<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:
        dp = [[-1 for i in range(len(coins))] for j in range(amount + 1)]
        #coins.sort()
        def helper(ind, tar):
            if tar == 0:
                return 0
             
            if ind == -1:
                return float("inf")

            if dp[tar][ind] != -1:
                return dp[tar][ind]
            r1 = float("inf")
            if coins[ind] <= tar:
                r1 = helper(ind, tar - coins[ind])
            r2 = helper(ind - 1, tar)
            dp[tar][ind] = min(1 + r1, r2)
            return dp[tar][ind]
        
        ans = helper(len(coins) - 1 , amount)
        #print(dp)
        if ans == float("inf"):
            return -1
        else:
            return ans
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