322.零钱兑换-python

动态规划问题，稍后更新思路

class Solution(object):
    def coinChange(self, coins, amount):
        """
        :type coins: List[int]
        :type amount: int
        :rtype: int
        """
        INF = float('inf')
        dp = []
        N = len(coins)
        for _ in range(N):
            tmp = [INF] * (amount+1)
            tmp[0] = 0
            dp.append(tmp)

        for j in range(1, amount+1):
            if j >= coins[0] and dp[0][j-coins[0]] != INF:
                dp[0][j] = dp[0][j-coins[0]] + 1
        for i in range(1, N):
            for j in range(1, amount+1):
                if j >= coins[i]:
                    dp[i][j] = min(dp[i - 1][j], dp[i][j-coins[i]] + 1)
                else:
                    dp[i][j] = dp[i - 1][j]
        return dp[len(coins)- 1][amount] if dp[N-1][amount] != INF else -1

进行空间压缩：

class Solution(object):
    def coinChange(self, coins, amount):
        """
        :type coins: List[int]
        :type amount: int
        :rtype: int
        """
        INF = float('inf')
        dp = [0] + [INF]*amount
        N = len(coins)
        for i in range(amount+1):
            for j in range(N):
                if i >= coins[j]:
                    dp[i] = min(dp[i], dp[i-coins[j]]+1)
        return dp[amount] if dp[amount] <= amount else -1