<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>

unordered_map<int, pair<int, int>> store;
class Solution {
public:
    int coinChange(vector<int>& coins, int amount) {
        sort(coins.begin(), coins.end(), greater<int>());
        store.clear();

        return change(coins, amount, 0);
    }
    int change(vector<int>& coins, int amount, int index) {
        if(amount==0) return 0;
        if(amount<0) return -1;

        int mini=INT_MAX;
        bool flag=false;
        for(int i=index; i<coins.size(); i++){
            
            int out;
            if(store.find(amount-coins[i])!=store.end() && store[amount-coins[i]].second<=i){
                out=store[amount-coins[i]].first;
            }else{
                out= change(coins, amount-coins[i], i);
                store[amount-coins[i]]={out, i};
            }
            if(out==-1)continue;
            mini=min(out, mini);
            flag=true;
        }
        if(flag){
            return mini+1;
        }
        return -1;
    }
};
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