What is the concept of interpolation search?

Interpolation search is a searching algorithm that is used to find a specific element in a sorted array or list of elements. It is an improvement over binary search, as it makes intelligent guesses about the location of the target element based on the values of the elements in the array.

The concept of interpolation search is based on the idea of linear interpolation. It assumes that the elements in the array are uniformly distributed, which means that the difference between consecutive elements is approximately the same. This assumption allows the algorithm to estimate the position of the target element more accurately.

The interpolation search algorithm starts by comparing the target element with the first and last elements of the array. If the target element is equal to the first or last element, the search is complete. Otherwise, it estimates the position of the target element using the following formula:

position = start + ((target - array[start]) * (end - start)) / (array[end] - array[start])

Here, 'start' and 'end' represent the indices of the first and last elements in the array, respectively. The formula calculates the position by considering the proportion of the difference between the target element and the first element to the difference between the first and last elements.

Once the position is estimated, the algorithm compares the target element with the element at the estimated position. If they are equal, the search is complete. If the target element is smaller, the algorithm updates the 'end' index to be the position minus one and repeats the process. If the target element is larger, the algorithm updates the 'start' index to be the position plus one and repeats the process. This process continues until the target element is found or the 'start' index becomes greater than the 'end' index, indicating that the target element is not present in the array.

The interpolation search algorithm has a time complexity of O(log log n) on average, making it faster than binary search in certain scenarios. However, it may perform poorly if the elements in the array are not uniformly distributed, as the estimation may not be accurate. In such cases, binary search or other algorithms may be more suitable.