Question

Write, in brief, a note on searching and sorting with examples.

Hint:

Searching and Sorting are essential operations in computer science. 1. {Searching Algorithms}:
-{Linear Search}: Checks each element sequentially, \(O(n)\) time complexity.
-{Binary Search}: Works on sorted data, repeatedly divides the list in half, \(O(\log n)\) time complexity. 2. {Sorting Algorithms}:
-{Bubble Sort}: Compares and swaps adjacent elements until sorted, \(O(n^2)\) time complexity.
-{Merge Sort}: Divides the list, recursively sorts, and merges, \(O(n \log n)\) time complexity.

Answer 1

Searching and Sorting are two fundamental operations in computer science, commonly used to manipulate and retrieve data from collections such as arrays, lists, and databases.
1. Searching:
Searching is the process of finding a specific element in a collection of data. There are different search algorithms based on the type of data and its organization. Common Searching Algorithms:
- Linear Search: - In this search method, each element of the collection is checked sequentially until the target element is found.
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Example:
If we want to find the number 8 in the list \([1, 3, 5, 8, 10]\), we check each element in the list until we find 8.
- Time Complexity: \(O(n)\) where \(n\) is the number of elements.
- Binary Search: - This method works on sorted data. It repeatedly divides the list in half and checks if the middle element is the target. If not, it continues the search in the left or right half based on the comparison.
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Example:
For a sorted list \([1, 3, 5, 8, 10]\), to find 8, the middle element (5) is compared, and the search moves to the right half of the list.
- Time Complexity: \(O(\log n)\) where \(n\) is the number of elements.
2. Sorting:
Sorting is the process of arranging elements in a specific order, usually in ascending or descending order. It is often a precursor to efficient searching. Common Sorting Algorithms:
- Bubble Sort: - In this method, each pair of adjacent elements is compared and swapped if they are in the wrong order. The process repeats until no swaps are needed.
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Example:
For the list \([5, 2, 9, 1]\), the algorithm will compare adjacent elements and swap them until the entire list is sorted.
- Time Complexity: \(O(n^2)\) where \(n\) is the number of elements.
- Merge Sort: - This is a divide-and-conquer algorithm that splits the list into two halves, recursively sorts them, and then merges the sorted halves.
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Example:
For a list \([5, 2, 9, 1]\), it will first split into \([5, 2]\) and \([9, 1]\), then sort and merge the halves.
- Time Complexity: \(O(n \log n)\) where \(n\) is the number of elements.