LC 0322 [M] Coin Change (min coins to make amount)

for coin problems, remember to loop through the denoms, and think about the case not to take when the denom exceeds (or equals) the index

each coin we add we +1

class Solution:
    def coinChange(self, coins: List[int], amount: int) -> int:
        T = [float('inf')] * (amount + 1)
        
        T[0] = 0 # making amount = 0 counts as 0 coins used, not -1

        for denom in coins:
          for i in range(1, amount + 1):
            r = i - denom # remaining amount if we took this denom
            if r == 0:
              T[i] = 1
              continue
            elif r < 0: # can't make that amount (denom > i)
              continue
            else:
              if T[r] < T[i]:
                T[i] = T[r] + 1
            
        return T[-1] if T[-1] != float('inf') else -1

    def short(self, coins: List[int], amount: int) -> int:
        T = [math.inf] * (amount + 1)
        
        T[0] = 0

        for denom in coins:
          for amt in range(1, amount + 1):
            if denom < amt:
              T[amt] = min(T[amt], T[amt-denom] + 1)
            
        return T[-1] if T[-1] != math.inf else -1

class Solution():
    def coinChange(self, coins, amount):
        coins.sort()
        memo = {0: 0}
        
        def minCoinsToMake(amount):
            if amount in memo: return memo[amount]
            
            minCoins = math.inf
            
            for denom in coins:
                if amount - denom < 0: break # or just continue if unsorted
                includeCoin = minCoinsToMake(amount - denom) + 1
                minCoins = min(minCoins, includeCoin)
                
            memo[amount] = minCoins
            return minCoins
        
        res = minCoinsToMake(amount)
        if res == math.inf: return -1
        return res