<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 {

    unordered_map<int, unordered_map<int,int>> resMap;
    unordered_map<int, int> resMap2;
public:
    int coinChange(vector<int>& coins, int amount, int end) {

        
        if(amount == 0)
        {
            return 0;
        }

        if(amount < 0)
        {
            return -1;
        }

        if(end == -1 )
        {
            return -1;
        }

        if(resMap.find(end) != resMap.end() && resMap[end].find(amount) != resMap[end].end())
        {
            return resMap[end][amount];
        }

        // cout<<coins[end]<<endl;

        int result =0;
        if(amount%coins[end] == 0)
        {
            resMap[end][amount] =amount/coins[end];
            return amount/coins[end];
        }
        else{

            int minCoins = INT_MAX;
            for(int i = amount/coins[end]; i>=0; --i)
            {
                int nextCoins = coinChange(coins, amount - i*coins[end],end - 1);
                // cout<<coins[end]<<"::"<<i<<"::"<<nextCoins<<endl;
                if(nextCoins != -1 && minCoins > i+nextCoins)
                {
                    minCoins = i+nextCoins;
                }

            }

            if ( minCoins == INT_MAX)
            {
                resMap[end][amount] =-1;
                return -1;
            }
            else
            {
                resMap[end][amount] =minCoins;
                return minCoins;
            }
        }


        
    }
    int coinChange2(vector<int>& coins, int amount){

        if(amount ==0 )
        {
            return 0;
        }

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

        if(resMap2.find(amount) != resMap2.end())
        {
            return resMap2[amount];
        }

        int mincoins = INT_MAX;
        for(int idx = coins.size() -1; idx >=0; idx-- )
        {
            int nextcoins =  amount % coins[idx] == 0 ? amount/coins[idx] -1 : coinChange2(coins, amount - coins[idx]);

            if(nextcoins != -1 && mincoins > nextcoins+1 )
            {
                mincoins =  nextcoins+1;
            }

        }

        if(mincoins == INT_MAX)
        {
            resMap2[amount] =-1;
            return -1;
        }
        else{
            resMap2[amount] = mincoins;
            return mincoins;
        }

    }
    int coinChange(vector<int>& coins, int amount) {
    
        sort(coins.begin(), coins.end());
        // return coinChange(coins, amount,coins.size()-1);
        return coinChange2(coins, amount);
    }
};
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