<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> cache;
public:
    int coinChange(vector<int>& coins, int amount) {
        if (amount == 0) return 0;
        if (amount < 0 || coins.size() == 0) return -1;
        auto r = coinChangeR(coins, amount);
        return r == INT_MAX ? -1: r;
    }
    int coinChangeR(vector<int>& coins, int amount) {
        if (amount == 0) return 0;
        if (amount < 0 || coins.size() == 0) return INT_MAX;
        if (!cache.count(amount)) {
            int change = INT_MAX;
            for (const auto& c: coins) {
                change = min(change, coinChangeR(coins, amount - c));
            }
            if (change != INT_MAX) {
                cache[amount] = change + 1;
            }
            else {
                cache[amount] = INT_MAX;
            }
        }
        return cache[amount];
    }
};
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