Like Binary Search, Jump Search (or Block Search) is a searching algorithm for sorted arrays. The basic idea is to check fewer elements (than linear search) by jumping ahead by fixed steps or skipping some elements in place of searching all elements.
For example, suppose we have an array
arr of size
n and block (to be jumped)
m. Then we search at the indexes
arr[2 * m], ...,
arr[k * m] and
so on. Once we find the interval
arr[k * m] < x < arr[(k+1) * m], we perform a
linear search operation from the index
k * m to find the element
What is the optimal block size to be skipped?
In the worst case, we have to do
n/m jumps and if the last checked value is
greater than the element to be searched for, we perform
m - 1 comparisons more
for linear search. Therefore the total number of comparisons in the worst case
((n/m) + m - 1). The value of the function
((n/m) + m - 1) will be
m = √n. Therefore, the best step size is
m = √n.
O(√n) - because we do search by blocks of size