Linear Array
Linear Arrays
• A linear array is a list of finite number n of
homogeneous data elements.
• Length = UB-LB+1
• UB: largest index, LB: smallest index
Memory representation
• Let LOC(LA[K]) denotes address of the
element LA[K] of the array LA
• LOC(LA[K])=Base(LA)+W(K-LB)
Example-1
• AUTO which records the
number of automobiles sold
each year from 1932 to 1984.
Base(Auto)=200
W=4 words per memory cell
• Find the address of element which
store the info about sale in year 1965?
Example 2
Find the address for LA[6]
Each element of the array occupy
1 byte
200
LA[1]
201
LA[2]
202
LA[3]
203
LA[4]
204
LA[5]
205
LA[6]
206
LA[7]
207
LA[8]
LOC(LA[K]) = Base(LA) + w(K – lower bound)
:
LOC(LA[6]) = 200 + 1(6 – 1) = 205
5
Example 3
Find the address for LA[16]
Each element of the array occupy
2 byte
200
LA[1]
201
202
LA[2]
203
204
LA[3]
205
206
LA[4]
207
LOC(LA[K]) = Base(LA) + w(K – lower bound)
:
LOC(LA[16]) = 200 + 2(16 – 1) = 230
6
Basic Operations on linear Array
Following are the basic operations supported by an
array:
1. Traverse − print all the array elements one by
one.
2. Insertion − add an element at given index.
3. Deletion − delete an element at given index.
4. Search − search an element using given index or
by value.
5. Sort − arrange elements in ascending or
descending order
Algorithm for inserting an element
into an array
• INSERT (LA, N, K, ITEM): Here LA is a linear array with N elements
and K is a positive integer such that K <= N. This algorithm inserts
an element ITEM into the Kth position in LA.
1. [Initialize counter.] Set J := N.
2. Repeat Steps 3 and 4 while J >= K.
3. [Move Jth element downward.] Set LA[J+1] := LA[J].
4. [Decrease counter.] Set J := J – 1.
[End of Step 2 loop.]
5. [Insert element.] Set LA[K] := ITEM.
6. [Reset N.] Set N := N + 1.
7. Exit.
Assignment-1: Implementation of
Insertion algorithm in C
#include <stdio. h>
main() {
Int LA[ ] = {1, 3, 5, 7, 8};
Int item = 10, k = 3, n = 5;
Int i = 0, j = n;
printf(" The original array elements are : \n" );
for(i = 0; i<n; i++) {
printf(" LA[ %d] = %d \n" , i, LA[ i] );
}
n = n + 1;
while( j >= k){
LA[ j+1] = LA[ j] ;
j = j - 1;
}
LA[ k] = item;
printf(" The array elements after insertion : \n" );
for(i = 0; i<n; i++) {
printf(" LA[ %d] = %d \n" , i, LA[ i] );
}
}
Algorithm for deleting an element
from an array
DELETE (LA, N, K, ITEM): LA is a linear array with N
elements and K is a positive integer such that K <= N.
This algorithm deletes the Kth element from LA.
1. Set ITEM := LA[K].
2. Repeat for J = K to N - 1.
[Move J + 1st element upward.] Set LA[J] := LA[J + 1].
[End of loop.]
3. [Reset the number N of elements in LA.]
Set N := N - 1.
4. Exit.
Assignment-2: Deleting and element
from the array in C language
#include <stdio. h>
main() {
int LA[ ] = {1, 3, 5, 7, 8};
int k = 3, n = 5;
int i, j;
printf(" The original array elements are : \n" );
for(i = 0; i<n; i++) {
printf(" LA[ %d] = %d \n" , i, LA[ i] );
}
j= k;
while( j < n){
LA[ j- 1] = LA[ j] ;
j = j + 1;
}
n= n - 1;
printf(" The array elements after deletion : \n" );
for(i = 0; i<n; i++) {
printf(" LA[ %d] = %d \n" , i, LA[ i] );
}
}