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Find the local minima in a given array
Objective: Given an array of integers 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 anyone.\
Approach:
Naïve: Use for loop and compare every element with its neighbor.
Time Complexity – O(n)
Binary Search Approach:
 Check if the mid element is smaller than its left and right neighbors.
 If the 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 the 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:
Output:
Local Minima is: 2
Reference: this
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