Recursive Binary Search in JavaThe binary search algorithm is one of the commonly used algorithms in programming. It is used to search and find an element in a sorted array. The binary search algorithm is a highly efficient search technique used to locate a specific element in a sorted dataset. It works by repeatedly dividing the dataset in half and comparing the target value with the middle value until the target value is discovered or determined to be absent. Binary search is based on the divideandconquer principle, which involves breaking down a large problem into smaller, more manageable subproblems. In the case of binary search, the large problem is finding a specific element in a sorted dataset. The subproblems are then recursively solved until the target element is found or determined to be absent. The divide and conquer principle are a powerful technique that can be used to solve a wide variety of problems. The divide and conquer principle in programming is a problemsolving technique that involves breaking down a large problem into smaller, more manageable subproblems. The subproblems are then solved recursively until the original problem is solved.
How does Binary Search algorithm work?The binary search algorithm is a divide and conquer algorithm that searches for a specific element in a sorted array. Note that the collection of elements/array must be sorted for the algorithm to work efficiently. Initialize the search interval. The search interval is the range of elements in the dataset that are currently being considered. Initially, the search interval is the entire dataset. Step 1: Find the middle element of the search interval. It is done by calculating the average of the first and last elements in the search interval. Step 2: Compare the target value to the middle element. If the target value is equal to the middle element, then the search is successful and the index of the target element is returned. Step 3: If the target value is less than the middle element, then the search interval is narrowed down to the left half of the original search interval. Step 4: If the target value is greater than the middle element, then the search interval is narrowed down to the right half of the original search interval. Step 5: Steps 2 through 5 are repeated until the target element is found or the search interval becomes empty. Binary Search AlgorithmNote: X is the element that we want to search.
BinarySearch.java Output: Element found at index 3 ComplexityBest Case: For the best case the time complexity is O(1). The best case occurs when the target element is the middle element of the array. In this case, the algorithm only needs to compare the target element to the middle element and returns the index of the target element. Average Case: For the average case the time complexity is O(n). The average case occurs when the target element is not the middle element of the array. In this case, the algorithm will need to divide the array in half and compare the target element to the middle element. The algorithm will then recursively search the appropriate half of the array. The process will continue until the target element is found or the array becomes empty. Worst Case: The worst case complexity is O(n log n). The worst case occurs when the target element is not in the array. In this case, the algorithm will divide the array in half and compare the target element to the middle element. The algorithm will then recursively search the appropriate half of the array. This process will continue until the array becomes empty. Applications of Binary Search:
Advantages of Binary Search
Disadvantages of Binary SearchOne disadvantage of binary search is that it requires the dataset to be sorted. This can add overhead to the search algorithm, especially for large datasets. Additionally, binary search is not as effective as linear search for searching small datasets.
Next TopicSet Intersection in Java
