Find the local minima in a given array

Objec­tive:  Given an array of integer write an algorithm to find the local minima.

Local Minima: An element is considered as local minima if it is less than both of its neighbors (if neighbors exist).

Example:

int [] arrA = {11, 4, 2, 5, 11, 13, 5};
Output: Local Minima is: 2

int []arrA = {1,2,3,4};
Output: 1

int []arrA = {3};
Output: 3

int []arrA = {6,4};
Output: 4

NOTE: There could be many local minima’s, we need to find any one.

Approach:

Naïve: Use for loop and compare every element with its neighbor.

Time Complexity – O(n)

Binary Search Approach:

• Check if mid element is smaller than its left and right neighbors.
• If left neighbor is less than the mid element then make a recursive call to the left half of the array. (There will be at least one local minima in the left half, take few examples to check)
• If right neighbor is less than the mid element then make a recursive call to the right half of the array.

Time Complexity – O(logn)

Code: Run Code

Output:

Local Minima is: 2

Reference: http://www.geeksforgeeks.org/find-local-minima-array/