an Introduction to binary search algorithm

an Introduction to binary search algorithm

• 1.
  Binary Search Efficient SearchingAlgorithm
• 2.
  Introduction • Binary searchis a divide-and-conquer algorithm used for searching in a sorted array. • It efficiently finds the position of a target value within the array.
• 3.
  How Binary SearchWorks • Binary search starts by comparing the target value with the middle element of the array. • If the middle element is the target, the search is successful. • If the target is smaller, the search continues on the left half of the array. • If the target is larger, the search continues on the right half of the array. • This process is repeated until the target is found or the search range becomes empty.
• 4.
  Algorithm Steps • Startwith a sorted array and a target value. • Set the search range to the entire array. • Calculate the middle index of the search range. • Compare the middle element with the target value. • If they are equal, the search is successful. • If the target is smaller, update the search range to the left half of the array and go to step 3. • If the target is larger, update the search range to the right half of the array and go to step 3. • Repeat steps 3-7 until the target is found or the search range is empty.
• 5.
  Implementation • It canbe implemented using iteration as well as recursion
• 6.
  Algorithm Steps int binarySearch(intarray[], int x, int start, int end) { // Iterative Binary Search // Repeat until the pointers start and end meet each other while (start <= end) { int mid = (start + start) / 2; if (array[mid] == x) return mid;
• 7.
  Algorithm Steps if (array[mid]< x) start = mid + 1; else end = mid - 1; } return -1; }
• 8.
  Algorithm Steps // RecursiveBinary Search int binarySearchRecursive(int arr[], int left, int right, int target) { if (left <= right) { int mid = left + (right - left) / 2; if (arr[mid] == target) return mid; else if (arr[mid] > target) return binarySearchRecursive(arr, left, mid - 1, target); else return binarySearchRecursive(arr, mid + 1, right, target); } return -1; }
• 9.
  Time Complexity • Binarysearch has a time complexity of O(log n), where n is the number of elements in the array. • It reduces the search space by half in each iteration, leading to a logarithmic time complexity.
• 10.
  Advantages of BinarySearch • Efficient searching algorithm for sorted arrays. • Works well even with large datasets. • Requires fewer comparisons compared to linear search.
• 11.
  Limitations of BinarySearch • Requires a sorted array as input. • Insertion and deletion operations are costly since the array needs to be maintained in a sorted order. • Binary search is not suitable for unsorted arrays.
• 12.
  Use Cases • Searchingfor an element in a phonebook. • Finding a specific word in a dictionary. • Implementing autocomplete functionality.
• 13.
  Conclusion • Binary searchis a powerful algorithm for efficient searching in sorted arrays. • It reduces the search space in each iteration, resulting in a logarithmic time complexity. • Understanding binary search can help optimize search operations in various applications.