Time complexity of Binary Search

In this blog, you will learn about Binary Search Algorithms, the time complexity of binary search, how binary search works, its various advantages, and applications.

What is Meant by Binary Search?

The binary search finds a specific element within a sorted data collection. Moreover, binary search is one of the top search techniques that provides the fastest way to locate the sorted list item. It works by the "divide and conquer" principle, which constantly divides the search space until the target item is found. However, the collected data must be sorted in ascending or descending order so that the binary search works perfectly. Moreover, the time complexity of binary search makes the binary search work much faster than other search algorithms. 

The algorithm begins by comparing the target and the central element of the group. If both parts match, the binary search is successful. The search moves on to the lower half of the group if the target element is less than the middle element. Otherwise, the search will continue to the upper half. 

In this way, by repeatedly reducing the search space, binary search removes half of the remaining elements with each comparison. This binary search property makes it much more efficient and effective in the case of vast data collection. Further, the binary search algorithm divides the search space until the search space becomes empty or the target element is found.

Moreover, binary search has a time complexity known as O(log n), where "n" denotes the number of elements within the collection. A logarithmic time complexity makes it much faster than a linear search, with a time complexity of O(n). Here the big "O" notation is used because it presents the volume of operations an algorithm performs. 

It should be noted that binary search requires sorting the collection and is frequently carried out through iterative or recursive methods.

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How does the Binary Search Algorithm Work?

The binary search algorithm is a robust search algorithm that helps to find the target value's position within a sorted list. It repeatedly splits the search space into half and eliminates the other half that doesn't contain the target value. However, the following steps will explain to you how the binary search works:

1) Input: 

At first, the search algorithm takes the input of a sorted list and a target value to search for.

2) Initialization: 

The next step in this regard is to set the beginning index low to the array's first element and the last index high to the array's previous feature. 

3) Search Process: 

It is the actual search process where you need to repeat the below steps until the low value becomes more significant than the high:

Compute the middle index mid as the average value of the low and high elements. If the central index mid's value equals the target value, the binary search is booming, and the algorithm will return the index mid. 
If the element value at the middle index mid is greater than the target value, then update the high value to mid - 1 to search in the left half of the remaining array.
Modify the element value from low to mid + 1 to find the right half of the entire array. It is applicable if the deal at the middle index, central, is less than the desired value.

4) Target Not Found: 

The search algorithm produces a unique value to show that the target is not present in the array after the binary search procedure is finished and the target value has not been discovered.

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Benefits of Binary Search

Binary search offers multiple benefits over other searching algorithms and deals with large and sorted datasets. The following are some key benefits of binary search: 

  • The binary search is simpler and easier to implement than other complex algorithms. It follows a simple recursive or iterative method, making the algorithm much easier to know and use.
  • Binary search includes an O(log n) time complexity, allowing faster runtime than linear search algorithms. 
  • This popular search algorithm eliminates a large part of the dataset in every repetition dividing the search space into half. This reduced comparison makes binary search more efficient to use than other algorithms. 
  • It can be noted that binary search is most effective when the large dataset is sorted. It may take some time to sort the data, but the binary search becomes more efficient if you perform multiple searches on the same data. It is because it helps to sort data only once.
  • Binary search is highly versatile and widely applicable in multiple programming areas. It is applied to several data structures like arrays, lists, trees, etc. It is based on sorted data.
  • Moreover, binary search has a predictable behavior that follows the divide-and-win approach. Each repetition of data divides the search space in half, reducing uncertainty and ensuring that the algorithm meets the required element. 

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Applications of Binary Search Algorithm 

There are many applications of binary search algorithms. It is a technique primarily helpful in searching for a specific element within a sorted array. It sorts out the details by repeatedly splitting the search space into half and eliminates half of the remaining parts at each stage. However, the following are the various applications of binary search algorithm:  

  • Searching :The binary search algorithm is primarily helpful for searching in sorted data collections. The feature time complexity of binary search makes it much faster to search. It also enables quick recovery of elements by continuously splitting the search space in half. Therefore, it can quickly deal with large datasets. 
  • Insertion and Deletion:Binary search is also helpful to find the correct position for element insertion into a sorted list through an order. It is also helpful for locating the element's position for removal.
  • Range Queries:The most extensive application of binary search algorithms is to find the elements within a specific range. You can perform a binary search to find a field's starting and ending positions, where you can quickly recover all the elements within the specific range. 
  • Dictionary:You can use binary search to find a word in a dictionary where all the words are arranged in a lexicographical order. Binary search will help to find the alphabet without going to each letter in the dictionary.  
  • Dynamic Programming: Binary search is effectively helpful in the issues related to dynamic programming to optimize solutions. By applying a binary search algorithm to assess the correct parameter value, you can minimize the time complexity of binary search and improve the algorithm's efficiency.
  • Square Root Approximation:Another application of binary search is to approximate the value of a square root. You can define the range in which the square root lies and repeatedly reduce the range until the desired results are achieved. 

What is meant by the Time Complexity of Binary Search?

The Time Complexity of Binary Search refers to O(log n), where the element "n" indicates the number of elements with the sorted array being searched. As a result, the amount of input has a logarithmic effect on how long it takes to complete a binary search.

The binary search works by regularly splitting the search space into half until it finds the target element. The search function compares the target element with the middle element of the present search area at each stage and changes the borders as necessary.

Hence, this behavior makes the binary search an efficient algorithm useful for large sorted lists. Dividing the search area by half with each repetition works much faster. It leads to a significantly faster search than other (linear) search functions with a time complexity of O(n). Here the time complexity of the binary search is O(log n), making it faster to search an element through a split-and-conquer approach.

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Thus, the above details are about the time complexity of binary search and its various aspects, including its application and benefits. Using a binary search algorithm, you can make any complex search much faster to get the quick and desired results than any other search algorithm. Therefore, it is a highly used approach in complex searches. Stay tuned in this space for more updates and ideas.

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As a content writer at HKR trainings, I deliver content on various technologies. I hold my graduation degree in Information technology. I am passionate about helping people understand technology-related content through my easily digestible content. My writings include Data Science, Machine Learning, Artificial Intelligence, Python, Salesforce, Servicenow and etc.