<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>

import numpy as np

class Solution:
    def coinChange(self, coins: List[int], amount: int) -> int:
        def dfs(amount, i):
            if i >= len(coins):
                return float('inf')
            if amount == 0:
                return 0
            if amount < 0:
                return float('inf')
            return min(1 + dfs(amount - coins[i], i), dfs(amount, i + 1))
        
        dp = [[float('inf') for _ in range(len(coins) + 1)] for _ in range(amount + 1)]
        #setting amount row to 0 like dfs
        for j in range(len(coins) + 1):
            dp[0][j] = 0

        for i in range(1, amount + 1):
            for j in range(len(coins) - 1, -1, -1):
                if i - coins[j] < 0:
                    dp[i][j] = dp[i][j + 1]
                else:
                    dp[i][j] = min(dp[i][j + 1], 1 + dp[i - coins[j]][j])

        return dp[amount][0] if dp[amount][0] != float('inf') else -1



            
            

        
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