Searching techniques in Data Structure And Algorithm

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SEARCHING TECHNIQUES
DATA STRUCTURE AND
ANALYSIS
Instructor
Pir Syed M Ayaz Farid Shah

What is searching?
 Searching is an operation or a technique that
helps finds the place of a given element or
value in the list. Any search is said to be
successful or unsuccessful depending upon
whether the element that is being searched is
found or not.

Most read

Binary Search Algorithm
 Compare x with the middle element.
 If x matches with middle element, we return
the mid index.
 Else If x is greater than the mid element, then
x can only lie in right half subarray after the
mid element. So we recur for right half.
 Else (x is smaller) recur for the left half.

Binary vs. Linear Search
•Input data needs to be sorted in Binary Search and not in Linear Search
•Linear search does the sequential access whereas Binary search access
data randomly.
•Time complexity of linear search -O(n) , Binary search has time complexity
O(log n).
• Linear search performs equality comparisons and Binary search performs
ordering comparisons

Interpolation Search
Interpolation search is an improved variant of binary
search. This search algorithm works on the probing
position of the required value. For this algorithm to work
properly, the data collection should be in a sorted form
and equally distributed.
Binary search has a huge advantage of time complexity
over linear search. Linear search has worst-case
complexity of Ο(n) whereas binary search has Ο(log n).
There are cases where the location of target data may
be known in advance. For example, in case of a
telephone directory, if we want to search the telephone
number of Morphius. Here, linear search and even
binary search will seem slow as we can directly jump to
memory space where the names start from 'M' are
stored.

Interpolation Search Algorithm
Step 1 − Start searching data from middle of the list.
Step 2 − If it is a match, return the index of the item, and exit.
Step 3 − If it is not a match, probe position.
Step 4 − Divide the list using probing formula and find the new midle.
Step 5 − If data is greater than middle, search in higher sub-list.
Step 6 − If data is smaller than middle, search in lower sub-list.
Step 7 − Repeat until match.

Binary vs. Interpolation Search
 Positioning in Binary Search
 Position Probing in Interpolation Search

Searching Techniques
There are tow types of searching in data
structure and analysis
 Linear Search
 Binary Search
 Interpolation Search

Linear Search
Linear search is a very simple search algorithm.
In this type of search, a sequential search
is made over all items one by one. Every item is
checked and if a match is found then that
particular item is returned, otherwise the search
continues till the end of the data
collection.

Linear Search Algorithm
 Linear Search ( Array A, Value x)
 Step 1: Set i to 1
 Step 2: if i > n then go to step 7
 Step 3: if A[i] = x then go to step 6
 Step 4: Set i to i + 1
 Step 5: Go to Step 2
 Step 6: Print Element x Found at index i and go to
step 8
 Step 7: Print element not found
 Step 8: Exit

Binary search
Binary search is a fast search algorithm with run-time complexity of Ο(log n).
This search
algorithm works on the principle of divide and conquer. For this algorithm to
work properly,
the data collection should be in the sorted form.
Binary search looks for a particular item by comparing the middle most item of
the
collection. If a match occurs, then the index of item is returned. If the middle
item is
greater than the item, then the item is searched in the sub-array to the right of
the middle
item. Otherwise, the item is searched for in the sub-array to the left of the
middle item.
This process continues on the sub-array as well until the size of the subarray
reduces to
zero.

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this is the very imporantant in data struvture.Searching is a fundamental operation in data structures and plays a crucial role in various computer science and programming tasks. It involves looking for a specific element, value, or key within a given data structure to determine whether it exists or to retrieve it if found. The efficiency and effectiveness of searching algorithms can vary depending on the data structure being used and the specific requirements of the task. Here are some common data structures and descriptions of how searching works in each of them: Searching Algorithms: Linear Search: A basic algorithm that sequentially checks each element in a data structure until a match is found. Binary Search: A more efficient algorithm for sorted arrays or lists that repeatedly divides the search interval in half. Hashing: Using a hash function to map keys to specific locations for quick retrieval (e.g., in hash tables). Data Structures for Searching: Arrays: Basic data structure often used in linear searches. Lists: Linked lists or dynamic arrays can be used for searching. Trees: Binary Search Tree (BST): A binary tree where the left subtree contains values less than the root, and the right subtree contains values greater than the root. Balanced Trees: Trees like AVL and Red-Black trees maintain balance for efficient searching. Heaps: Used for priority queues and can support efficient operations for finding the minimum or maximum. Hash Tables: Utilizes hash functions for quick lookups. Search Variations: Searching for Minimum/Maximum: Algorithms designed to find the minimum or maximum element in a data structure efficiently. Substring Search: Searching for a specific substring within a larger text or string. Pattern Matching: Searching for a specific pattern or sequence of elements within a data structure. Advanced Search Techniques: Trie: A tree-like data structure used for efficient string searching and storage. Bloom Filter: A probabilistic data structure for quickly checking whether an element is a member of a set. K-Dimensional Trees: Used for multidimensional data, like spatial searching in geographic information systems. Optimizations and Indexing: Indexing: Techniques to create indexes or data structures that accelerate searching in large datasets. Skip Lists: A data structure that uses multiple levels of linked lists to speed up searches. Parallel and Distributed Searching: Parallel Search Algorithms: Techniques for searching in parallel processing environments. Distributed Search: Strategies for searching in distributed systems or databases. Search Complexity and Analysis: Time Complexity: Analyzing the efficiency of search algorithms in terms of the number of operations required. Space Complexity: Analyzing the memory usage of search data structures. Searching in Specialized Applications: Graph Search: Techniques for traversing and searching in graphs. Geospatial Search: Searching .

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Sequential and interval searching algorithms are used to search for elements in data structures. Sequential searches, like linear search, sequentially check each element until finding a match. Interval searches, like binary search, target the center of the search structure and divide the search space in half with each iteration. Other searching techniques include sentinel search, which adds a sentinel value to reduce comparisons, and Fibonacci search, which divides the search space into unequal parts based on Fibonacci numbers.

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Searching techniques in Data Structure And Algorithm

1. SEARCHING TECHNIQUES DATA STRUCTURE AND ANALYSIS Instructor Pir Syed M Ayaz Farid Shah

2. What is searching?  Searching is an operation or a technique that helps finds the place of a given element or value in the list. Any search is said to be successful or unsuccessful depending upon whether the element that is being searched is found or not.

3. Searching Techniques There are tow types of searching in data structure and analysis  Linear Search  Binary Search  Interpolation Search

4. Linear Search Linear search is a very simple search algorithm. In this type of search, a sequential search is made over all items one by one. Every item is checked and if a match is found then that particular item is returned, otherwise the search continues till the end of the data collection.

5. Linear Search Algorithm  Linear Search ( Array A, Value x)  Step 1: Set i to 1  Step 2: if i > n then go to step 7  Step 3: if A[i] = x then go to step 6  Step 4: Set i to i + 1  Step 5: Go to Step 2  Step 6: Print Element x Found at index i and go to step 8  Step 7: Print element not found  Step 8: Exit

6. Binary search Binary search is a fast search algorithm with run-time complexity of Ο(log n). This search algorithm works on the principle of divide and conquer. For this algorithm to work properly, the data collection should be in the sorted form. Binary search looks for a particular item by comparing the middle most item of the collection. If a match occurs, then the index of item is returned. If the middle item is greater than the item, then the item is searched in the sub-array to the right of the middle item. Otherwise, the item is searched for in the sub-array to the left of the middle item. This process continues on the sub-array as well until the size of the subarray reduces to zero.

7. Binary Search Algorithm  Compare x with the middle element.  If x matches with middle element, we return the mid index.  Else If x is greater than the mid element, then x can only lie in right half subarray after the mid element. So we recur for right half.  Else (x is smaller) recur for the left half.

8. Binary vs. Linear Search •Input data needs to be sorted in Binary Search and not in Linear Search •Linear search does the sequential access whereas Binary search access data randomly. •Time complexity of linear search -O(n) , Binary search has time complexity O(log n). • Linear search performs equality comparisons and Binary search performs ordering comparisons

9. Interpolation Search Interpolation search is an improved variant of binary search. This search algorithm works on the probing position of the required value. For this algorithm to work properly, the data collection should be in a sorted form and equally distributed. Binary search has a huge advantage of time complexity over linear search. Linear search has worst-case complexity of Ο(n) whereas binary search has Ο(log n). There are cases where the location of target data may be known in advance. For example, in case of a telephone directory, if we want to search the telephone number of Morphius. Here, linear search and even binary search will seem slow as we can directly jump to memory space where the names start from 'M' are stored.

10. Interpolation Search Algorithm Step 1 − Start searching data from middle of the list. Step 2 − If it is a match, return the index of the item, and exit. Step 3 − If it is not a match, probe position. Step 4 − Divide the list using probing formula and find the new midle. Step 5 − If data is greater than middle, search in higher sub-list. Step 6 − If data is smaller than middle, search in lower sub-list. Step 7 − Repeat until match.

11. Binary vs. Interpolation Search  Positioning in Binary Search  Position Probing in Interpolation Search

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#5: A schedule design for optional periods of time/objectives.
#7: Objectives for instruction and expected results and/or skills developed from learning.
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#12: Example graph/chart.

Searching techniques in Data Structure And Algorithm

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