The search algorithm that gives an overall time complexity of O(log i) + O(log n) isGroup of answer choices

The search algorithm that gives an overall time complexity of O(log i) + O(log n) is Interpolation Search.

Here's a step-by-step explanation:

1. Interpolation search is an improved variant of binary search. This search algorithm works on the probing position of the required value. For this algorithm to work properly, the data collection should be in a sorted form and equally distributed.

2. Initially, the probe position is the position of the middle most item of the collection. If a match occurs, then the index of the item is returned. If the middle item is greater than the item, then the probe position is again calculated in the sub-array to the right of the middle item. Otherwise, the item is searched in the subarray to the left of the middle item. This process continues on the sub-array as well until the size of subarray reduces to zero.

3. There is a specific formula to calculate the position of the item which is derived from the probe position formula by taking the assumption of uniform distribution of values in the array. This formula is:

   pos = lo + [ (x-arr[lo])*(hi-lo) / (arr[hi]-arr[Lo]) ]

   arr[] ==> Array where elements need to be searched x ==> Element to be searched lo ==> Starting index in arr[] hi ==> Ending index in arr[]

4. The time complexity of this algorithm is O(log log n) for a uniform distribution and in worst case it can go up to O(n).