Divide an array into k segments to maximize maximum of segment minimums

Given an array of n integers, divide it into k segments and find the maximum of the minimums of k segments. Output the maximum integer that can be obtained among all ways to segment in k subarrays.

Examples: 

Input : arr[] = {1, 2, 3, 6, 5} 
 k = 2
Output: 5
Explanation: There are many ways to create 
two segments. The optimal segments are (1, 2, 3)
and (6, 5). Minimum of both segments are 1 and 5, 
hence the maximum(1, 5) is 5. 


Input: -4 -5 -3 -2 -1 k=1
Output: -5 
Explanation: only one segment, so minimum is -5.

There will be 3 cases that need to be considered. 

1. k >= 3: When k is greater than 2, one segment will only compose of {max element}, so that max of minimum segments will always be the max.
2. k = 2: For k = 2 the answer is the maximum of the first and last element.
3. k = 1: Only possible partition is one segment equal to the whole array. So the answer is the minimum value on the whole array.

Below is the implementation of the above approach 

-5

Time complexity: O(n) 
Auxiliary Space: O(1)