Searching Algorithms Questions Long
The concept of binary interpolation search is a variation of the binary search algorithm that aims to improve the efficiency of searching for a specific element in a sorted array. It is particularly useful when the elements in the array are uniformly distributed.
Binary interpolation search works by estimating the position of the target element within the array based on its value and the values of the first and last elements in the array. This estimation is done using interpolation formula:
position = low + ((target - arr[low]) * (high - low)) / (arr[high] - arr[low])
In this formula, "low" represents the index of the first element in the array, "high" represents the index of the last element, "target" is the value being searched for, and "arr" is the sorted array.
Once the position is estimated, the algorithm compares the target value with the element at the estimated position. If they match, the search is successful. If the target value is smaller, the algorithm updates the "high" index to be one less than the estimated position and repeats the process. If the target value is larger, the algorithm updates the "low" index to be one more than the estimated position and repeats the process. This process continues until the target value is found or the search range is exhausted.
Binary interpolation search has a time complexity of O(log(log(n))) on average, making it more efficient than traditional binary search in certain scenarios. However, it is important to note that binary interpolation search requires a sorted array and may not perform well if the elements are not uniformly distributed.