print(dp[-1])
+
+```
+
 ### Go：
 
 

From 1c4b9a252fd004a9ec3771b6dbfc707818e4f1d4 Mon Sep 17 00:00:00 2001
From: matthew <1123957599@qq.com>
Date: Sat, 6 Apr 2024 10:38:12 +0800
Subject: [PATCH 4/4] =?UTF-8?q?=E6=B7=BB=E5=8A=A00583=20=E4=B8=A4=E4=B8=AA?=
 =?UTF-8?q?=E5=AD=97=E7=AC=A6=E4=B8=B2=E7=9A=84=E5=88=A0=E9=99=A4=E6=93=8D?=
 =?UTF-8?q?=E4=BD=9C=20Python=E8=A7=A3=E6=B3=952?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 .../0583.两个字符串的删除操作.md    | 19 +++++++++++++++++++
 1 file changed, 19 insertions(+)

diff --git a/problems/0583.两个字符串的删除操作.md b/problems/0583.两个字符串的删除操作.md
index 7dbb8ef5..4816c37c 100644
--- a/problems/0583.两个字符串的删除操作.md
+++ b/problems/0583.两个字符串的删除操作.md
@@ -234,6 +234,25 @@ class Solution:
         return dp[-1][-1]
 ```
 
+> 版本 2
+
+```python
+class Solution(object):
+    def minDistance(self, word1, word2):
+        m, n = len(word1), len(word2)
+        
+        # dp 求解两字符串最长公共子序列
+        dp = [[0] * (n+1) for _ in range(m+1)]
+        for i in range(1, m+1):
+            for j in range(1, n+1):
+                if word1[i-1] == word2[j-1]:
+                    dp[i][j] = dp[i-1][j-1] + 1
+                else:
+                    dp[i][j] = max(dp[i-1][j], dp[i][j-1])
+                    
+        # 删去最长公共子序列以外元素
+        return m + n - 2 * dp[-1][-1]
+```
 ### Go：
 
 ```go