1. Array(ADT)
Linear Data Structure
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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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
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