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 linear interpolation.
The steps involved in binary interpolation search are as follows:
1. Initialize the variables "low" and "high" to the first and last indices of the array, respectively.
2. Calculate the value of the target element using linear interpolation:
- Estimate the position of the target element within the array using the formula:
pos = low + ((target - arr[low]) * (high - low)) / (arr[high] - arr[low])
- Here, "target" is the value being searched for, "arr" is the sorted array, and "pos" is the estimated position of the target element.
3. Compare the estimated value at position "pos" with the target element:
- If the estimated value is equal to the target element, return the position "pos".
- If the estimated value is greater than the target element, update "high" to "pos - 1" and repeat step 2.
- If the estimated value is less than the target element, update "low" to "pos + 1" and repeat step 2.
4. Repeat steps 2 and 3 until the target element is found or "low" becomes greater than "high".
5. If the target element is not found, return -1 to indicate that it does not exist in the array.
Binary interpolation search has a time complexity of O(log(log(n))) on average, where "n" is the number of elements in the array. This makes it more efficient than traditional binary search, especially when the elements are uniformly distributed. However, it may perform poorly when the distribution of elements is skewed or uneven.