Algorithm Design Questions
The interpolation search algorithm is a searching technique used to find a specific element in a sorted array. It is an improvement over binary search as it uses the value of the element being searched for to estimate its position within the array.
The algorithm works by first assuming that the elements in the array are uniformly distributed. It then calculates an approximate position for the target element by using the formula:
position = low + ((target - arr[low]) * (high - low)) / (arr[high] - arr[low])
Here, 'low' and 'high' represent the indices of the first and last elements in the array, respectively. 'target' is the element being searched for.
Once the approximate 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 subarray. If the target element is larger, the algorithm narrows down the search range to the right subarray.
The process is repeated until the target element is found or the search range becomes empty. If the search range becomes empty, it means the target element is not present in the array.
Interpolation search has an average time complexity of O(log(log n)) for uniformly distributed arrays, making it faster than binary search in certain scenarios. However, it can perform poorly if the array is not uniformly distributed or if the target element is located towards the ends of the array.