Binary search in ds
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This document discusses binary search, an algorithm that searches a sorted list by dividing the list in half at each step. It works by comparing the search key to the middle element of the list and eliminating half of the elements from further consideration based on whether the key is smaller or larger than the middle element. The algorithm has a runtime complexity of O(log n), making it very efficient for large lists. An example implementation is provided that starts by comparing the search key to the middle element, and recursively searches either the left or right half of the list depending on the comparison.
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![Algorithm
binarySearch(arr, x, low, high)
if low > high
return False
else
mid = (low + high) / 2
if x == arr[mid]
return mid
else if x > data[mid] // x is on the right side
return binarySearch(arr, x, mid + 1, high)
else // x is on the right side
return binarySearch(arr, x, low, mid - 1)](https://image.slidesharecdn.com/binarysearchinds-200516065206/85/Binary-search-in-ds-7-320.jpg)
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- 1. Binary Search in Data Structure Prof. Neeraj Bhargava Kapil Chauhan Department of Computer Science School of Engineering & Systems Sciences MDS University, Ajmer
- 2. Introduction A binary search is an advanced type of search algorithm that finds and fetches data from a sorted list of items. Its core working principle involves dividing the data in the list to half until the required value is located and displayed to the user in the search result. Binary search is commonly known as a half-interval search or a logarithmic search.
- 3. Cont.. This search algorithm works on the principle of divide and conquer. Binary Search is used for searching an element in a sorted array. It is a fast search algorithm with run-time complexity of O(log n).
- 4. Cont.. Binary search works on the principle of divide and conquer. This searching technique looks for a particular element by comparing the middle most element of the collection. It is useful when there are large number of elements in an array.
- 5. Example
- 6. Implementation Binary searching starts with middle element. If the element is equal to the element that we are searching then return true. If the element is less than then move to the right of the list or if the element is greater than then move to the left of the list. Repeat this, till you find an element.
- 7. Algorithm binarySearch(arr, x, low, high) if low > high return False else mid = (low + high) / 2 if x == arr[mid] return mid else if x > data[mid] // x is on the right side return binarySearch(arr, x, mid + 1, high) else // x is on the right side return binarySearch(arr, x, low, mid - 1)
- 8. Assignment Explain Binary search in DS with suitable example and also discuss algorithm.