Question

A peak item in an array is the item that is greater than its neighbors. If there are more than one peak item, simply return one of them. Input: [1,5,3,2,4,0] Output: 4 Input: [1,2,3,4,5,6] Output: 6 Input: [7,6,5,4,3,2] Output: 7 Describe a divide-and-conquer algorithm that solves this problem in Q(logn) time where n is the size of the array. Answer: (please write your answer here, add required space if needed)

Answer 1

To find a peak element using divide and conquer, you check the middle element and its neighbors, then recursively search the side that may contain a peak, halving the array each time, ensuring O(logn) time complexity.

Step-by-step explanation:

Divide and Conquer Algorithm to Find a Peak Element

To solve the problem of finding a peak element in an array with a divide and conquer approach in O(logn) time complexity, you can use the following algorithm:

1. Consider the middle element of the array. If it is not at the ends, check if it is greater than its neighbors. If so, return this element as a peak.
2. If the middle element is less than its right neighbor, then there must be a peak element on the right half of the array. Recursively apply the algorithm on the right half.
3. If the middle element is less than its left neighbor, then a peak must exist on the left half of the array. Recursively apply the algorithm on the left half.
4. If the middle element is at one of the ends, compare it with its single neighbor to determine if it's a peak.

By recursively halving the array, this approach ensures that the time complexity remains O(logn), since you reduce the problem size by half with each recursive call.