peak-index-in-a-mountain-array

Peak Index in a Mountain Array

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peakIndexInMountainArray

An array <code>arr</code> a mountain if the following properties hold:

<ul>
	<li><code>arr.length &gt;= 3</code></li>
	<li>There exists some <code>i</code> with <code>0 &lt; i &lt; arr.length - 1</code> such that:
	<ul>
		<li><code>arr[0] &lt; arr[1] &lt; ... &lt; arr[i - 1] &lt; arr[i] </code></li>
		<li><code>arr[i] &gt; arr[i + 1] &gt; ... &gt; arr[arr.length - 1]</code></li>
	</ul>
	</li>
</ul>

Given a mountain array <code>arr</code>, return the index <code>i</code> such that <code>arr[0] &lt; arr[1] &lt; ... &lt; arr[i - 1] &lt; arr[i] &gt; arr[i + 1] &gt; ... &gt; arr[arr.length - 1]</code>.

You must solve it in <code>O(log(arr.length))</code> time complexity.

&nbsp;
Example 1:

<pre>
Input: arr = [0,1,0]
Output: 1
</pre>

Example 2:

<pre>
Input: arr = [0,2,1,0]
Output: 1
</pre>

Example 3:

<pre>
Input: arr = [0,10,5,2]
Output: 1
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>3 &lt;= arr.length &lt;= 105</code></li>
	<li><code>0 &lt;= arr[i] &lt;= 106</code></li>
	<li><code>arr</code> is guaranteed to be a mountain array.</li>
</ul>

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