Linear Search

Linear search is a basic search algorithm used to find an element in a list. It works by iterating through the elements of the list one by one until it finds the target element or until it has searched the entire list. Linear search is also known as sequential search, as it searches the list sequentially.

Advantages

Linear search is a simple and intuitive algorithm. It is easy to implement and requires no special data structures or complex algorithms. It is also useful for searching small lists, where the overhead of more complex algorithms, such as binary search, is not worth the additional performance gain.

Disadvantages

Linear search has a time complexity of O(n), where n is the size of the list. This means that the time taken to search the list increases linearly with the list size. Therefore, linear search is not an efficient algorithm for large lists. Binary search and other more complex algorithms can provide better performance for large lists.

Implementation

Here is an example implementation of linear search in Java.

Main


              123456789
            
public static int linearSearch(int[] arr, int target) {
    for (int i = 0; i < arr.length; i++) {
        if (arr[i] == target) {
            return i;
        }
    }

    return -1;
}

This implementation takes an array of integers and a target element as input and returns the index of the target element in the array. If the target element is not found, it returns -1.

Optimizations

There are several ways to optimize the linear search algorithm, such as:

Sorted list: If the list is sorted, binary search can be used instead of linear search. Binary search has a time complexity of O(log n), which is much faster than linear search.
Move to front: If an element is found in the list, it can be moved to the front of the list to speed up future searches. This is called the "move-to-front" heuristic.
Transposition: If an element is found in the list, it can be swapped with the previous element to improve the locality of the reference. This is called the "transposition" heuristic.
Sentinel: A sentinel value can be added to the end of the list to eliminate the need for bounds check in the loop. The sentinel value is set to the target element, so the loop will terminate as soon as the target element is found.

1. What is the time complexity of linear search?

2. When is linear search a good choice of algorithm?

Tudo estava claro?

Seção 2. Capítulo 4