<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>

#include<map>

class Solution {
public:
    int *arr;
    int dimx, dimy;
    int coinChange(vector<int>& coins, int amount) {
        dimx = coins.size();
        dimy = amount;
        arr = new int[dimx * dimy + 1];
        std::cout << dimx * dimy << "\n";
        for (unsigned i = 0; i < dimx * dimy + 1; i++) {
            arr[i] = -2;
        }
        int answer = coinChangeHelp(coins, coins.size()-1, amount);
        return answer;
    }

    int coinChangeHelp(vector<int>& coins, int idx, int amount) {
        if (idx < 0) {
            return -1;
        }
        if (amount == 0) {
            return 0;
        }
        if (amount < 0) {
            return -1;
        }

        int key = idx * dimy + amount;
        int memo = arr[key];
        if (memo != -2) {
            return memo;
        }

        int choose_coin = coinChangeHelp(coins, idx, amount - coins[idx]);
        int dont_choose = coinChangeHelp(coins, idx - 1, amount);

        if (choose_coin == -1) {
            arr[key] = dont_choose;
        } else if (dont_choose == -1) {  
            arr[key] = choose_coin + 1;
        } else {
            arr[key] = std::min(dont_choose, choose_coin + 1);
        }

        return arr[key];
    }
};
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