<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:
    map<int,int> cache;

    int solve(vector<int>& coins, int amount){
        if (amount ==0) return 0;
        if (amount < coins.back()) return -1;

        auto it = cache.find(amount);
        if (it != cache.end()) return it->second;

        int ans = -1;
        for(int c : coins){
            if (amount ==c) {
                ans = 0;
                break;
            }
            if (amount >c){
                int subAns = solve(coins, amount-c);
                if (subAns >= 0){
                    if (ans <0 || ans >subAns){
                        ans = subAns;
                    }
                }
            }
        }

        if (ans >=0) ans ++;

        cache[amount] = ans;
        return ans;
    }

    int coinChange(vector<int>& coins, int amount) {
        sort(coins.begin(), coins.end(), greater<int>());
        return solve(coins, amount);
    }
};
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