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
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---
 .../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