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 position of a value within a range based on the values at the boundaries of that range. In the case of exponential interpolation search, the estimation is done exponentially.
The algorithm starts by comparing the target value with the element at the first position of the array. If they match, the search is successful and the position is returned. If the target value is greater than the first element, the algorithm doubles the position and checks the element at that position. This process continues until an element greater than the target value is found or the end of the array is reached.
Once an element greater than the target value is found, the algorithm performs interpolation between the previous and current positions to estimate the exact position of the target value. This estimation is done using the formula:
position = previous_position + ((target_value - array[previous_position]) * (current_position - previous_position)) / (array[current_position] - array[previous_position])
After estimating the position, the algorithm checks if the element at that position is equal to the target value. If they match, the search is successful and the position is returned. If the element is greater than the target value, the algorithm updates the current position to be the estimated position minus one and repeats the process. If the element is smaller than the target value, the algorithm updates the previous position to be the estimated position and repeats the process.
This process continues until the target value is found or the search range becomes empty. If the target value is not found, the algorithm returns -1 to indicate that the value is not present in the array.
Exponential interpolation search has a time complexity of O(log(log(n))) on average, making it more efficient than binary search in certain scenarios. However, it requires a sorted array and may not perform well if the array is not uniformly distributed.