<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 {
    // //int dp[13][10001];
    // int help(int i, vector<int>& coins, int amount) {
    //     if(i==coins.size()-1) {
    //         if(amount%coins[i]==0) return amount/coins[i];
    //         return 1e9;
    //     }

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

    //     int pick = 1e9, notPick=1e9;

    //     if(amount >= coins[i]) {
    //         pick = 1 + help(i, coins, amount-coins[i]);
    //     }
    //     notPick = help(i+1, coins, amount);
    //     return dp[i][amount] = min(pick, notPick);
    // }
public:
    int coinChange(vector<int>& coins, int amount) {
        int n = coins.size();
        //memset(dp, -1, sizeof(dp));

        // int ans = help(0, coins, amount);
        // return ans>=1e9 ? -1 : ans;
        vector<vector<int>>dp(n+2, vector<int>(amount+2, 0));
        for(int i=0; i<=amount; ++i) {
            if(i % coins[n-1] == 0) dp[n-1][i] = i/coins[n-1];
            else dp[n-1][i] = 1e9;
        }

        for(int i=n-2; i>=0; --i) {
            for(int target=0; target<=amount; ++target) {
                int pick = 1e9;
                int notPick = dp[i+1][target];
                if(coins[i] <= target) {
                    pick = 1 + dp[i][target-coins[i]];
                }
                dp[i][target] = min(pick, notPick);
            }
        }
        return dp[0][amount] >= 1e9 ? -1 : dp[0][amount];
    }
};
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