<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:
       long long int dp[100000][13];
      long long int helper(vector<int>& coins, int amount , long long int sum , int index)
      {
        if(index == coins.size() ||  sum > amount){
            return INT_MAX -1;  
        }
        if(sum == amount){
            return 0; 
        }
        if(dp[sum][index] !=-1)  {
             return dp[sum][index];

        }
      
        long long int take =1+ helper(coins, amount , sum+coins[index] , index);
        long long int notake =0+ helper(coins, amount , sum , index+1);
        long long int mini = min(take,notake);
        dp[sum][index] =min( take , notake);         
        return mini;
        
      }

    int coinChange(vector<int>& coins, int amount) {
        memset(dp,-1,sizeof(dp));
        long long int sum = 0;
        int index = 0;
        int ans = helper(coins , amount , sum , index );
        if(ans == INT_MAX-1){
            return -1;
        }
         
        return ans;
    }
};
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