recursion, c and beyond "… but it clearly is the only right way. the fact that everybody else...

Recursion, C and Beyond

"… but it clearly is the only right way. The fact that everybody else does it some other way only means that they are wrong!"

--Linus Torvalds

BYU CS 124 Advanced C 2

CS 224

Chapter Project HomeworkS00: Introduction

Unit 1: Digital Logic

S01: Data TypesS02: Digital Logic

L01: Warm-upL02: FSM

HW01HW02

Unit 2: ISA

S03: ISAS04: MicroarchitectureS05: Stacks / InterruptsS06: Assembly

L03: BlinkyL04: MicroarchL05b: Traffic LightL06a: Morse Code

HW03HW04HW05HW06

Unit 3: C

S07: C LanguageS08: PointersS09: StructsS10: I/O, Recursion

L07b: Morse IIL08a: LifeL09b: Snake

HW07

HW08

Advanced C 3BYU CS 124

Learning Objectives…

Recursion Factorial

Running Sum Binary Search Fibonacci Numbers Integer to ASCII Line Draw

Activation Records

Find and use standard C functions.

Interpret a data stream according to a specified format.

Direct character output to a data stream.

Assign a data stream to an I/O device, file, or memory.

Students will be able to: Topics:


Recursion

The idea behind recursion is simple. (The visualization is difficult!)

A recursive function is one that performs its task by calling itself on smaller pieces of the same task.

When applied correctly, recursion can simplify programming tasks.

“Build a wall that is ten feet high.” First build a 9 foot high wall, and then add an extra foot of bricks. Conceptually, this is like saying the "build wall" function takes a

height and if that height is greater than one, first calls itself to build a lower wall, and then adds one a foot of bricks.

Recursive tasks must have a “base case”. Recursion is an iterative programming construct.

Recursion


Recursion

Factorial is the classic example: 6! = 6 5! 6! = 6 5 x 4!… 6! = 6 5 4 3 2 1

The factorial function can be easily written as a recursive function:

int Factorial(int n) { if (n < 2) return 1; /* base case */ return (n * Factorial(n – 1));}

Recursion


Binary Search

Given a sorted set of exams, in alphabetical order,find the exam for a particular student.

1. Look at the exam halfway through the pile. 2. If it matches the name, we're done. 3a. else if the name is greater (alphabetically), then

search the upper half of the stack.3b. else search the lower half of the stack.

Binary Search

FindExam(studentName, start, end){

halfwayPoint = (end + start)/2;if (end < start)

ExamNotFound(); /* exam not in stack */else if (studentName == NameOfExam(halfwayPoint))

ExamFound(halfwayPoint); /* found exam! */else if (studentName < NameOfExam(halfwayPoint))

FindExam(studentName, start, halfwayPoint - 1); /* search lower half */else FindExam(studentName, halfwayPoint + 1, end); /* search upper half */

}


Fibonacci Numbers

f(n) = f(n-1) + f(n-2)f(0) = 1f(1) = 1

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987…

Fibonacci Numbers

int Fibonacci(int n){ if (n <= 1) return 1; /* base case */ return (Fibonacci(n-1) + Fibonacci(n-2));}


Call Tree for Fibonacci

Fibonacci(4)

main()

int Fibonacci(int n){ if (n==0 || n ==1) return 1; else return (Fibonacci(n-1) + Fibonacci(n-2));}

int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers


Fibonacci(4)

Fibonacci(3)

main()


int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers




Fibonacci(4)

Fibonacci(3)

Fibonacci(2)

main()


int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers



Fibonacci(4)

Fibonacci(3)

Fibonacci(2)

Fibonacci(1)

main()


int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers



Fibonacci(4)

Fibonacci(3)

Fibonacci(2)

Fibonacci(1)1

main()


int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers



Fibonacci(4)

Fibonacci(3)

Fibonacci(2)

Fibonacci(1) Fibonacci(0)1

main()


int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers



Fibonacci(4)

Fibonacci(3)

Fibonacci(2)

Fibonacci(1) Fibonacci(0)1 1

main()


int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers



Fibonacci(4)

Fibonacci(3)

Fibonacci(2)

Fibonacci(1) Fibonacci(0)

+1 1

main()


int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers



Fibonacci(4)

Fibonacci(3)

Fibonacci(2)


+1 1

2

main()


int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers



Fibonacci(4)

Fibonacci(3)



+1 1

2

main()


int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers



Fibonacci(4)

Fibonacci(3)



+1 1

12

main()


int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers



Fibonacci(4)

Fibonacci(3)



+

+

1 1

12

main()


int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers



Fibonacci(4)

Fibonacci(3)



+

+

1 1

12

3

main()


int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers



Fibonacci(4)

Fibonacci(3)


Fibonacci(2)


+

+

1 1

12

3

main()


int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers



Fibonacci(4)

Fibonacci(3)


Fibonacci(2)

Fibonacci(1)


+

+

1 1

12

3

main()


int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers



Fibonacci(4)

Fibonacci(3)


Fibonacci(2)

Fibonacci(1)


+

+

1 1

12

3

1

main()


int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers



Fibonacci(4)

Fibonacci(3)


Fibonacci(2)



+

+

1 1

12

3

1

main()


int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers



Fibonacci(4)

Fibonacci(3)


Fibonacci(2)



+

+

1 1

12

3

1 1

main()


int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers



Fibonacci(4)

Fibonacci(3)


Fibonacci(2)



+

+ +

1 1

12

3

1 1

main()


int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers



Fibonacci(4)

Fibonacci(3)


Fibonacci(2)



+

+ +

1 1

12

3

1 1

main()


2

int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers



Fibonacci(4)

Fibonacci(3)


Fibonacci(2)



+

+

+

+

1 1

12

3

1 1

2

main()


int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers



Fibonacci(4)

Fibonacci(3)


Fibonacci(2)



+

+

+

+

1 1

12

3

1 1

2

main()


5

int main(){ int x;

x = Fibonacci(4);}

Fibonacci Numbers


Activation Records

A new activation record is pushed on the stack for each subroutine call.

Fib(1)

SP

Fib(2)

Fib(3)

main

main calls Fibonacci(3)

Fibonacci(3) calls Fibonacci(2)

Fibonacci(2) calls Fibonacci(1)

SP

Fib(3)

main

SP

Fib(2)

Fib(3)

main

Activation Records


Activation Records

Fibonacci(1) returns,Fibonacci(2) calls

Fibonacci(0)

Fibonacci(2) returns,Fibonacci(3) calls

Fibonacci(1)

Fibonacci(3)returns

SP

main

SP

Fib(1)

Fib(3)

main

Fib(0)

SP

Fib(2)

Fib(3)

main

Activation Records


MSP430 Fibonacci Fibonacci:0xa064: 120A PUSH R100xa066: 8321 DECD.W SP0xa068: 4C81 0000 MOV.W R12,0x0000(SP)0xa06c: 93A1 0000 CMP.W #2,0x0000(SP)0xa070: 3402 JGE (C$L1)0xa072: 431C MOV.W #1,R120xa074: 3C09 JMP (C$L2) C$L1:0xa076: 831C DEC.W R120xa078: 12B0 A064 CALL #Fibonacci0xa07c: 4C0A MOV.W R12,R100xa07e: 412C MOV.W @SP,R120xa080: 832C DECD.W R120xa082: 12B0 A064 CALL #Fibonacci0xa086: 5A0C ADD.W R10,R12 C$L2:0xa088: 5321 INCD.W SP0xa08a: 413A POP.W R100xa08c: 4130 RET

Activation Records

Recursive call

R12 = Fibonacci(n-1)

Base case

R12 = Fibonacci(n-2)

Pop activationrecord, restoreCallee-safe


Printing an Integer

Recursively converts an unsigned integer as a string of ASCII characters. If integer <10, convert to char and print. Else, call self on first (n-1) digits and then print last

digit.

void IntToAscii(int num) { int prefix, currDigit;

if (num < 10) putchar(num + '0'); /* print single char */else{ prefix = num / 10; /* shift right one digit */

IntToAscii(prefix); /* print shifted num */currDigit = num % 10;putchar(currDigit + '0'); /* print shifted digit */

}}

Integer to ASCII


Trace of IntToAscii

Calling IntToAscii with parameter 12345:

IntToAscii(12345) IntToAscii(1234) IntToAscii(123) IntToAscii(12) IntToAscii(1) putchar('1') putchar('2') putchar('3') putchar('4')putchar('5')

Integer to ASCII


Recursive Line Draw

void lcd_draw_line(int16 x0, int16 y0, int16 x1, int16 y1){ if ((abs(x1 - x0) <= 1) && (abs(y1 - y0) <= 1)) { lcd_point(x0, y0, PS); lcd_point(x1, y1, PS); } else { int16 newX = ((x0 + x1) / 2); int16 newY = ((y0 + y1) / 2); lcd_draw_line(newX, newY, x1, y1); lcd_draw_line(x0, y0, newX, newY); }} // end lcd_draw_line

Line Draw


Moving from C to C++

In the 1980’s Bjourn Stroustrup, working for AT&T, took the C language to its next progression.

He added features to correct some of the problems in the C language, while changing the way programmers view programs by introducing object orientation (OOP) to the language.

The original C++ language was not a compiler, but a pre-compiler of C++ code into regular C code.

C++ has much stronger data typing, whereas C is known as a weakly type language.

The biggest C++ advantage is data hiding – protecting data. Data is only accessed through methods. Only those functions that should change the data can change the data. The user has no knowledge of your variables and is concerned only with

the results of your program, not the source code or the variables that produce the result.



10 Major Differences C to C++

1. C follows the procedural programming paradigm while C++ is a multi-paradigm language(procedural as well as object oriented).

2. C data is not secured while the data is secured(hidden) in C++.

3. C is a low-level language while C++ is a middle-level language.

4. C uses the top-down approach while C++ uses the bottom-up approach.

5. C is function-driven while C++ is object-driven.

6. C++ supports function overloading (polymorphism) while C does not.

7. We can use functions inside structures in C++ but not in C.

8. C++ uses NAMESPACE to avoid name collisions while C uses static.

9. The standard input & output functions differ in the two languages (C uses scanf & printf while C++ uses cin>> & cout<< )

10. C++ allows the use of reference variables while C does not.



typedef struct{

double sales;double profit;char name[25];

} Store;

Store big_store;strcpy(big_store.name, “Mom’s Food”);big_store.sales = 100.00;big_store.profit = 10.00;

structs vs classesclass Store{

double sales;double profit;char name[25];

};

Store big_store;strcpy(big_store.name, “Mom’s Food”);

class Store{ private:

double sales;double profit;

public:char name[25];

double Store::getSales();double Store::getProfit();void Store::setSales(double);void Store::setProfit(double);

};

Store big_store;strcpy(big_store.name, “Mom’s Food”);big_store.setSales(100.00);big_store.setProfit(10.00);



Polymorphism

Polymorphism means that something has many (poly), forms (morph). The same function name can work on different types of objects Keeps the clutter out of your code.

Example: employee.print(); // Print the employee objects customer.print(); // Print the customer objects


#include <iostream>using namespace std;

int size(int x);int size(int a, int b);int main() { cout << "Size of a square with side 5: " << size(5) << '\n'; cout << "Size of rectangle of with sides 5,4: " << size(5,4) << endl; return 0;}int size(int x) { return (x*x);}int size(int a, int b) { return (a*b);}


Sundry Additions

Call by reference (ie: myfunc(int &a, int &b);) Strongly typed enums Generic, type-save data structures (using templates) New keywords

typeid, bool, dynamic_cast, mutable, catch, explicit, namespace, static_cast, using, export, new, virtual, class, operator, private, template, const_cast, protected, this, wchar_t, public, throw, friend, delete, reinterpret_cast, try

Constructors/destructors Namespaces


What?

The semester’s over already?


See you soon!

recursion, c and beyond "… but it clearly is the only right way. the fact that everybody else...

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