Searching Algorithms Questions Long
The time complexity of binary interpolation search is O(log(log(n))) on average, where n is the size of the sorted array being searched.
Binary interpolation search is an improvement over binary search, which has a time complexity of O(log(n)). It is a searching algorithm that works on uniformly distributed sorted arrays.
The algorithm starts by calculating the position of the target value using interpolation formula:
pos = low + ((target - arr[low]) * (high - low)) / (arr[high] - arr[low])
Here, "low" and "high" represent the indices of the current search range, and "arr" is the sorted array being searched. The formula estimates the position of the target value based on its value and the values at the boundaries of the search range.
Once the position is calculated, the algorithm checks if the target value is found at that position. If it is, the search is successful. If not, the algorithm adjusts the search range by updating "low" and "high" based on whether the target value is smaller or larger than the value at the estimated position.
The time complexity of binary interpolation search is determined by the number of iterations required to find the target value. In the best-case scenario, the target value is found in the first iteration, resulting in a time complexity of O(1). However, in the worst-case scenario, the target value is not present in the array, and the search range keeps getting halved until it becomes empty. This results in a time complexity of O(log(log(n))).
The reason for the improved time complexity compared to binary search is that binary interpolation search estimates the position of the target value based on its value, allowing it to make more informed decisions about where to search next. This reduces the number of iterations required to find the target value, especially when the array is uniformly distributed.
It is important to note that the time complexity mentioned above is an average case analysis. In the worst-case scenario, binary interpolation search can still have a time complexity of O(n), similar to binary search. This occurs when the array is not uniformly distributed, leading to poor estimation of the target value's position.