Searching Algorithms Questions Long
Exponential interpolation search is a searching algorithm that is used to find the position of a target value within a sorted array. It is an improvement over the traditional binary search algorithm, as it uses exponential increments to narrow down the search range.
The concept of exponential interpolation search involves estimating the position of the target value by using interpolation. Interpolation is a technique that estimates the value of a function between two known values based on the assumption that the function is approximately linear within that interval.
In exponential interpolation search, the algorithm starts by comparing the target value with the element at the first position of the array. If the target value is found at this position, the search is successful. Otherwise, the algorithm estimates the position of the target value by using interpolation.
To estimate the position, the algorithm calculates the position using the formula:
pos = low + ((target - arr[low]) / (arr[high] - arr[low])) * (high - low)
Here, "low" represents the lower bound of the current search range, "high" represents the upper bound, and "arr" represents the sorted array. The formula calculates the position by considering the proportion of the difference between the target value and the element at the lower bound to the difference between the elements at the lower and upper bounds.
Once the position is estimated, the algorithm compares the target value with the element at that position. If the target value is found, the search is successful. Otherwise, the algorithm adjusts the search range based on the comparison result.
If the target value is greater than the element at the estimated position, the algorithm updates the lower bound to be one position ahead of the estimated position and doubles the search range. This is done to exponentially increase the search range, as the target value is expected to be closer to the higher end of the array.
If the target value is smaller than the element at the estimated position, the algorithm updates the upper bound to be one position behind the estimated position. This is done to narrow down the search range, as the target value is expected to be closer to the lower end of the array.
The algorithm repeats these steps until the target value is found or the search range becomes empty. If the search range becomes empty, it means that the target value is not present in the array.
Exponential interpolation search has a time complexity of O(log(log(n))), where "n" represents the size of the array. This makes it more efficient than traditional binary search in certain scenarios, especially when the target value is located towards the higher end of the array. However, it may not always outperform binary search, as its performance heavily depends on the distribution of the data.