<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 getCoins(vector<int>& coins, int amount,unordered_map<int,int>& mp) {
        if(amount == 0)
            return 0;
        if(mp[amount] != 0)
            return mp[amount];
        else {
            mp[amount] = INT_MAX;
        }
        for(int i = 1;i<= amount;i++) {
            mp[i] = INT_MAX;
            for(int coin: coins) {
                if(i-coin >= 0){
                    int val = getCoins(coins,i-coin,mp)+1;
                    if(val == 0)
                        val = INT_MAX;
                    mp[i]= min(val,mp[i]);
                }
            }
            if(mp[i] == INT_MAX)
                mp[i] = -1;

        }
        return mp[amount];
    }

    int coinChange(vector<int>& coins, int amount) {
        std::sort(coins.rbegin(),coins.rend());
        unordered_map<int,int>mp;
        mp[0] = 0;
        return getCoins(coins,amount,mp);

    }
};
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