Lecture P4: Structs and Data Types Goal: Deal with Large Amounts of Data

Why Data Structures?

Lecture P4: Structs and Data Types Goal: deal with large amounts of data. addr value ■ Organize data so that it is easy to manipulate. 0 0 ■ Time and space efficient. 1 1 2 1 Basic computer memory abstraction. 3 1 ■ Indexed sequence of bits. 4 0 struct student { ■ Address = index. char name[20]; 5 1 int age; Need higher level abstractions to bridge gap. 6 0 double salary; ■ 7 0 } Hal, Bill; Array.

■ STRUCT. 8 1

■ Linked list. 9 0

■ Binary tree. 10 1 ■ Database...... ■ . . . 256GB 1

Structs C Representation of C Students

student.c Fundamental data structure. #include ■ HETEROGENEOUS collection of values (possibly different type). – Database records, complex numbers, linked list nodes, etc. struct struct student { declaration ■ Store values in FIELDS. char name[16]; int grade; ■ Associate NAME with each field. }; name grade ■ Use struct name and field name to access value.

Built-in to C. int main(void) { can initialize struct student t; ■ To access rate field of structure x use x.rate struct fields in struct student x = {"Bill Gates", 60}; ■ Basis for building "user-defined types" in C. declaration struct student y = {"Steve Jobs", 70};

access structs if (x.grade > y.grade) name of field id rate first last as ordinary t = x; else %s for string struct variables value 166316754 11.50 "Bill" "Gates" t = y; printf("Better student: %s\n", t.name); return 0; field field field field } 3 4 Typedef A Data Type: Points

User definition of type name. Define structures for points in the plane, and operations on them.

■ Put type descriptions in one place - makes code more portable. point data type ■ Avoid typing struct - makes code more readable. #include typedef struct { double x; typedef int Grade; double y; typedef char Name[16]; a } Point; 2 + 2 struct student { dx dy double distance(Point a, Point b) { Name name; dy double dx = a.x - b.x; Grade grade; double dy = a.y - b.y; }; b return sqrt(dx*dx + dy*dy); dx } typedef struct student Student; Point randomPoint(double s) { Point p; random point with x . . . p.x = randomDouble(s); and y coordinates p.y = randomDouble(s); between 0.0 and s Student x = {"Bill Gates", 60}; return p; }

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Another Data Type: Circles Using Data Types: Estimating Pi

Define struct for circles, and operations on them. Estimate pi. pi.c circle data structure ■ Generate N random points #define N 100000 #include in 2 x 2 square. ■ Determine fraction that lie int main(void) { typedef struct { in unit circle. int i, cnt = 0; Point center; ■ On average pi / 4 fraction Point p = {1.0, 1.0}; double radius; center should lie in circle. Circle c; } Circle; c.center = p; c.radius = 1.0; ■ Use 4 * fraction as p estimate of pi. int inCircle(Point p, Circle c) { for (i = 0; i < N; i++) { return distance(p, c.center) <= c.radius; p = randomPoint(2.0); } if (inCircle(p, c)) (2, 2) cnt++; double area(Circle c) { } return 3.14 * c.radius * c.radius; (1, 1) } printf("pi = %f\n", 4.0*cnt/N); return 0; int intersectCircles(Circle c, Circle d) { 1 } return distance(c.center, d.center) <= c.radius + d.radius; (0, 0) } 7 9 Standard Data Type Implementation Intuition

Data type:

■ Set of values and collection of operations on those values.

Example (built-in): int, double, char. multiply Example (user defined): complex numbers.

■ Set of values: 4 + 2i, 1.3 - 6.7i, etc. add Complex show ■ Operations: add, multiply, show, etc. Client Interface Implementation Separate implementation from specification. - volume - cathode ray tube . . . ■ INTERFACE: specifies allowed operations. - change channel - electron gun - adjust picture - Sony Wega 36XBR250 ■ IMPLEMENTATION: provides code for operations. - decode NTSC, PAL - 241 pounds, $2,500 ■ CLIENT: uses data type as black box. signals

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Complex Number Data Type Complex Number Data Type: Interface

Create data structure to represent complex numbers. Interface lists allowable operations on complex data type.

■ See Sedgewick 4.8. ■ Name interface with .h extension.

■ Store in rectangular form: real and imaginary parts. COMPLEX.h

typedef struct { typedef struct { double re; store in double re; multiply double im; rectangular form double im; } Complex; } Complex; add Complex show can't reuse Complex COMPLEXadd (Complex, Complex); +, * symbols Complex COMPLEXmult (Complex, Complex); Complex COMPLEXpow (Complex, Complex); . . . Complex COMPLEXconj (Complex); function double COMPLEXabs (Complex); prototypes double COMPLEXreal (Complex); double COMPLEXimag (Complex); Complex COMPLEXinit (double, double); void COMPLEXshow (Complex);

13 14 Complex Number Data Type: Client Complex Number Data Type: Another Client

Client program uses interface operations to calculate something: Redo Mandelbrot with equivalent complex number update: client.c r Ä x, s Ä y c Ä z = x + iy while (r2 + s2 ≤ 4) while (|c| ≤ 2) #include r' Ä r2 -s2 + x c Ä c2 + z #include "COMPLEX.h" client can use interface s' Ä 2rs + y int main(void) { clientmand.c Complex a, b, c; #define MAXIT 255 a = COMPLEXinit( 5.0, 6.0); #include "COMPLEX.h" b = COMPLEXinit(-2.0, 3.0); c = COMPLEXmult(a, b); (5 + 6i) * (-2 + 3i) = int mand(Complex z) { COMPLEXshow(a); -28 + 3i int i = 0; printf(" * "); Complex c = z; COMPLEXshow(b); while (COMPLEXabs(c) <= 2.0 && i < MAXIT) { printf(" = "); c = COMPLEXadd(COMPLEXmult(c, c), z); COMPLEXshow(c); i++; printf("\n"); } return 0; return i; } } 15 16

Complex Number Data Type: Implementation Complex Number Data Type: Implementation

Write code for interface functions. Write code for interface functions.

complex.c complex.c (cont)

#include double COMPLEXabs(Complex a) { #include implementation and function in return sqrt(a.re * a.re + a.im * a.im); #include "COMPLEX.h" client need to agree on math library interface } Complex COMPLEXadd(Complex a, Complex b) { void COMPLEXshow(Complex a) { Complex t; printf("%f + %f i\n", a.re, a.im); t.re = a.re + b.re; } t.im = a.im + b.im; return t; Complex COMPLEXinit(double x, double y) { } Complex t; t.re = x; Complex COMPLEXmult(Complex a, Complex b) { t.im = y; Complex t; return t; t.re = a.re * b.re - a.im * b.im; } t.im = a.re * b.im + a.im * b.re; return t; } 17 18 Compilation Client, Interface, Implementation

Client and implementation both include COMPLEX.h

Compile jointly. %gcc client.c complex.c -lm

Or compile separately. %gcc -c complex.c %gcc -c client.c %gcc client.o complex.o -lm Client Interface Implementation couchpotato.c #include"TV.h" #include tvplasma.c

client needs to know implementation needs to know Unix how to use interface what interface to implement % gcc126 client.c complex.c % a.out (5.00 + 6.00 i) * (-2.00 + 3.00 i) = (-28.00 + 3.00 i) Implementation and client need to agree on interface ahead of time.

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Can Change Implementation Alternate Interface

Can use alternate representation of complex numbers. Interface lists allowable operations on complex data type.

■ Store in polar form: modulus and angle. COMPLEX.h

z = x + i y = r ( cos θ + i sin θ ) = r ei θ typedef struct { double r; polar representation double theta; } Complex; typedef struct { double r; Complex COMPLEXadd (Complex, Complex); double theta; Complex COMPLEXmult (Complex, Complex); } Complex; Complex COMPLEXpow (Complex, Complex); Complex COMPLEXconj (Complex); double COMPLEXabs (Complex); double COMPLEXreal (Complex); double COMPLEXimag (Complex); Complex COMPLEXinit (double, double); void COMPLEXshow (Complex);

21 22 Alternate Implementation Alternate Implementation

Write code for interface functions. Write code for interface functions.

complexpolar.c complexpolar.c

#include "COMPLEX.h" Complex COMPLEXadd(Complex a, Complex b) { #include Complex t; #include double x, y; x = a.r * cos(a.theta) + b.r * cos(b.theta); Complex COMPLEXabs(Complex a) { y = a.r * sin(a.theta) + b.r * sin(b.theta); return a.r; t.r = sqrt(x*x + y*y); } t.theta = arctan(y/x); return t; Complex COMPLEXmult(Complex a, Complex b) { } Complex t; t.r = a.r * b.r; Others are more annoying. t.theta = a.theta + b.theta; }

Some interface functions are now faster and easier to code.

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Multiple Implementations Rational Number Data Type

Usually, several ways to represent and implement a data type. See Assignment 3.

■ You will create data type for Rational numbers.

How to represent complex numbers: rectangular vs. polar? ■ Add associated operations to Rational number data type.

■ Depends on application.

■ Rectangular are better for additions and subtractions. typedef struct { – no need for arctangent int num; int den; ■ Polar are better for multiply and modulus. } Rational; – no need for square root

■ Get used to making tradeoffs.

■ Simple version relatively easy to implement. This example may seem artificial. ■ Improved implementation staves off overflow by: ■ Essential for many real applications. – reducing fractions ■ Crucial software engineering principle. – order of computation

25 26 Conclusions

Basic computer memory abstraction. Lecture P4: Supplemental Notes ■ Indexed sequence of bits.

■ Address = index.

Need higher level abstractions to bridge gap.

■ Array. – homogeneous collection of values

■ Struct. – heterogeneous collection of values

Data type.

■ Set of values and collection of operations on those values.

Client-interface-implementation paradigm.

■ Consistent way to implement data types.

Pass By Value, Pass By Reference

Arrays and structs are passed to functions in very DIFFERENT ways.

Pass-by-value: void mystery(Point a) { a.y = 17.0; ■ int, float, char, struct } Unix ■ a COPY of value % a.out is passed to function Point a = {1.0, 2.0}; 1.0 mystery(a); printf("%4.1f\n", a.y);

void mystery(double a[]) { "Pass-by-reference": a[1] = 17.0; Unix ■ arrays }

■ function has direct % a.out access to array double a[] = {1.0, 2.0}; 17.0 elements mystery(a); printf("%4.1f\n", a[1]);