data structure

2. • A digital computer can manipulate only primitive data in the
terms of
• real life application various kinds primitive data involved
• manipulation of real life data

4. • manipulation various kinds of data concept of ds comes in
• domain-Range of the values data may have also calledobjaect
• function -Set of the operations which may legally appilies
elements of the data object ds specify set of operations
• axioms-Set of rules with which different operationsbelonging to f
cn actually implemented
• A ds D is a triplet that is D=(d,f,a)D is set of data object
• f is set of functions a is the set of rules implements a
function
• D=(0,+1,+2,+3)f=(+,-,*,/.%) a=set of binary operations

5. • it can be usually recognaized that the triplet(d,f,a)is nothing but
an abstract data type
• also the elements in set d arenot necessirely from primitive data
• it may contins element from some other abstact data type
• implement ds data type or an abstrct data type
• complex has an abstract dta type
• any variable of the complex data type has two parts
Z=x+iy x ,y is the real and imaginary prts

6. continuee
• Both x and y are real data type which is another abstract data
type so the abstract data type complex cn be defined ds Real as
• complex z{
• x:REAL
• y:REAL
• }
• d of the complex can be realizes from the domain of x and
ywhich is real f=(+,-,*,/,%)
• z1=x1+iy1 and z2=x2+iy2 are two data of the complex data type
• f is giving axioms

7. continueee
• A={
• Z=Z1+Z2=(X1+X2)+I(Y1+Y2)
• Z=Z1-Z2=(X1-X2)-I(Y1-Y2) (complex sub)
• Z=Z1*Z2=(X1*X2-Y1*Y2)+I(X1*Y2+X2*Y1)(
• Z=z1/z2
•
• =x1*x2+y1*y2/x2+y2+ix2*y1-x1*y2/x2+y2

8. Thank you