<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 {
    private:
    int fl(vector<int>& arr, int ind, int t, vector<vector<int>>& dp){
        if (ind == 0) {
            if (t % arr[0] == 0){
             return t / arr[0];
            }
            else {
            return 1e9; 
            }
        }

        if (dp[ind][t] != -1) return dp[ind][t];

        int notTaken = 0+fl(arr, ind - 1, t, dp);  

        int taken = INT_MAX;
        if (arr[ind] <= t) { 
            taken = 1 + fl(arr, ind, t - arr[ind], dp);  
        }

        return dp[ind][t] = min(notTaken, taken);  
    }

    public:
    int coinChange(vector<int>& coins, int amount) {
        int n = coins.size();
        vector<vector<int>> dp(n, vector<int>(amount + 1, -1)); 
        int a = fl(coins, n - 1, amount, dp);
        if(a >= 1e9) {
           return -1;
   }
        return a;
    }
};



// class Solution{
//     private:

// int minimumElementsUtil(vector<int>& arr, int ind, int T, vector<vector<int>>& dp){

   
//     if(ind == 0){
       
//         if(T % arr[0] == 0)
//             return T / arr[0]; 
//         else
//             return 1e9; 
//     }
    
    
//     if(dp[ind][T] != -1)
//         return dp[ind][T];
     
//     int notTaken = 0 + minimumElementsUtil(arr, ind - 1, T, dp);
    

//     int taken = 1e9;
//     if(arr[ind] <= T)
//         taken = 1 + minimumElementsUtil(arr, ind, T - arr[ind], dp);
        
   
//     return dp[ind][T] = min(notTaken, taken);
// }
// public:
//  int coinChange(vector<int>& coins, int amount){
    
//     int n = coins.size();
 
//     vector<vector<int>> dp(n, vector<int>(amount + 1, -1));
    
//     int ans =  minimumElementsUtil(coins, n - 1, amount, dp);
  
//     if(ans >= 1e9)
//         return -1;
//     return ans; 
// }
// };
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