Array linear data_structure_2 (1)
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An array is a linear data structure that stores a collection of elements of the same data type in adjacent memory locations. Arrays allow storing multiple elements and accessing them using an index. Common array operations include traversal, search, insertion, deletion, and sorting. Algorithms for performing these operations on arrays are presented, including pseudocode for array traversal, insertion, deletion, linear search, and sorting.
![Algorithm for Array Traversal
● Let A be a linear Aay with Lower Bound LB and Upper Bound UB. The
following algorithm traverses A applying an operations PROCESS to each
element of A
Step 1. Initialize Counter
Set Counter = LB
Step 2. Repeat steps 3 and 4 while counter <= UB
Else GoTo Step 5
Step 3. Visit element
Apply PROCESS to A[counter]
Step 4. Increase Counter
Set counter = counter + 1
GoTo 2
Step 5. Exit
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![Algorithm for Insertion
Let A be a Linear Array, N is number of elements, k is the positive integer such
that k<=N, VAL to insert element at kth Position in an Array A
Step 1. Start
Step 2. Initialize Counter
Set J = N
Step 3. Repeat Steps 3 and 4 while J>=k otherwise GoTo Step
Step 4. Move Jth element downward
Set A[J+1] = A[J]
Step 5. Decrease Counter
Set J = J + 1
End of step 2 loop
Step 6. Insert element
Set A[k] = ITEM
Step 7. Reset N
Set N = N + 1
Step 8. Exit
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![Algorithm for Deletion
DELETE(A, N, K, VAL)
Let A be an linear Aay. N is the number of elements, k is the positive
integer such that k<=N. The algorithm deletes kth element from the
Aay.
Step 1. Start
Step 2. Set VAL = A[k]
Step 3. Repeat for J = k to N-1
[Move J+1 element Upward]
Set A[J] = A[J+1)
End of Loop
Step 4. Reset the number N of elements in A
Set N = N– 1
Step 5. Exit
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![Algorithm for Linear Search
Suppose A is linear Array with N elements, and VAL is the given item of
information. This algorithm finds the location LOC of item in A or sets LOC=0 if
search is unsuccessful
Step 1. Start
Step 2. [Insert VAL at the end of A]
Set A[N+1] = VAL
Step 3. [Initialize counter]
SET LOC = 1
Step 4. [Search for VAL]
Repeat while A[LOC] != VAL
Set LOC = LOC + 1
[End of loop]
Step 5. [Successful ?]
if LOC = N+1 then set LOC = 0
Step 6. Exit
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![Algorithm for sorting
Let A be an Aay of N elements. The following algorithm sorts
the elements of A.
Step 1. Start
Step 2. Repeat Steps 2 and 3 for k=1 to N-1
Step 3. Set PTR = 1 [Initialize pass pointer PTR]
Step 4. Repeat while PTR<=N-K [Execute Pass]
a. If A[PTR] > A[PTR+1], then
Interchange A[PTR] and A[PTR+1]
[End of if structure]
b. Set PTR = PTR + 1
[End of inner loop]
[End of step1 outer loop]
Step 5. Exit
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Array linear data_structure_2 (1)
- 1. Array(ADT) Linear Data Structure www.eshikshak.co.in
- 2. What are Arrays ? ● An Aay is collection of elements stored in adjacent memory locations. ● By ‘finite’ – specific number of elements in an Aay ● By ‘similar’ – all the elements in an Aay are of the same data type www.eshikshak.co.in
- 3. What are Arrays ? (cont.) ● An Aay containing number of element is reference using an index values 0, 1, …n-1 ○ Lower bound–Lowest index value ○ Upper bound–Highest index value ● An Aay is set of pairs of an index and a value, for each index there is value associated with it. ● Various categories of Aay ○ 1D, 2D and Multi-D www.eshikshak.co.in
- 4. What are Arrays ? (Cont.) ● The number of elements in the Aay is called its range. ● No matter how big an Aay is, its elements are always stored in contiguous memory locations. www.eshikshak.co.in
- 5. Array Operations Operation Description Traversal Processing each element in the Aay Search Finding the location of an element with a given value Insertion Adding new element to an Aay Deletion Removing an element from an Aay Sorting Organizing the elements in some order Merging Combining two Aays into a single Aay Reversing Reversing the elements of an Aay www.eshikshak.co.in
- 6. Row-Major and Column-Major Arrangement ● All the elements of Aay are stored in adjacent memory. ● This leads to two possible Aangements of elements in memory ○ Row Major ○ ColumnMajor ● Base address , no. of rows ,& no. of columns helps to know any element in an Aay www.eshikshak.co.in
- 7. Algorithm for Array Traversal ● Let A be a linear Aay with Lower Bound LB and Upper Bound UB. The following algorithm traverses A applying an operations PROCESS to each element of A Step 1. Initialize Counter Set Counter = LB Step 2. Repeat steps 3 and 4 while counter <= UB Else GoTo Step 5 Step 3. Visit element Apply PROCESS to A[counter] Step 4. Increase Counter Set counter = counter + 1 GoTo 2 Step 5. Exit www.eshikshak.co.in
- 8. Algorithm for Insertion Let A be a Linear Array, N is number of elements, k is the positive integer such that k<=N, VAL to insert element at kth Position in an Array A Step 1. Start Step 2. Initialize Counter Set J = N Step 3. Repeat Steps 3 and 4 while J>=k otherwise GoTo Step Step 4. Move Jth element downward Set A[J+1] = A[J] Step 5. Decrease Counter Set J = J + 1 End of step 2 loop Step 6. Insert element Set A[k] = ITEM Step 7. Reset N Set N = N + 1 Step 8. Exit www.eshikshak.co.in
- 9. Algorithm for Deletion DELETE(A, N, K, VAL) Let A be an linear Aay. N is the number of elements, k is the positive integer such that k<=N. The algorithm deletes kth element from the Aay. Step 1. Start Step 2. Set VAL = A[k] Step 3. Repeat for J = k to N-1 [Move J+1 element Upward] Set A[J] = A[J+1) End of Loop Step 4. Reset the number N of elements in A Set N = N– 1 Step 5. Exit www.eshikshak.co.in
- 10. Algorithm for Linear Search Suppose A is linear Array with N elements, and VAL is the given item of information. This algorithm finds the location LOC of item in A or sets LOC=0 if search is unsuccessful Step 1. Start Step 2. [Insert VAL at the end of A] Set A[N+1] = VAL Step 3. [Initialize counter] SET LOC = 1 Step 4. [Search for VAL] Repeat while A[LOC] != VAL Set LOC = LOC + 1 [End of loop] Step 5. [Successful ?] if LOC = N+1 then set LOC = 0 Step 6. Exit www.eshikshak.co.in
- 11. Algorithm for sorting Let A be an Aay of N elements. The following algorithm sorts the elements of A. Step 1. Start Step 2. Repeat Steps 2 and 3 for k=1 to N-1 Step 3. Set PTR = 1 [Initialize pass pointer PTR] Step 4. Repeat while PTR<=N-K [Execute Pass] a. If A[PTR] > A[PTR+1], then Interchange A[PTR] and A[PTR+1] [End of if structure] b. Set PTR = PTR + 1 [End of inner loop] [End of step1 outer loop] Step 5. Exit www.eshikshak.co.in