![TRAVERSING
Traversal in a Linear Array is the process of
visiting each element once.
Traversal is done by starting with the first
element of the array and reaching to the last.
ALGORITHM:
TRAVERSAL(A, N)
Step1: FOR I = 0 to N-1
PROCESS(A[I])
[ end of FOR ]
Step2: Stop](https://image.slidesharecdn.com/datastructures-mln-250414051742-ef989359/85/Data-Structures-Types-Arrays-stacks-MLN-ppt-11-320.jpg)
![INSERTION
ALGORITHM:
INSERTION(A, N, ELE, POS)
Step1: FOR I = N-1 DOWNTO POS
A[I+1] = A[I]
[end of FOR]
Step2: A[POS] = ELE
Step3: N = N + 1
Step4: Stop](https://image.slidesharecdn.com/datastructures-mln-250414051742-ef989359/85/Data-Structures-Types-Arrays-stacks-MLN-ppt-13-320.jpg)
![DELETION
ALGORITHM:
DELETION(A, N, ELE, POS)
Step1: ELE = A[POS]
Step2 FOR I = POS TO N – 2
A[I] = A[I+1]
[end of FOR]
Step3: N = N – 1
Step4: Stop](https://image.slidesharecdn.com/datastructures-mln-250414051742-ef989359/85/Data-Structures-Types-Arrays-stacks-MLN-ppt-15-320.jpg)
![LINEAR SEARCH
It is also called Sequential Search.
It can be applied on unsorted array.
Algorithm:
LINEARSEARCH(A, N, KEY)
Step1: LOC = -1
Step2: FOR I = 1 TO N
IF (KEY == A[I])
LOC = I
goto Step3
[end of IF]
[end of FOR]
Step3: IF (LOC == – 1)
Print “ Element not found”
ELSE
Print “Element found at “, LOC
Step4: Stop](https://image.slidesharecdn.com/datastructures-mln-250414051742-ef989359/85/Data-Structures-Types-Arrays-stacks-MLN-ppt-17-320.jpg)
![BINARY SEARCH
It can be applied only on sorted array.
It is based on Divide and Conquer Technique.
Algorithm:
BINARYSEARCH(A, N, KEY)
Step1: LOC = -1, BEG = 0, END = N–1
Step2: Repeat WHILE (BEG <= END)
MID = (BEG + END)/2
IF ( KEY == A[MID] )
LOC = MID
goto Step3
ELSE IF (KEY < A[MID])
END = MID – 1
ELSE
BEG = MID + 1
[ end of IF ]
[ end of WHILE ]
Step3: IF (LOC == – 1)
Print “ Element not found”](https://image.slidesharecdn.com/datastructures-mln-250414051742-ef989359/85/Data-Structures-Types-Arrays-stacks-MLN-ppt-18-320.jpg)
![BINARY SEARCH
Step3: IF (LOC == – 1)
Print “ Element not found”
ELSE
Print “Element found at “, LOC
[ end of IF ]
Step4: Stop](https://image.slidesharecdn.com/datastructures-mln-250414051742-ef989359/85/Data-Structures-Types-Arrays-stacks-MLN-ppt-19-320.jpg)
![BUBBLE SORT
Algorithm:
BUBBLESORT(A, N)
Sept1. FOR I = 1 to N – 1
FOR J = 1 to N–I–1
IF ( A[J] > A[J+1]
TEMP = A[J]
A[J] = A[J+1]
A[J+1] = TEMP
[ end of IF ]
[ end of FOR ]
[ end of FOR ]](https://image.slidesharecdn.com/datastructures-mln-250414051742-ef989359/85/Data-Structures-Types-Arrays-stacks-MLN-ppt-21-320.jpg)
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Data Structures Types, Arrays, stacks - MLN.ppt
- 1. DATA STRUCTURES NAGARAJU M L ASSISTANT PROFESSOR DEPARTMENT OF MCA ACHARYA INSTITUTE OF GRADUATE STUDIES SOLADEVANAHALLI, BANGALORE
- 2. DATA STRUCTURE Definition: Logical or Mathematical model of a particular organisation of data is called Data Structure. Example: Character, Integer, Float, Pointer, Arrays, Liked List, Stacks, Queues, Trees, Graphs. Need: Data Structures are necessary for designing efficient algorithms.
- 4. Definition: Data Structure which can be manipulated directly by machine instructions. Example: Character, Integer, Float, Pointer Operations: 1. Create: int x; 2. Select: cout<<x; 3. Update: x = x + 10; 4. Destroy: delete x; PRIMITIVE DATA STRUCTURE
- 5. Definition: Data Structure which can not be manipulated directly by machine instructions. Example: Arrays, Linked List, Stacks, Queues, Trees, Graphs. Operations: 1. Traversing 2. Insertion 3. Deletion 4. Searching 5. Sorting 6. Merging NON-PRIMITIVE DATA STRUCTURE
- 6. Definition: Data Structure in which there is a sequential relationship between the elements. Example: Arrays, Liked List, Stacks, Queues. Array: Liked List: Stacks: Queues: LINEAR DATA STRUCTURE
- 7. Definition: Data Structure in which there is no sequential relationship between the elements. There will be an adjacency or hierarchical relationships. Example: Trees, Graphs. NON-LINEAR DATA STRUCTURE
- 8. ARRAYS Definition: Collection of homogeneous elements with only one name is called Arrays. Characteristics: Types: 1. One-Dimensional Array or Linear Array 2. Two-Dimensional Array 3. Multi-Dimensional Array
- 9. TYPES OF ARRAYS One-Dimensional Array or Linear Array: The array in which the elements are accessed by using only one index. Two-Dimensional Array: The array in which the elements are accessed by using two indexes. Multi-Dimensional Array: The array in which the elements are accessed by using more than two indexes.
- 10. OPERATIONS ON ONE-DIMENSIONALARRAY The following operations can be performed on linear array. 1. Traversing 2. Insertion 3. Deletion 4. Searching 5. Sorting 6. Merging
- 11. TRAVERSING Traversal in a Linear Array is the process of visiting each element once. Traversal is done by starting with the first element of the array and reaching to the last. ALGORITHM: TRAVERSAL(A, N) Step1: FOR I = 0 to N-1 PROCESS(A[I]) [ end of FOR ] Step2: Stop
- 12. INSERTION Adding new element into the array Initially After movement of Elements After Insertion
- 13. INSERTION ALGORITHM: INSERTION(A, N, ELE, POS) Step1: FOR I = N-1 DOWNTO POS A[I+1] = A[I] [end of FOR] Step2: A[POS] = ELE Step3: N = N + 1 Step4: Stop
- 14. DELETION Removing an element from the array Initially After Deletion After Movement of elements
- 15. DELETION ALGORITHM: DELETION(A, N, ELE, POS) Step1: ELE = A[POS] Step2 FOR I = POS TO N – 2 A[I] = A[I+1] [end of FOR] Step3: N = N – 1 Step4: Stop
- 16. SEARCHING Definition: Checking weather the given element is there in an array or not is called Searching. Methods: 1. Linear Search or Sequential Search 2. Binary Search
- 17. LINEAR SEARCH It is also called Sequential Search. It can be applied on unsorted array. Algorithm: LINEARSEARCH(A, N, KEY) Step1: LOC = -1 Step2: FOR I = 1 TO N IF (KEY == A[I]) LOC = I goto Step3 [end of IF] [end of FOR] Step3: IF (LOC == – 1) Print “ Element not found” ELSE Print “Element found at “, LOC Step4: Stop
- 18. BINARY SEARCH It can be applied only on sorted array. It is based on Divide and Conquer Technique. Algorithm: BINARYSEARCH(A, N, KEY) Step1: LOC = -1, BEG = 0, END = N–1 Step2: Repeat WHILE (BEG <= END) MID = (BEG + END)/2 IF ( KEY == A[MID] ) LOC = MID goto Step3 ELSE IF (KEY < A[MID]) END = MID – 1 ELSE BEG = MID + 1 [ end of IF ] [ end of WHILE ] Step3: IF (LOC == – 1) Print “ Element not found”
- 19. BINARY SEARCH Step3: IF (LOC == – 1) Print “ Element not found” ELSE Print “Element found at “, LOC [ end of IF ] Step4: Stop
- 20. SORTING Definition: Arranging the elements in a particular order is called sorting. Methods: 1. Bubble Sort 2. Selection Sort 3. Insertion Sort 4. Merge Sort 5. Quick Sort 6. Radix Sort 7. Heap Sort
- 21. BUBBLE SORT Algorithm: BUBBLESORT(A, N) Sept1. FOR I = 1 to N – 1 FOR J = 1 to N–I–1 IF ( A[J] > A[J+1] TEMP = A[J] A[J] = A[J+1] A[J+1] = TEMP [ end of IF ] [ end of FOR ] [ end of FOR ]
- 22. THANK YOU