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 O(log n) time where n is the size of the array.

Answer 1

The question is about finding a peak element in an array using a divide-and-conquer algorithm with O(log n) time complexity, similar to a binary search.

Step-by-step explanation:

Divide-and-Conquer Algorithm for Finding a Peak Element

To solve the problem of finding a peak element in an array in O(log n) time, we can use a divide-and-conquer algorithm. The approach is similar to binary search. Here's a step-by-step algorithm:

Start with the middle element of the array.

Check if the middle element is a peak (greater than its neighbors).

If it is, return the middle element as the peak.

If the left neighbor is greater, recursively apply the algorithm to the left subarray.

If the right neighbor is greater, recursively apply the algorithm to the right subarray.

This algorithm exploits the fact that if an element is not a peak and has a neighbor that is greater, then a peak must exist in the direction of the greater neighbor, due to the properties of peaks. The process is repeated by dividing the array in half each time, leading to the logarithmic time complexity.