<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 bfs(vector<int> &coins, int amount)
    {
        queue<pair<int,int>> q;

        vector<bool> isVisited(amount+1,false);

        for(int i=0;i<coins.size();i++)
        {
            if(coins[i]<=amount)
            {
                q.push({coins[i],1});
            }
        }

        while(!q.empty())
        {
            int cur = q.front().first;
            int cnt = q.front().second;
            q.pop();

            if(isVisited[cur]) continue;
            if(cur == amount) return cnt;

            isVisited[cur] = true;

            for(int i=0;i<coins.size();i++)
            {   
                if(coins[i]>amount) continue;
                int next = coins[i] + cur;
                if(next<0||next>amount||isVisited[next]) continue;

                q.push({next,cnt+1});
            }
        }

        return -1;
    }
    int coinChange(vector<int>& coins, int amount) {
        
        sort(coins.begin(),coins.end());

        if(amount == 0) return 0;
        if(coins[0]>amount)
        {
            return -1;
        }

        return bfs(coins,amount);
    }
};
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