<p>You are given an integer array <code>coins</code> representing coins of different denominations and an integer <code>amount</code> representing a total amount of money.</p>

<p>Return <em>the fewest number of coins that you need to make up that amount</em>. If that amount of money cannot be made up by any combination of the coins, return <code>-1</code>.</p>

<p>You may assume that you have an infinite number of each kind of coin.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> coins = [1,2,5], amount = 11
<strong>Output:</strong> 3
<strong>Explanation:</strong> 11 = 5 + 5 + 1
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> coins = [2], amount = 3
<strong>Output:</strong> -1
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> coins = [1], amount = 0
<strong>Output:</strong> 0
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= coins.length &lt;= 12</code></li>
	<li><code>1 &lt;= coins[i] &lt;= 2<sup>31</sup> - 1</code></li>
	<li><code>0 &lt;= amount &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution:
    def coinChange(self, coins: List[int], amount: int) -> int:
        min_coins = [amount+1 for _ in range(amount+1)]
        min_coins[0] = 0
        '''
        for i in range(1,amount+1):
            for coin in coins:
                if i - coin >= 0:
                    min_coins[i] = min(min_coins[i-coin]+1, min_coins[i])
        if min_coins[-1] > amount:
            return -1
        else:
            return min_coins[-1]
        '''

        visited = {}
        def roundcounter(n,coins,visited):
            if n in visited:
                return visited[n]
            if n == 0:
                result = 0 
            elif n < 0:
                result = amount + 1
            else:
                results = []
                for coin in coins:
                    results.append(roundcounter(n-coin,coins,visited))
                result = min(results) + 1
            visited[n] = result
            return result
        
        answer = roundcounter(amount,coins,visited)
        if answer > amount:
            answer = -1
        return answer




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