Uniform Binary Search

Uniform Binary Search is an optimization of Binary Search algorithm when many searches are made on same array or many arrays of same size. In normal binary search, we do arithmetic operations to find the mid points. Here we precompute mid points and fills them in lookup table. The array look-up generally works faster than arithmetic done (addition and shift) to find the mid point. 

Examples: 

Input : array={1, 3, 5, 6, 7, 8, 9}, v=3
Output : Position of 3 in array = 2

Input :array={1, 3, 5, 6, 7, 8, 9}, v=7
Output :Position of 7 in array = 5

The algorithm is very similar to Binary Search algorithm, The only difference is a lookup table is created for an array and the lookup table is used to modify the index of the pointer in the array which makes the search faster . Instead of maintaining lower and upper bound the algorithm maintains an index and the index is modified using the lookup table. 

Position of 3 in array = 1

Time Complexity : O(log n).

 Auxiliary Space Complexity : O(log n) 

References : https://en.wikipedia.org/wiki/Uniform_binary_search