<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:
        coins = sorted(coins)
        x = {}
        def recur(s):
            if s == 0:
                return 0
            if s in x:
                return x[s]
            arr = []
            for c in coins:
                if c > s:
                    break
                arr.append(1+recur(s-c))
            x[s] = min(arr) if len(arr) > 0 else float('inf')
            return x[s]
        res = recur(amount)
        return res if res < float('inf') else -1
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        
        """
        coins = sorted(set(coins))
        dp = [0]*(amount+1)
        for v in range(1, amount+1):
            dp[v] = float('inf')
            for c in coins:
                if v-c<0:
                    break
                dp[v] = min(dp[v], 1+dp[v-c])
        return dp[amount] if dp[amount] != float('inf') else -1
        """
        
        
        
        # dp = {}
        # def recur(v):
        #     if v == 0:
        #         return 0
        #     if v in dp:
        #         return dp[v]
        #     dp[v] = float('inf')
        #     for j in range(len(coins)):
        #         if v-coins[j]>=0:
        #             dp[v] = min(dp[v], 1+recur(v-coins[j]))
        #     return dp[v]
        # x = recur(amount)
        # return -1 if x == float('inf') else x
    
        """
        def recur(sofar, num_sofar, i):
            if sofar > amount:
                return float('inf')
            if sofar == amount:
                return num_sofar
            res = float('inf')
            for j in range(i, len(coins)):
                if sofar + coins[j] > amount:
                    break
                res = min(res, recur(sofar+coins[j], num_sofar+1, j))
            return res
        
        x = recur(0, 0, 0)
        return -1 if x == float('inf') else x
        """
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