<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 sol(int i,long s,int amount,vector<int>&coins,vector<vector<int>>&v)
    {
        int n = coins.size();
        if(v[i][s]!=-1) return v[i][s];
        if(i==n-1)
        {
            if((amount-s)%coins[i]==0)
            {
                return (amount-s)/coins[i];
            }
            return 9999;
        }

        // use pick non pick algorithm
        int take=INT_MAX,nonTake;

        s+=coins[i];
        if(s<=amount && coins[i]<=amount)
        {
            take = 1+sol(i,s,amount,coins,v);
        }  

        s-=coins[i];
        nonTake = sol(i+1,s,amount,coins,v);

        return v[i][s]=min(take,nonTake);
    }

    int coinChange(vector<int>& coins, int amount) 
    {
        if(amount == 0) return 0;
        vector<vector<int>> v(coins.size()+3,vector<int>(amount+5,-1));
        int ans = sol(0,0,amount,coins,v);
        if(ans == 9999) return -1;// this value is from base condition which
        //we return when we don't find the target amount
        return ans;
    }
};
59836