diff --git a/problems/0343.整数拆分.md b/problems/0343.整数拆分.md
index fefaa293..cf60575f 100644
--- a/problems/0343.整数拆分.md
+++ b/problems/0343.整数拆分.md
@@ -218,7 +218,7 @@ class Solution:
             # 假设对正整数 i 拆分出的第一个正整数是 j（1 <= j < i），则有以下两种方案：
             # 1) 将 i 拆分成 j 和 i−j 的和，且 i−j 不再拆分成多个正整数，此时的乘积是 j * (i-j)
             # 2) 将 i 拆分成 j 和 i−j 的和，且 i−j 继续拆分成多个正整数，此时的乘积是 j * dp[i-j]
-            for j in range(1, i):
+            for j in range(1, i - 1):
                 dp[i] = max(dp[i], max(j * (i - j), j * dp[i - j]))
         return dp[n]
 ```
diff --git a/problems/背包理论基础01背包-1.md b/problems/背包理论基础01背包-1.md
index 852c489b..1269d9c1 100644
--- a/problems/背包理论基础01背包-1.md
+++ b/problems/背包理论基础01背包-1.md
@@ -268,7 +268,7 @@ 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 bagSize = 4;
@@ -307,6 +307,41 @@ Java：
 
 
 Python：
+```python
+def test_2_wei_bag_problem1(bag_size, weight, value) -> int: 
+	rows, cols = len(weight), bag_size + 1
+	dp = [[0 for _ in range(cols)] for _ in range(rows)]
+	res = 0
+    
+	# 初始化dp数组. 
+	for i in range(rows): 
+		dp[i][0] = 0
+	first_item_weight, first_item_value = weight[0], value[0]
+	for j in range(1, cols): 	
+		if first_item_weight <= j: 
+			dp[0][j] = first_item_value
+
+	# 更新dp数组: 先遍历物品, 再遍历背包. 
+	for i in range(1, len(weight)): 
+		cur_weight, cur_val = weight[i], value[i]
+		for j in range(1, cols): 
+			if cur_weight > j: # 说明背包装不下当前物品. 
+				dp[i][j] = dp[i - 1][j] # 所以不装当前物品. 
+			else: 
+				# 定义dp数组: dp[i][j] 前i个物品里，放进容量为j的背包，价值总和最大是多少。
+				dp[i][j] = max(dp[i - 1][j], dp[i - 1][j - cur_weight]+ cur_val)
+				if dp[i][j] > res: 
+					res = dp[i][j]
+
+	print(dp)
+
+
+if __name__ == "__main__": 
+	bag_size = 4
+	weight = [1, 3, 4]
+	value = [15, 20, 30]
+	test_2_wei_bag_problem1(bag_size, weight, value)
+```
 
 
 Go：