<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:
    vector<vector<int>> dp;
    int f(int i, int target, vector<int>& coins) {
        if(i == 0) {
            if(target % coins[i] == 0) return target / coins[i];
            return 1e9;
        }

        if(dp[i][target] != -1) return dp[i][target];

        int notpick = f(i-1, target, coins);
        int pick = 1e9;
        if(coins[i] <= target) {
            pick = 1 + f(i, target - coins[i], coins);
        }

        return dp[i][target] = min(pick, notpick);
    }
    int coinChange(vector<int>& coins, int amount) {
        if(amount == 0) return 0;
        int n = coins.size();
        vector<vector<int>> dp(n, vector<int>(amount + 1, -1));
        this->dp = dp;
        int ans = f(n -1, amount, coins);
        return ans  == 1e9 ? -1: ans;
    }
};
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