You are given coins of different denominations and a total amount of money amount. Write a function to compute the fewest number of coins that you need to make up that amount. If that amount of money cannot be made up by any combination of the coins, return -1.
You may assume that you have an infinite number of each kind of coin.
Example 1:
Input: coins = [1,2,5], amount = 11
Output: 3
Explanation: 11 = 5 + 5 + 1
Example 2:
Input: coins = [2], amount = 3
Output: -1
Example 3:
Input: coins = [1], amount = 0
Output: 0
Example 4:
Input: coins = [1], amount = 1
Output: 1
Example 5:
Input: coins = [1], amount = 2
Output: 2
Constraints:
1 <= coins.length <= 12
1 <= coins[i] <= 231 - 1
0 <= amount <= 104
class Solution:
    def coinChange(self, coins: List[int], amount: int) -> int:
        coins.sort(reverse = True)
        
        count = 0
        self.maxcount = float('inf')
        
        self.dfs(coins, count, amount)
        
        return -1 if self.maxcount == float('inf') else self.maxcount
    
    def dfs(self,coins,count,amount):
        if amount == 0: self.maxcount = min(self.maxcount,count)
        
        for i in range(len(coins)):
            if amount >= coins[i] and count + math.ceil(amount/coins[i])<self.maxcount:
                self.dfs(coins[i:],count+1,amount-coins[i])
class Solution:
    def coinChange(self, coins: List[int], amount: int) -> int:
        coins.sort(reverse = True)
        
        count = 0
        self.maxcount = float('inf')
        
        self.dfs(coins, count, amount)
        
        return -1 if self.maxcount == float('inf') else self.maxcount
    
    def dfs(self,coins,count,amount):
        if amount == 0: self.maxcount = min(self.maxcount,count)
        
        for i in range(len(coins)):
            if amount >= coins[i] and count + math.ceil(amount/coins[i])<self.maxcount:
                self.dfs(coins[i:],count+1,amount-coins[i])