shortest-impossible-sequence-of-rolls

Shortest Impossible Sequence of Rolls

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shortestSequence

You are given an integer array <code>rolls</code> of length <code>n</code> and an integer <code>k</code>. You roll a <code>k</code> sided dice numbered from <code>1</code> to <code>k</code>, <code>n</code> times, where the result of the <code>ith</code> roll is <code>rolls[i]</code>.

Return the length of the shortest sequence of rolls that cannot be taken from <code>rolls</code>.

A sequence of rolls of length <code>len</code> is the result of rolling a <code>k</code> sided dice <code>len</code> times.

Note that the sequence taken does not have to be consecutive as long as it is in order.

&nbsp;
Example 1:

<pre>
Input: rolls = [4,2,1,2,3,3,2,4,1], k = 4
Output: 3
Explanation: Every sequence of rolls of length 1, [1], [2], [3], [4], can be taken from rolls.
Every sequence of rolls of length 2, [1, 1], [1, 2], ..., [4, 4], can be taken from rolls.
The sequence [1, 4, 2] cannot be taken from rolls, so we return 3.
Note that there are other sequences that cannot be taken from rolls.</pre>

Example 2:

<pre>
Input: rolls = [1,1,2,2], k = 2
Output: 2
Explanation: Every sequence of rolls of length 1, [1], [2], can be taken from rolls.
The sequence [2, 1] cannot be taken from rolls, so we return 2.
Note that there are other sequences that cannot be taken from rolls but [2, 1] is the shortest.
</pre>

Example 3:

<pre>
Input: rolls = [1,1,3,2,2,2,3,3], k = 4
Output: 1
Explanation: The sequence [4] cannot be taken from rolls, so we return 1.
Note that there are other sequences that cannot be taken from rolls but [4] is the shortest.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>n == rolls.length</code></li>
	<li><code>1 &lt;= n &lt;= 105</code></li>
	<li><code>1 &lt;= rolls[i] &lt;= k &lt;= 105</code></li>
</ul>

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