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, "high" represents the index of the last element, "target" is the value being searched, and "arr" is the sorted array.
Once the position is estimated, the algorithm compares the target element with the element at the estimated position. If they match, the search is successful. If the target element is smaller, the algorithm narrows down the search range to the left half of the array. If the target element is larger, the algorithm narrows down the search range to the right half of the array. This process continues until the target element is found or the search range is reduced to zero.
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.