<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:

        # Create a dp array with size (amount + 1), initialized to a large number (inf)
        dp = [float('inf')] * (amount + 1)
        
        # Base case: No coins are needed to make amount 0
        dp[0] = 0
        
        # Iterate over each coin in the coins array
        for coin in coins:
            # For each coin, update the dp array for all amounts from the coin to the amount
            for i in range(coin, amount + 1):
                dp[i] = min(dp[i], dp[i - coin] + 1)
        
        # If the value in dp[amount] is still infinity, it means it's impossible to make that amount
        return dp[amount] if dp[amount] != float('inf') else -1

        """
        sorted_coins = sorted(coins)
        if amount == 0:
            return 0

        if sorted_coins[0] > amount:
            return -1

        
        remaining_amount = amount
        n_coins = 0
        j = len(sorted_coins) - 1
        while(remaining_amount > 0):
            if sorted_coins[j] <= remaining_amount:
                remaining_amount-=sorted_coins[j]
                n_coins+=1
            else:
                j-=1
                if j < 0:
                    return -1
        
        return n_coins
        """
16703