<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) {
        if(amount == 0){return 0;}
        sort(coins.begin(), coins.end());
        int ind = coins.size()-1;
        int minn = 1e9;
        queue<pair<pair<int,int>,int>> q;
        q.push({{amount,0},ind});
        unordered_set<int> st;
        while(!q.empty()){
            auto top = q.front();
            q.pop();
            int amt = top.first.first;
            int cnt = top.first.second;
            int ind = top.second;
            if(amt == 0){return cnt;}
            // if(amt<0){continue;}
            for(int i = ind; i>=0; i--){
                // cout<<"here "<<i<<endl;
                if(amt-coins[i]>=0 && st.find(amt-coins[i])==st.end()){
                    q.push({{amt-coins[i],cnt+1},i});
                    st.insert(amt-coins[i]);
                }
            }
        }
        return -1;               
    }
};
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