Searching Algorithms Questions Long
Binary interpolation search is a variant of the binary search algorithm that aims to improve the efficiency of searching for a specific element in a sorted array. It is based on the concept of interpolation, which involves estimating the position of the target element within the array.
The binary interpolation search algorithm starts by assuming that the elements in the array are uniformly distributed. It then uses this assumption to estimate the probable position of the target element by interpolating between the minimum and maximum values of the array.
The formula used for interpolation is:
position = low + ((target - array[low]) * (high - low)) / (array[high] - array[low])
In this formula, "low" represents the index of the lowest element in the array, "high" represents the index of the highest element, "target" represents the value being searched for, and "array" represents the sorted array.
Once the estimated position is calculated, 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 is repeated 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 uniformly distributed array for accurate estimations. If the array is not uniformly distributed, the algorithm may not provide accurate results and may even perform worse than binary search.
In conclusion, binary interpolation search is a searching algorithm that estimates the position of a target element in a sorted array using interpolation. It offers improved efficiency compared to binary search in certain scenarios, but its accuracy relies on the assumption of a uniformly distributed array.