<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 minCoins(vector<int>& coins, int amount, int idx, vector<vector<int>>& dp)
    {
        if(idx == 0)
        {
            if(amount % coins[idx] == 0)
                return amount / coins[idx]; 
            return 1e9; 
        }
        if(dp[idx][amount] != -1)
            return dp[idx][amount]; 
        int notPick = 0 + minCoins(coins, amount, idx - 1, dp); 
        int pick = INT_MAX; 
        if(amount - coins[idx] >= 0)
            pick = 1 + minCoins(coins, amount - coins[idx], idx, dp); 
        
        return dp[idx][amount] = min(pick, notPick);
    }

    int coinChange(vector<int>& coins, int amount) {
        vector<vector<int>> dp(coins.size() + 1, vector<int> (amount + 1, -1)); 
        int n = coins.size(); 
        // int ans = minCoins(coins, amount, n-1, dp);
        // if(ans > 1e4)
        //     return -1; 
        return tabulation(coins, amount); 
    }
    int tabulation(vector<int>& coins, int amount)
    {
        // vector<vector<int>> dp(coins.size() + 1, vector<int> (amount + 1, 0)); 
        vector<int> prev(amount + 1, 0), curr(amount + 1, 0); 
        int n = coins.size(); 
        for(int T=1; T<amount + 1; T++)
        {
            if(T % coins[0] == 0)
            {
                prev[T] = T / coins[0]; 
            }
            else prev[T] = 1e9;
        }
        for(int i=1; i<n; i++)
        {
            for(int j=0; j < amount + 1; j++)
            {
                int notPick = prev[j];
                int pick = INT_MAX; 
                if(j >= coins[i])
                {
                    pick = 1 + curr[j - coins[i]]; 
                }
                curr[j] = min(pick, notPick); 
            }
            prev = curr; 
        }
        if(prev[amount] >= 1e9)
            return -1; 
        return prev[amount]; 
    }
};
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