minimum-jumps-to-reach-home

Minimum Jumps to Reach Home

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minimumJumps

A certain bug&#39;s home is on the x-axis at position <code>x</code>. Help them get there from position <code>0</code>.

The bug jumps according to the following rules:

<ul>
	<li>It can jump exactly <code>a</code> positions forward (to the right).</li>
	<li>It can jump exactly <code>b</code> positions backward (to the left).</li>
	<li>It cannot jump backward twice in a row.</li>
	<li>It cannot jump to any <code>forbidden</code> positions.</li>
</ul>

The bug may jump forward beyond its home, but it cannot jump to positions numbered with negative integers.

Given an array of integers <code>forbidden</code>, where <code>forbidden[i]</code> means that the bug cannot jump to the position <code>forbidden[i]</code>, and integers <code>a</code>, <code>b</code>, and <code>x</code>, return the minimum number of jumps needed for the bug to reach its home. If there is no possible sequence of jumps that lands the bug on position <code>x</code>, return <code>-1.</code>

&nbsp;
Example 1:

<pre>
Input: forbidden = [14,4,18,1,15], a = 3, b = 15, x = 9
Output: 3
Explanation: 3 jumps forward (0 -&gt; 3 -&gt; 6 -&gt; 9) will get the bug home.
</pre>

Example 2:

<pre>
Input: forbidden = [8,3,16,6,12,20], a = 15, b = 13, x = 11
Output: -1
</pre>

Example 3:

<pre>
Input: forbidden = [1,6,2,14,5,17,4], a = 16, b = 9, x = 7
Output: 2
Explanation: One jump forward (0 -&gt; 16) then one jump backward (16 -&gt; 7) will get the bug home.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= forbidden.length &lt;= 1000</code></li>
	<li><code>1 &lt;= a, b, forbidden[i] &lt;= 2000</code></li>
	<li><code>0 &lt;= x &lt;= 2000</code></li>
	<li>All the elements in <code>forbidden</code> are distinct.</li>
	<li>Position <code>x</code> is not forbidden.</li>
</ul>

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