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.
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 an unknown data point based on the values of known data points. In this case, exponential interpolation is used to estimate the position of the target value within the array.
The algorithm starts by comparing the target value with the first element of the array. If they are equal, 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. If the target value is less than the element at the current position, the algorithm performs a binary search between the previous position and the current position.
By doubling the position at each step, the algorithm narrows down the search range exponentially. This is based on the assumption that the elements in the array are uniformly distributed. The exponential increment allows the algorithm to skip over large portions of the array, reducing the number of comparisons required.
If the target value is found during the binary search, the position is returned. Otherwise, the algorithm continues doubling the position until the target value is found or the position exceeds the size of the array. If the position exceeds the size of the array, the algorithm concludes that the target value is not present.
Exponential interpolation search has a time complexity of O(log(log(n))), where n is the size of the array. This makes it more efficient than binary search, especially for large arrays. However, it requires the array to be sorted and uniformly distributed for optimal performance.
In conclusion, exponential interpolation search is a searching algorithm that uses exponential increments and interpolation to estimate the position of a target value within a sorted array. It offers improved efficiency compared to binary search for large arrays, but relies on the assumption of uniform distribution of elements.