Like Binary Search, Jump 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 a block (to be jumped) of size m. Then we search in the indexes arr, arr[m], arr[2m]…..arr[km] and so on. Once we find the interval (arr[km] < x < arr[(k+1)m]), we perform a linear search operation from the index km to find the element x.
Let’s consider the following array: (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610). The length of the array is 16. The Jump search will find the value of 55 with the following steps assuming that the block size to be jumped is 4.
STEP 1: Jump from index 0 to index 4;
STEP 2: Jump from index 4 to index 8;
STEP 3: Jump from index 8 to index 12;
STEP 4: Since the element at index 12 is greater than 55, we will jump back a step to come to index 8.
STEP 5: Perform a linear search from index 8 to get the element 55.
Performance in comparison to linear and binary search:
If we compare it with linear and binary search then it comes out than it is better than linear search but not better than binary search.
The increasing order of performance is:
linear search < jump search < binary search
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 will be ((n/m) + m-1). The value of the function ((n/m) + m-1) will be minimum when m = √n. Therefore, the best step size is m = √n.