How do you check if an array is bitonic or not?

Understanding the nature of a bitonic array is crucial in identifying its properties. A bitonic array is characterized by an initial strictly increasing sequence followed by a strictly decreasing sequence, or vice versa. Determining whether an array possesses this bitonic pattern involves a structured approach.

One effective method to verify if an array is bitonic involves calculating the midpoint (`mid`) within the range `[left, right]`. This step serves as a starting point for further analysis, as it allows us to compare the element at `mid` with its immediate neighbors.

The next step is to compare the element at index `mid` with its adjacent elements, `arr[mid-1]` and `arr[mid+1]`. If the element at `mid` is greater than both its neighbors, it indicates that we might have found a peak within the bitonic sequence. However, this condition alone is not sufficient to conclude that the entire array is bitonic.

Recognizing the peak element at `mid` as a potential turning point, we need to validate the bitonic property by recursively examining the subarrays to the left and right of `mid`. The left subarray should be strictly increasing up to `mid`, while the right subarray should be strictly decreasing from `mid`.

To ensure the left subarray is increasing, we recursively apply the same check starting from `left` to `mid-1`. Similarly, for the right subarray, we perform the check from `mid+1` to `right`. This recursive verification process ensures that the entire array adheres to the bitonic pattern.