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 improved version of the binary search algorithm, which reduces the number of comparisons required to find the target value.
The time complexity of exponential interpolation search can be analyzed as follows:
1. Best-case time complexity:
In the best-case scenario, the target value is found at the first position itself. In this case, the time complexity of exponential interpolation search would be O(1), as only one comparison is required.
2. Average-case time complexity:
The average-case time complexity of exponential interpolation search is O(log(log(n))), where 'n' represents the size of the array. This is because the algorithm uses exponential interpolation to estimate the position of the target value. It starts by comparing the target value with the element at the first position, and if it is smaller, it returns -1 (indicating that the target value is not present in the array). Otherwise, it calculates the position using the formula:
pos = low + ((target - arr[low]) / (arr[high] - arr[low])) * (high - low)
Here, 'low' and 'high' represent the current range of the array being searched. The algorithm then compares the target value with the element at the calculated position. If they are equal, the target value is found. Otherwise, it adjusts the range based on whether the target value is smaller or larger than the element at the calculated position, and repeats the process until the target value is found or the range becomes empty.
The exponential interpolation technique allows the algorithm to make larger jumps towards the target value, reducing the number of comparisons required. However, the time complexity is still logarithmic due to the halving of the range in each iteration.
3. Worst-case time complexity:
The worst-case time complexity of exponential interpolation search is O(n), which occurs when the target value is located at the end of the array or is not present in the array at all. In this case, the algorithm would need to compare the target value with each element in the array until the end is reached or the target value is found.
It is important to note that the time complexity analysis assumes that the array is sorted in ascending order. If the array is not sorted, an additional step of sorting the array would be required, which would have a time complexity of O(n log(n)).
In conclusion, the time complexity of exponential interpolation search is O(log(log(n))) on average, O(1) in the best-case scenario, and O(n) in the worst-case scenario.