<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 {
public:
    int coinChange(vector<int>& coins, int amount) {
        const unsigned tot_coins = coins.size();
        const unsigned max_amount = amount + 1;
        const unsigned arr_dimm = tot_coins * max_amount;
        int* arr = new int[arr_dimm];
        for (unsigned coin = 0; coin < tot_coins; coin++) {
            arr[coin * max_amount + 0] = 0;
        }

        for (unsigned coin = 0; coin < tot_coins; coin++) {
            int coin_val = coins[coin];
            for (unsigned amount = 1; amount < max_amount; amount++) {
                int idx = (coin * max_amount + amount);
                arr[idx] = -1;
                // Take one coin; reconsider
                if (amount >= coin_val) {
                    int lookup = arr[coin * max_amount + amount - coin_val];
                    if (lookup != -1) {
                        arr[idx] = lookup + 1;
                    }
                }
                // Skip coin; consider next
                if (coin > 0) {
                    int lookup = arr[(coin - 1) * max_amount + amount];
                    if (lookup != -1) {
                        if (arr[idx] == -1) {
                            arr[idx] = lookup;
                        } else if (arr[idx] > lookup) {
                            arr[idx] = lookup;
                        }
                    }
                }
            }
        }

        return arr[(tot_coins - 1) * max_amount + amount];
    }
};
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