Binary search and linear search are two of the methods we use to search the elements in an array. Well, searching refers to the process of searching for an element in a list of elements that are stored in any order, or randomly. Generally, people believe that binary is faster than using linear. It takes you less time to find an element in the sorted list. As a result, it is evident that binary search is more efficient than linear search.
However, the binary search requires that the elements be sorted, while linear searches do not require such a prerequisite. Both searching methods employ different techniques, which will be discussed below at algo.monster.
Binary Search Definition (What is binary search?)
Binary search is a very efficient algorithm. This search method takes less time and allows for fewer comparisons. First, sort the array elements to perform the binary search.
Below is the logic behind this technique:
Find the middle element in the array first.
You will compare the element you need to search with the middle element of an array.
Three possible scenarios could be triggered:
This search will be successful if the element is found in the required element.
If the element is smaller than the item you are looking for, search only the first part of the array.
If the element is larger than the desired one, search for the second half.
Continue to repeat the process until you find or exhaust an element in your search area. This algorithm reduces the search area every time. Also, the number of comparisons is limited to log (N+1). Hence, it tends to be more efficient than using linear. However, the array must be sorted before the binary search can be performed.
Definition of Linear Search (What is linear search?)
Each element in an array is searched linearly. It is then retrieved one at a time, in a logical sequence, and checked to see if it is the desired element. If all elements have been accessed and the desired element has not been found, a search will fail. Also, the worst-case scenario is that we might have to scan half the size array in order to find the desired element.
Actually, linear search is a technique that traverses an array sequentially in order to find the item.
Linear search efficiency
Normally, the efficiency of a technique is determined by its time consumption and the number of comparisons that are made when searching for a record in a search engine. Only one comparison will be made if the desired record is in the first search table position. If the desired record is in the last position of the search table, then there must be n comparisons.
So, when the record is to be spotted somewhere in the search list, the average number of comparisons will be (n+1/2). This technique has an O(n) efficiency. Also, it stands for the order of execution.
Overall comparison
Let’s look at the table below:
| Algorithms | Binary search | Linear search |
| Also know as | Half-interval sarch and logarithmic search. | Sequential search. |
| Type of Algorhtms/Appraoches | In nature, it is divide and conquer algorithms. | Iterative. |
| Basics | It is based on divide and conquer algorithm. Search the value in a sorted array. | From the beginning to the end, it searches for the mathcing element by comparing with each one sequentially. |
| Time compliexy | O(log2 n) | O(n) |
| Efficiency | More efficient compared with linear search. | Not efficient enough in large data set searching. |
| When is the best case | When a match element is available at the first dividing as in the middle of the array. | The best case is when the matching value is at the first position of the array. |
| Best case time | When it’s in the center, O(1) | When it appears as the first element, O(1) |
| Need any prerequisite for the array? | Need the array to be in sorted order. | No specific requirements. |
| N number of elements worst case | Could come to the conclustion after only log2 N comparisons. | Need to complete N comparisons. |
| Implementation | Isn’t able to be implemented on linked list directly. | Both linked list and array. |
| Applications | It needs the elements in the array to be in order. | Relatively reasy to apply, needs no ordered elements. |
| Code lines | More. | Usually, much less. |
The key differences between Binary Search and Linear Search
Well, after an overall comparison, it’s necessary to check out some of the most important points:
The linear search uses a sequential approach and is iterative by nature. Binary search, on the other hand, uses a divide and conquer approach.
Then, binary search has Olog2N while linear search has O(N).
In linear search, the best case time is for O(1), which is the first element. Binary search is different. It’s for the middle element (O(1)).
The worst-case scenario for searching an element in linear search is N comparisons. It is log2N for binary searches, however.
Usually, we can use linear search both in an array and in a linked list to solve problems. Yet, you can not apply binary search directly on linked lists.
Binary search, as we all know, requires a sorted array. This is why it requires processing to insert the element at its correct place in order to maintain a sorted listing. Linear search, on the other hand, does not require sorted elements. Therefore you can insert elements at any point in the list.
Linear search is simple to use and does not require any ordered elements. Binary search is more difficult, however, you need to arrange all elements in an orderly fashion.
Conclusion
Depending on the application, both linear and binary search algorithms may be used. Binary search is best for quick searches when an array is the data structure with elements arranged in sorted order. Because binary search cannot be implemented directly, the linear search can be used if the linked list contains the same data structure.
However, you cannot use binary search algorithms in link lists. This is because link lists are dynamic and it is not possible to spot the middle element. Because binary searches are faster than linear searches, it is necessary to create a variant of the binary search algorithm that works on linked lists.
For more information about searching algorithms or relevant areas, please visit algo.monster.
