Dice Roll Simulation
<p>A die simulator generates a random number from <code>1</code> to <code>6</code> for each roll. You introduced a constraint to the generator such that it cannot roll the number <code>i</code> more than <code>rollMax[i]</code> (<strong>1-indexed</strong>) consecutive times.</p>

<p>Given an array of integers <code>rollMax</code> and an integer <code>n</code>, return <em>the number of distinct sequences that can be obtained with exact </em><code>n</code><em> rolls</em>. Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>Two sequences are considered different if at least one element differs from each other.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 2, rollMax = [1,1,2,2,2,3]
<strong>Output:</strong> 34
<strong>Explanation:</strong> There will be 2 rolls of die, if there are no constraints on the die, there are 6 * 6 = 36 possible combinations. In this case, looking at rollMax array, the numbers 1 and 2 appear at most once consecutively, therefore sequences (1,1) and (2,2) cannot occur, so the final answer is 36-2 = 34.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 2, rollMax = [1,1,1,1,1,1]
<strong>Output:</strong> 30
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 3, rollMax = [1,1,1,2,2,3]
<strong>Output:</strong> 181
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 5000</code></li>
	<li><code>rollMax.length == 6</code></li>
	<li><code>1 &lt;= rollMax[i] &lt;= 15</code></li>
</ul>
Array; Dynamic Programming
class Solution {
    private Integer[][][] f;
    private int[] rollMax;

    public int dieSimulator(int n, int[] rollMax) {
        f = new Integer[n][7][16];
        this.rollMax = rollMax;
        return dfs(0, 0, 0);
    }

    private int dfs(int i, int j, int x) {
        if (i >= f.length) {
            return 1;
        }
        if (f[i][j][x] != null) {
            return f[i][j][x];
        }
        long ans = 0;
        for (int k = 1; k <= 6; ++k) {
            if (k != j) {
                ans += dfs(i + 1, k, 1);
            } else if (x < rollMax[j - 1]) {
                ans += dfs(i + 1, j, x + 1);
            }
        }
        ans %= 1000000007;
        return f[i][j][x] = (int) ans;
    }
}