How do you solve the coin change problem?

def coin_change(coins, amount):
    dp = [0] + [float('inf')] * amount
    for a in range(1, amount + 1):
        for c in coins:
            if c <= a:
                dp[a] = min(dp[a], dp[a - c] + 1)
    return dp[amount] if dp[amount] != float('inf') else -1


# --- demo ---
print(coin_change([1, 3, 4], 6))   # 2  (3+3, beats greedy's 4+1+1)
print(coin_change([2], 3))         # -1 (impossible)