![22
Data Structures بيانات هياكل
Data Structures - Computer and Control Engineering- First Term
25 October 2024
Linear / Sequential 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: STOP
procedure linear_search (list, value)
for each item in the list
if match item == value
return the item’s location
end if
end for
end procedure](https://image.slidesharecdn.com/datastructurelecture4-241114123835-7f831750/85/Data-Structure-lecture-4-linked-list-pdf-22-320.jpg)
![23
Data Structures بيانات هياكل
Data Structures - Computer and Control Engineering- First Term
25 October 2024
Linear Search
Flowchart: Sequential Search with Array
Start
i = 0
K = A[i]?
Print "Successful"
Print "Unsuccessful"
i = i+1
i ≥ n
Stop
Yes
Yes
No
No](https://image.slidesharecdn.com/datastructurelecture4-241114123835-7f831750/85/Data-Structure-lecture-4-linked-list-pdf-23-320.jpg)
![l u
mid = (l+u)/2
(a) An ordered array of elemnets with index values l, u and mid
l u
mid
(b) Search the entire list turns into the searching of left-half only
u = mid-1
Serach this half the same way
if K < A[mid]
l u
mid
l = mid+1 Serach this half the same way
if K > A[mid]
(c) Search the entire list turns into the searching of right-half only
Binary Search Technique
Data Structures - Computer and Control Engineering- First Term
25 October 2024
Data Structures بيانات هياكل](https://image.slidesharecdn.com/datastructurelecture4-241114123835-7f831750/85/Data-Structure-lecture-4-linked-list-pdf-27-320.jpg)
![28
Data Structures بيانات هياكل
Data Structures - Computer and Control Engineering- First Term
25 October 2024
Flowchart: Binary Search with Array
mid = (l+u)/2
K = A[mid]?
Start
Search is successful
YES NO
K < A[mid]?
YES
u = mid-1 l = mid+1
NO
Stop
(l>u)?
Start
Search is unsuccessful
YES
NO](https://image.slidesharecdn.com/datastructurelecture4-241114123835-7f831750/85/Data-Structure-lecture-4-linked-list-pdf-28-320.jpg)
Data Structure lecture 4 linked list.pdf
- 1. Data Structures CCE 411(2013) CCE 332(2019) El-Shorouk Academy The Higher Institute of Engineering, El-Shorouk City Dr. Ahmed El-Shafei Communications and Computer Engineering Department Data Structures - Computer and Control Engineering- First Term 25 October 2024
- 2. 1 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Notes Group (2) Group (1) Lecture # L_01_DS_24-25 2/10/2024 30/9/2024 1 L_01_DS_24-25 9/10/2024 7/10/2024 2 L_02_DS_24-25 16/10/2024 14/10/2024 3 L_03_DS_24-25 23/10/2024 21/10/2024 4 5 6 7 8 9 10 11 12 13
- 3. 3 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Lists Lecture 4
- 4. 4 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Lists Merging Two sorted link lists ▪ To merge two sorted link list and create a third list in the same sequence of inputted link list. Algorithm: Step 1 PTR1 = FIRST1 PTR2 = FIRST2 Step 2 PTR = AVAIL AVAIL = LINK(AVAIL) FIRST = PTR Step 3 If INFO (PTR1) < INFO (PTR2) THEN INFO (PTR) = INFO(PTR1) PTR1 = LINK (PTR1) Otherwise INFO(PTR) = INFO (PTR2) PTR2 = LINK (PTR2) Step 4 Repeat Step 5 to Step 7 while PTR1 ≠ NULLAND PTR2 ≠ NULL Step 5 CPT = AVAIL AVAIL = LINK(AVAIL) Step 6 If INFO (PTR1) < INFO (PTR2) THEN INFO (CPT) = INFO(PTR1) PTR1 = LINK (PTR1) Otherwise INFO(CPT) = INFO (PTR2) PTR2 = LINK (PTR2)
- 5. 5 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Lists Merging Two sorted link lists Step 7 LINK (PTR) = CPT PTR = CPT Step 8 Repeat step 9 while PTR1 ≠ NULL Step 9 (i) CPT = AVAIL AVAIL = LINK (AVAIL) INFO (CPT) = INFO (PTR1) PTR1 = LINK (PTR1) (ii) LINK (PTR) = CPT PTR = CPT (iii) PTR2 = LINK (PTR1) Step 10 Repeat step 11 while PTR2 ≠ NULL Step 11 (i) CPT = AVAIL AVAIL = LINK (AVAIL) INFO (CPT) = INFO (PTR2) PTR1 = LINK (PTR1) (ii) LINK (PTR) = CPT PTR = CPT (iii) PTR2 = LINK (PTR2) Step 12 LINK (PTR) = NULL Step 13 STOP
- 6. 6 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Lists Example: Merge the following two sorted link lists. Merge these link lists into third link lists 5 8 12 20 NULL FIRST 1 2 10 15 NULL FIRST 2 Initially, PTR1 = FIRST1 and PTR2 = FIRST2 INFO (PTR1) = 5 INFO (PTR2) = 2 Here, INFO (PTR2) < INFO (PTR1) So, create a new node PTR and INFO (PTR) = INFO (PTR2) (for the new list that will include the merge result) PTR i.e., and PTR2 = LINK (PTR2) i.e., now 2 5 8 12 20 NULL PTR 1 2 10 15 NULL PTR 2 PTR 2
- 7. 7 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Lists INFO (PTR1) = 5 INFO (PTR2) = 10 Here, INFO (PTR2) < INFO (PTR1) So, create a new node CPT and INFO (CPT) = INFO (PTR1) LINK (PTR) = CPT PTR = CPT i.e., 2 PTR 5 and PTR1 = LINK (PTR1) Now, 5 8 12 20 NULL PTR 1 2 10 15 NULL PTR 2 2 5 PTR
- 8. 8 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Lists INFO (PTR1) = 8 INFO (PTR2) = 10 Here, INFO (PTR1) < INFO (PTR2) So, create a new node CPT and INFO (CPT) = INFO (PTR1) PTR1 = LINK (PTR1) LINK (PTR) = CPT PTR = CPT Now link lists are: 5 8 12 20 NULL PTR 1 2 10 15 NULL PTR 2 2 5 8 PTR
- 9. 9 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Lists INFO (PTR1) = 12 INFO (PTR2) = 10 Here, INFO (PTR2) < INFO (PTR1) So, create a new node CPT and INFO (CPT) = INFO (PTR2) PTR2 = LINK (PTR2) LINK (PTR) = CPT PTR = CPT Now link lists are: 5 8 12 20 NULL PTR 1 2 10 15 NULL PTR 2 2 5 8 PTR 10
- 10. 10 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Lists INFO (PTR1) = 12 INFO (PTR2) = 15 Here, INFO (PTR1) < INFO (PTR2) So, create a new node CPT and INFO (CPT) = INFO (PTR1) PTR1 = LINK (PTR1) LINK (PTR) = CPT PTR = CPT Now link lists are: 5 8 12 20 NULL PTR 1 2 10 15 NULL PTR 2 2 5 8 10 PTR 12
- 11. 11 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Lists INFO (PTR1) = 20 INFO (PTR2) = 15 Here, INFO (PTR2) < INFO (PTR1) So, create a new node CPT and INFO (CPT) = INFO (PTR2) PTR2 = LINK (PTR2) = NULL LINK (PTR) = CPT PTR = CPT Now link lists are: 5 8 12 20 NULL PTR 1 2 10 15 NULL 2 5 8 10 12 PTR 15
- 12. 12 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Lists Here PTR1 ≠ NULL and PTR2 = NULL INFO (PTR1) = 20 So, create a new node CPT and INFO (CPT) = INFO (PTR1) PTR1 = LINK (PTR1) = NULL LINK (PTR) = CPT PTR = CPT Now , PTR1 = NULL and PTR2 = NULL So, LINK (PTR) = NULL i.e., final link-list after merging is: 2 5 8 10 12 15 20 NULL
- 13. 13 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Lists Reversing a List ▪ To reverse a linear linked list, three pointer fields are used. These are tpt, ptr, cpt which hold the address of previous node, current node, and next node in the linear linked list. ▪ To begin with the address of the first node, which is held in pointer variable FIRST, is assigned to PTR and the tpt is assigned value NULL. ▪ Algorithm: Step 1 PTR = FIRST Step 2 TPT = NULL Step 3 Repeat step 4 while PTR ≠ NULL Step 4 (a) CPT = LINK (PTR) (b) LINK (PTR) = TPT (c) TPT = PTR (d) PTR = CPT Step 5 STOP
- 14. 14 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Lists Example: Reverse the following link list 5 10 15 20 NULL FIRST Solution: Initially, PTR = FIRST TPT = NULL PTR ≠ NULL So, CPT = LINK (PTR) LINK (PTR) = TPT i.e., NULL and TPT = PTR PTR = CPT i.e., 5 10 15 20 NULL PTR CPT TPT PTR Now, PTR is node 10, TPT is node 5 Again, PTR ≠ NULL, So, CPT = LINK(PTR), i.e., node 15 5 10 15 20 NULL TPT NULL PTR CPT
- 15. 15 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Lists Now, LINK(PTR) = TPT i.e., 10 5 PTR TPT NULL and TPT = PTR i.e., node 10 is now TPT PTR = CPT i.e., node 15 is now PTR Now, 10 5 TPT NULL 15 20 PTR CPT NULL
- 16. 16 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Lists Again, PTR ≠ NULL Now, CPT = LINK(PTR), i.e., node 20 LINK (PTR) = TPT i.e., 15 10 5 NULL PTR TPT and TPT = PTR i.e., node 15 PTR = CPT i.e., node 20 Now, 15 10 5 NULL TPT 20 NULL PTR
- 17. 17 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Lists Again, PTR ≠ NULL Now, CPT = LINK(PTR), i.e., NULL So, CPT = NULL LINK(PTR) = TPT, i.e., 15 10 5 NULL TPT 20 PTR and TPT = PTR i.e., node 20 PTR = CPT i.e., PTR = NULL Now, PTR = NULL so STOP, and the final link list is LINK(PTR) = TPT, i.e., 15 10 5 NULL 20
- 18. 18 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 SEARCHINING
- 19. 19 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024
- 20. 20 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 ▪ 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. ▪ Search algorithms are algorithms designed to search for or retrieve elements from a data Structures, where they are stored. They are essential to access desired elements in a data Structures and retrieve them when a need arises. ▪ A vital aspect of search algorithms is Path Finding, which is used to find paths that can be taken to traverse from one point to another, by finding the most optimum route. ▪ Some of the standard searching technique that is being followed in data Structures is listed below: ➢ Linear / Sequential Search ➢ Binary Search
- 21. 21 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 ➢ Linear / Sequential Search Linear search is a very basic and simple search algorithm. In Linear search, we search an element or value in a given array by traversing the array from the starting, till the desired element or value is found. It compares the element to be searched with all the elements present in the array and when the element is matched successfully, it returns the index of the element in the array, else it return -1. Linear Search is applied on unsorted or unordered lists, when there are fewer elements in a list. For Example, 10 14 19 26 27 31 33 35 42 44 50 56 62 69 70 75 Features of Linear Search Algorithm 1. It is used for unsorted and unordered small list of elements. 2. It has a time complexity of O(n), which means the time is linearly dependent on the number of elements, which is not bad, but not that good too. 3. It has a very simple implementation.
- 22. 22 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Linear / Sequential 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: STOP procedure linear_search (list, value) for each item in the list if match item == value return the item’s location end if end for end procedure
- 23. 23 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Linear Search Flowchart: Sequential Search with Array Start i = 0 K = A[i]? Print "Successful" Print "Unsuccessful" i = i+1 i ≥ n Stop Yes Yes No No
- 24. 24 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Complexity Analysis • Case 1: The key matches with the first element T(n) = 1 • Case 2: Key does not exist T(n) = n • Case 3: The key is present at any location in the array = = n i i i p n T 1 ) ( n p p p p n i 1 2 1 = = = = = = n i i n n T 1 1 ) ( 2 1 ) ( + = n n T Linear Search
- 25. 25 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Complexity Analysis : Summary Case Number of key comparisons Asymptotic complexity Remark Case 1 T(n) = 1 T(n) = O(1) Best case Case 2 T(n) = n T(n) = O(n) Worst case Case 3 T(n) = O(n) Average case 2 1 ) ( + = n n T Linear Search
- 26. 26 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Binary Search
- 27. l u mid = (l+u)/2 (a) An ordered array of elemnets with index values l, u and mid l u mid (b) Search the entire list turns into the searching of left-half only u = mid-1 Serach this half the same way if K < A[mid] l u mid l = mid+1 Serach this half the same way if K > A[mid] (c) Search the entire list turns into the searching of right-half only Binary Search Technique Data Structures - Computer and Control Engineering- First Term 25 October 2024 Data Structures بيانات هياكل
- 28. 28 Data Structures بيانات هياكل Data Structures - Computer and Control Engineering- First Term 25 October 2024 Flowchart: Binary Search with Array mid = (l+u)/2 K = A[mid]? Start Search is successful YES NO K < A[mid]? YES u = mid-1 l = mid+1 NO Stop (l>u)? Start Search is unsuccessful YES NO
- 29. ThankYou!