<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 f(vector<int>&coins,int ind,int amt,vector<vector<int>>&dp)
    {
        //base case here
            if(ind==0)
            {
                if(amt%coins[ind]==0)
                return amt/coins[ind];
                return 1e9;
            }
             if(dp[ind][amt]!=-1)
             return dp[ind][amt];
            int take=INT_MAX;
            int nottake=f(coins,ind-1,amt,dp);
            if(amt>=coins[ind])
            take=1+f(coins,ind,amt-coins[ind],dp);
            return dp[ind][amt]=std::min(take,nottake);
    }
    int coinChange(vector<int>& coins, int amount) {
      if(amount<=0)
      return 0;
      int n=coins.size();
      vector<int>prev(amount+1,0);
     
      for(int i=0;i<=amount;i++)
      {
        if(i%coins[0]==0)
        prev[i]=i/coins[0];
        else
        prev[i]=1e9;
      }
      for(int i=1;i<n;i++)
      {
        vector<int>cur(amount+1,0);
        for(int j=0;j<=amount;j++)
        {
          int take=INT_MAX;
          int nottake=prev[j];
            if(j>=coins[i])
            take=1+cur[j-coins[i]];
            cur[j]=std::min(take,nottake);  
        }
        prev=cur;
      }
    
      int ans=prev[amount];   
      if(ans>=1e9)
      return -1;
      return ans;
    }
};
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