Update 0322.零钱兑换.md

problems/0322.零钱兑换.md

@@ -216,37 +216,75 @@ class Solution {
 ```
 
 Python：
-
+先遍历物品 后遍历背包
 ```python
 class Solution:
     def coinChange(self, coins: List[int], amount: int) -> int:
-        '''版本一'''
-        # 初始化
-        dp = [float("inf")]*(amount + 1)
-        dp[0] = 0
-        # 遍历物品
-        for coin in coins:
-            # 遍历背包
-            for j in range(coin, amount + 1):
-                dp[j] = min(dp[j], dp[j - coin] + 1)
-        return dp[amount] if dp[amount] != float("inf") else -1
+        dp = [float('inf')] * (amount + 1)  # 创建动态规划数组，初始值为正无穷大
+        dp[0] = 0  # 初始化背包容量为0时的最小硬币数量为0
+
+        for coin in coins:  # 遍历硬币列表，相当于遍历物品
+            for i in range(coin, amount + 1):  # 遍历背包容量
+                if dp[i - coin] != float('inf'):  # 如果dp[i - coin]不是初始值，则进行状态转移
+                    dp[i] = min(dp[i - coin] + 1, dp[i])  # 更新最小硬币数量
+
+        if dp[amount] == float('inf'):  # 如果最终背包容量的最小硬币数量仍为正无穷大，表示无解
+            return -1
+        return dp[amount]  # 返回背包容量为amount时的最小硬币数量
 
-    def coinChange1(self, coins: List[int], amount: int) -> int:
-        '''版本二'''
-        # 初始化
-        dp = [float("inf")]*(amount + 1)
-        dp[0] = 0
-        # 遍历物品
-        for j in range(1, amount + 1):
-            # 遍历背包
-            for coin in coins:
-                if j >= coin:
-                	dp[j] = min(dp[j], dp[j - coin] + 1)
-        return dp[amount] if dp[amount] != float("inf") else -1
 ```
 
+先遍历背包 后遍历物品
+```python
+class Solution:
+    def coinChange(self, coins: List[int], amount: int) -> int:
+        dp = [float('inf')] * (amount + 1)  # 创建动态规划数组，初始值为正无穷大
+        dp[0] = 0  # 初始化背包容量为0时的最小硬币数量为0
+
+        for i in range(1, amount + 1):  # 遍历背包容量
+            for j in range(len(coins)):  # 遍历硬币列表，相当于遍历物品
+                if i - coins[j] >= 0 and dp[i - coins[j]] != float('inf'):  # 如果dp[i - coins[j]]不是初始值，则进行状态转移
+                    dp[i] = min(dp[i - coins[j]] + 1, dp[i])  # 更新最小硬币数量
+
+        if dp[amount] == float('inf'):  # 如果最终背包容量的最小硬币数量仍为正无穷大，表示无解
+            return -1
+        return dp[amount]  # 返回背包容量为amount时的最小硬币数量
+
+```
+先遍历物品 后遍历背包（优化版）
+```python
+class Solution:
+    def coinChange(self, coins: List[int], amount: int) -> int:
+        dp = [float('inf')] * (amount + 1)
+        dp[0] = 0
+
+        for coin in coins:
+            for i in range(coin, amount + 1):
+                # 更新凑成金额 i 所需的最少硬币数量
+                dp[i] = min(dp[i], dp[i - coin] + 1)
+
+        return dp[amount] if dp[amount] != float('inf') else -1
 
 
+```
+先遍历背包 后遍历物品（优化版）
+```python
+class Solution:
+    def coinChange(self, coins: List[int], amount: int) -> int:
+        dp = [float('inf')] * (amount + 1)
+        dp[0] = 0
+
+        for i in range(1, amount + 1):  # 遍历背包容量
+            for coin in coins:  # 遍历物品
+                if i - coin >= 0:
+                    # 更新凑成金额 i 所需的最少硬币数量
+                    dp[i] = min(dp[i], dp[i - coin] + 1)
+
+        return dp[amount] if dp[amount] != float('inf') else -1
+
+
+
+```
 
 Go：
 ```go