The document discusses several topics related to arrays in data structures and algorithms:
1) It explains how array elements are addressed in memory using the base address of the array, the size of each element, and the lower and upper bounds.
2) It provides an example of calculating the address of a specific element in a 1D array.
3) It presents an algorithm for finding the largest value in an array by iterating through the elements and tracking the largest.
4) It outlines an algorithm for inserting an element into an array at a specified location by shifting existing elements and making space for the new element.
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2. How array elements are addressed in memory
No, of elements in the array can be obtained by the
formula.
No. of elements = UB - LB + 1
= Upper Bound - Lower Bound + 1
In the data segment of program, the starting address of
the array is called its base address.
E.G. Here it starts from 60th byte. So 60 will be the base
address of the array. Let BA denotes the base address of
the array and S denote the size of each location, Then the
address of the location of array variable A is
A[ I ] = BA + ( I – LB ) * S
Let BA = 60 , S = 2 Dimension [0 : 6]
Note: integer occupy 2 bytes in memory
& in C language LB is equals to zero. ( LB = 0)
A[ 6 ] = 60 + ( 6 - 0 ) * 2
= 60 + 6 * 2
= 72 ( this will be the base address of A[ 6 ] )
A[0] A[1] A[2] A[3] A[4] A[5] A[6]
60 62 64 66 68 70 72
3. Given one dimensional array of dimension [11:20] assuming that each element of array is of
size 4 bits and base address is 500. Calculate the address of the element 15.
Solution:
here BA = 500 “Base Address”
S = 4 “Size of Each Element”
I = 15 “Element number to be accessed”
The Formula to access the ith element of one dimension array is:
A[ I ] = BA + ( I - LB ) * S
A[15] = 500 + (15 - 11) * 4
= 500 + 4 * 4
A[15] = 516
A[11] A[12] A[13] A[14] A[15] A[16] A[17] A[18] A[19] A[20]
500 504 508 512 516 520 524 528 532 536 540
4. Finding largest value in an array
START
Step 1 → Take an array A and define its values
Step 2 → Declare largest as integer
Step 3 → Set 'largest' to 0
Step 4 → Loop for each value of A
Step 5 → If A[n] > largest, Assign A[n] to largest
Step 6 → After loop finishes, Display largest as
largest element of array
STOP
5. Algorithm to inserting element in array
Algorithm Insert LA (DATA, N, ITEM, LOC)
Desc: This algorithm inserts new element ITEM in linear array DATA with N elements
If LOC=1 it means the element has to insert in beginning
If LOC =N+1 it means the element have to be inserted at the end
If LOC = J it means the elements have to be inserted at Jth Location
Begin
Step 1: [ Initialize counter I with index of last element ] I = N
Step 2: While I > = LOC repeat steps 3 and 4
Step 3: [ Move the current element one position backwards ] DATA[ I + 1 ] = DATA [ I
]
Step 4: [ Decrement counter I ] I = I - 1
Step 5:[ Insert new element at the Location ] DATA [ LOC ] = ITEM
Step 6:[ Update total under of array elements ] N = N + 1
Exit
![How array elements are addressed in memory
No, of elements in the array can be obtained by the
formula.
No. of elements = UB - LB + 1
= Upper Bound - Lower Bound + 1
In the data segment of program, the starting address of
the array is called its base address.
E.G. Here it starts from 60th byte. So 60 will be the base
address of the array. Let BA denotes the base address of
the array and S denote the size of each location, Then the
address of the location of array variable A is
A[ I ] = BA + ( I – LB ) * S
Let BA = 60 , S = 2 Dimension [0 : 6]
Note: integer occupy 2 bytes in memory
& in C language LB is equals to zero. ( LB = 0)
A[ 6 ] = 60 + ( 6 - 0 ) * 2
= 60 + 6 * 2
= 72 ( this will be the base address of A[ 6 ] )
A[0] A[1] A[2] A[3] A[4] A[5] A[6]
60 62 64 66 68 70 72](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)