freeCodeCamp/guide/english/algorithms/search-algorithms/jump-search/index.md

title

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Jump Search

Jump Search

A jump search locates an item in a sorted array by jumping k items in the array and then verifies if the item wanted is between the previous jump and current jump.

Worst Case Complexity

O(√N)

How does it work ?

1. Define the value of k, the number of jumps: The optimal jump size is √N where N is the length of the sorted array.
2. Jump over the array elements by k everytime, checking the following condition Array[i] < valueWanted < Array[i+k].
3. If the previous condition is true, then do a linear search between Array[i] and Array[i + k].
4. Return the position of the value if it is found in the array.

Code In Java.

public int jumpSearch(int[] arr, int x) 
{ 
	int n = arr.length; 

	// Finding the size to be jumped 
	int jumpSize = (int) Math.floor(Math.sqrt(n)); 

	// Finding the index where element is present 
	int index = 0; 
	while (arr[Math.min(jumpSize, n)-1] < x) 
	{ 
		index = jumpSize; 
		jumpSize += (int) Math.floor(Math.sqrt(n)); 
		if (index >= n) 
			return -1; 
	} 
	// Searching for x beginning with index. 
	while (arr[index] < x) 
	{ 
		index++; 
		// If we reached next index or end of array then element is not present. 
		if (index == Math.min(jumpSize, n)) 
			return -1; 
	} 
	// If element is found 
	if (arr[index] == x) 
		return index; 
	return -1; 
} 

Code

To view examples of code implementation for this method, access this link below:

Jump Search - OpenGenus/cosmos

Credits

The logic's array image