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 binary search, as it uses exponential increments to narrow down the search range, resulting in a faster search time.
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 smooth and continuous. In the case of exponential interpolation search, the interpolation 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. Otherwise, the algorithm checks if the target value is greater than the element at the first position. If it is, the algorithm doubles the position and continues to check until it finds an element greater than the target value or reaches the end of the array.
Once the algorithm finds an element greater than the target value, it performs interpolation between the previous position and the current position 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 compares the target value with the element at that position. If they match, the search is successful. If the target value is smaller, the algorithm updates the current position to be the previous position and repeats the interpolation process. If the target value is greater, the algorithm updates the previous position to be the current position and continues the interpolation process.
The algorithm repeats these steps until it either finds the target value or determines that it is not present in the array. The time complexity of exponential interpolation search is O(log(log(n))), where n is the size of the array. This makes it more efficient than binary search, especially for large arrays.
In conclusion, exponential interpolation search is a searching algorithm that uses exponential increments and interpolation to find the position of a target value within a sorted array. It provides a faster search time compared to binary search and is particularly useful for large arrays.