<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 {
    map<int, int> store;
public:
    int coinChange(vector<int>& coins, int amount) {
        if (amount == 0) return 0;

        bool notPossible = true;
        for (auto c : coins) {
            notPossible = notPossible && (c > amount);
        }
        if (notPossible) return -1;

        if(store.count(amount)) return store[amount];

        int minCount = 10000000;
        for (auto c : coins) {
            if (amount - c >= 0) {
                int curr = coinChange(coins, amount - c);
                if(curr != -1) minCount = minCount > 1 + curr ? 1 + curr : minCount; 
            }
        }
        if (minCount == 10000000) {
            store[amount] = -1;
        }
        else{
            store[amount] = minCount;
        }
        return store[amount];
        
    }
};
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