<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 rec (long long i, vector<int>& coins, long long n, long long amount, long long curramt, vector<vector<int>>& dp){
        if(i>=n) return 1e9;
        if (curramt == amount) return 0;
        if(dp[i][curramt]!=-1) return dp[i][curramt];
        long long take = 1e9;
        long long take2 = 1e9;
        long long nottake = 1e9;
        if(curramt+coins[i]<=amount) {
            take = 1 + rec(i,coins,n,amount,curramt+coins[i],dp); 
            take2 = rec(i+1,coins,n,amount,curramt,dp);
        }
        else nottake = rec(i+1,coins,n,amount,curramt,dp);
        return dp[i][curramt] = min({take,take2,nottake});
        
    }
    int coinChange(vector<int>& coins, int amount) {
        vector<vector<int>> dp(coins.size()+1,vector<int>(amount+1,-1));
        int res = rec(0, coins, coins.size(), amount, 0LL,dp);
        return (res == 1e9) ? -1 : res;
    }
};
54714