<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 solve(int ind, int amt, vector<int>& cns, vector<vector<int>>& dp) {
        if(amt==0){
            return 0;
        }
        if(ind>=cns.size()){
            return 1e9;
        }
        if(dp[ind][amt]!=-1){
            return dp[ind][amt];
        }
        if(amt>=cns[ind]){
            return dp[ind][amt]=min({1+solve(ind,amt-cns[ind],cns,dp) , 1+solve(ind+1,amt-cns[ind],cns,dp) , solve(ind+1,amt,cns,dp)});
        } else{
            return dp[ind][amt]=solve(ind+1,amt,cns,dp);
        }
    }
    int coinChange(vector<int>& cns, int amount) {
        if(amount ==0){
            return 0;
        }
        vector<vector<int>> dp(cns.size()+3, vector<int>(amount+3 , -1));
        int ta = solve(0,amount,cns,dp);
        return ta != 1e9?ta:-1;
    }
};
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