diff --git a/problems/0322.零钱兑换.md b/problems/0322.零钱兑换.md index 0e3947da..903777ca 100644 --- a/problems/0322.零钱兑换.md +++ b/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