Recursion and implementation of functions
Download
1 / 30

Recursion and Implementation of Functions - PowerPoint PPT Presentation


  • 122 Views
  • Uploaded on

Recursion and Implementation of Functions. CS-2303 System Programming Concepts (Slides include materials from The C Programming Language , 2 nd edition, by Kernighan and Ritchie and from C: How to Program , 5 th and 6 th editions, by Deitel and Deitel). Definition.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Recursion and Implementation of Functions' - bisa


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Recursion and implementation of functions

Recursion and Implementation of Functions

CS-2303System Programming Concepts

(Slides include materials from The C Programming Language, 2nd edition, by Kernighan and Ritchie and from C: How to Program, 5th and 6th editions, by Deitel and Deitel)

Recursion and Function Implementation


Definition
Definition

  • Recursive Function:–a function that calls itself

    • Directly or indirectly

  • Each recursive call is made with a new, independent set of arguments

    • Previous calls are suspended

  • Allows very simple programs for very complex problems

  • Recursion and Function Implementation


    Simplest example
    Simplest Example

    int factorial(int x) {

    if (x <= 1)

    return 1;

    else

    return x * factorial (x-1);

    } // factorial

    Recursion and Function Implementation


    More interesting example towers of hanoi
    More Interesting ExampleTowers of Hanoi

    • Move stack of disks from one peg to another

    • Move one disk at a time

    • Larger disk may never be on top of smaller disk

    Recursion and Function Implementation


    Tower of hanoi program

    #include <stdio.h>

    void move (int n, int a, int c, int b);

    int main() {

    int disks;

    printf ("How many disks?");

    scanf ("%d", &disks);

    move (disks, 1, 3, 2);

    return 0;

    } // main

    /* PRE: n >= 0. Disks are arranged small to large on the pegs a, b, and c. At least n disks on peg a. No disk on b or c is smaller than the top n disks of a.

    POST: The n disks have been moved from a to c. Small to large order is preserved. Other disks on a, b, c are undisturbed. */

    void move (int n, int a, int c, int b) {

    if (n > 0)

    {

    move (n-1, a, b, c);

    printf ("Move one disk from %d to %d\n", a, c);

    move (n-1, b, c, a);

    } // if (n > 0)

    return;

    } // move

    • Is pre-condition satisfied before this call to move?

    Tower of Hanoi Program

    Recursion and Function Implementation


    Tower of hanoi program1

    #include <stdio.h>

    void move (int n, int a, int c, int b);

    int main() {

    int disks;

    printf ("How many disks?");

    scanf ("%d", &disks);

    move (disks, 1, 3, 2);

    return 0;

    } // main

    /* PRE: n >= 0. Disks are arranged small to large on the pegs a, b, and c. At least n disks on peg a. No disk on b or c is smaller than the top n disks of a.

    POST: The n disks have been moved from a to c. Small to large order is preserved. Other disks on a, b, c are undisturbed. */

    void move (int n, int a, int c, int b) {

    if (n > 0)

    {

    move (n-1, a, b, c);

    printf ("Move one disk from %d to %d\n", a, c);

    move (n-1, b, c, a);

    } // if (n > 0)

    return;

    } // move

    • If pre-condition is satisfied here, is it still satisfied here?

    And here?

    Tower of Hanoi Program

    Recursion and Function Implementation


    Tower of hanoi program2

    #include <stdio.h>

    void move (int n, int a, int c, int b);

    int main() {

    int disks;

    printf ("How many disks?");

    scanf ("%d", &disks);

    move (disks, 1, 3, 2);

    return 0;

    } // main

    /* PRE: n >= 0. Disks are arranged small to large on the pegs a, b, and c. At least n disks on peg a. No disk on b or c is smaller than the top n disks of a.

    POST: The n disks have been moved from a to c. Small to large order is preserved. Other disks on a, b, c are undisturbed. */

    void move (int n, int a, int c, int b) {

    if (n > 0)

    {

    move (n-1, a, b, c);

    printf ("Move one disk from %d to %d\n", a, c);

    move (n-1, b, c, a);

    } // if (n > 0)

    return;

    } // move

    If pre-condition is true andif n = 1, does move satisfythe post-condition?

    Tower of Hanoi Program

    Can we reason that thisprogram correctly playsTower of Hanoi?

    Recursion and Function Implementation


    Why recursion
    Why Recursion?

    • Are article of faith among CS students and faculty but …

    • … a surprise to non-CS students.

    • Some problems are too hard to solve without recursion

      • Most notably, the compiler!

      • Tower of Hanoi problem

      • Most problems involving linked lists and trees

        • (Later in the course)

    Recursion and Function Implementation


    Recursion vs iteration
    Recursion vs. Iteration

    • Some simple recursive problems can be “unwound” into loops

      • But code becomes less compact, harder to follow!

  • Hard problems cannot easily be expressed in non-recursive code

    • Tower of Hanoi

    • Robots or avatars that “learn”

    • Advanced games

  • Recursion and Function Implementation


    Personal observation
    Personal Observation

    • From my own experience, programming languages, environments, and computer architectures that do not support recursion

    • … are usually not rich enough to support a diverse portfolio of applications

      • I.e., a wide variety of problems in many different disciplines

    Recursion and Function Implementation


    Questions

    Questions?

    Recursion and Function Implementation


    Implementing recursion the stack
    Implementing Recursion — The Stack

    • Definition – The Stack

      • A last-in, first-out data structure provided by the operating system for each running program

      • For temporary storage of automatic variables, arguments, function results, and other stuff

    • I.e., the working storage for each, separate function call.

    Recursion and Function Implementation


    The stack continued
    The Stack(continued)

    • Every single time a function is called, an area of the stack is reserved for that particular call.

    • Known as its activation record in compiler circles.

    Recursion and Function Implementation


    Recursion is so important
    Recursion is so important…

    • … that all modern computer architectures specifically support it

      • Stack register

      • Instructions for manipulating The Stack

  • … most modern programming languages allow it

    • But not Fortran and not Cobol

  • Recursion and Function Implementation


    Recursion in c
    Recursion in C

    • Parameters, results, and automatic variables allocated on the stack.

    • Allocated when function or compound statement is entered

    • Released when function or compound statement is exited

    • Values are not retained from one call to next (or among recursions)

    Recursion and Function Implementation


    Arguments and results
    Arguments and Results

    • Space for storing result is allocated by caller

      • On The Stack

      • Assigned by return statement of function

      • For use by caller

  • Arguments are values calculated by caller of function

    • Placed on The Stack by caller in locations set aside for the corresponding parameters

    • Function may assign new value to parameter, but …

    • …caller never looks at parameter/argument values again!

  • Arguments are removed when callee returns

    • Leaving only the result value for the caller

  • Recursion and Function Implementation


    Typical implementation of the stack
    Typical Implementation of The Stack

    • Linear region of memory

    • Stack Pointer “growing” downward

    • Each time some information is pushed onto The Stack, pointer moves downward

    • Each time info is popped off of The Stack, pointer moves back upward

    Recursion and Function Implementation


    Typical memory for running program windows linux

    0xFFFFFFFF

    stack

    (dynamically allocated)

    SP

    heap

    (dynamically allocated)

    address space

    static data

    program code

    (text)

    PC

    0x00000000

    Typical Memory for Running Program (Windows & Linux)

    Recursion and Function Implementation


    Typical memory for running program windows linux1

    Heap to be discussed later in course

    0xFFFFFFFF

    stack

    (dynamically allocated)

    SP

    heap

    (dynamically allocated)

    address space

    static data

    program code

    (text)

    PC

    0x00000000

    Typical Memory for Running Program (Windows & Linux)

    Recursion and Function Implementation


    How it works
    How it works

    • Imagine the following program:–

      int factorial(int n){

      /* body of factorial function */

      } // factorial

    • Imagine also the caller:–

      int x = factorial(100);

    • What does compiled code look like?

    Recursion and Function Implementation


    Compiled code the caller
    Compiled code: the caller

    int x = factorial(100);

    • Provide integer-sized space on stack for result, so that calling function can find it

    • Evaluate the expression “100” and leave it on the stack (after result)

    • Put the current program counter somewhere so that factorial function can return to the right place in calling function

    • Transfer control to the called function

    Recursion and Function Implementation


    Compiled code factorial function
    Compiled code: factorial function

    • Save the caller’s registers in a dedicated space in the activation record

    • Get the parameter n from the stack

    • Set aside some memory for local variables and intermediate results on the stack

    • Do whatever factorial was programmed to do

    • Put the result in the space allocated by the caller

    • Restore the caller’s registers

    • Transfer back to the program counter saved by the caller

    Recursion and Function Implementation


    Typical address space windows linux

    0xFFFFFFFF

    stack

    (dynamically allocated)

    SP

    heap

    (dynamically allocated)

    Memory address space

    static data

    program code

    (text)

    PC

    0x00000000

    Typical Address Space (Windows & Linux)

    Recursion and Function Implementation


    Note

    • Through the magic of operating systems, each running program has its own memory

      • Complete with stack & everything else

    • Called a process

      Windows, Linux, Unix, etc.

    Recursion and Function Implementation


    Note continued
    Note (continued)

    • Not necessarily true in small, embedded systems

      • Real-time & control systems

      • Mobile phone & PDA

      • Remote sensors, instrumentation, etc.

  • Multiple running programs share a memory

    • Each in own partition with own stack

    • Barriers to prevent each from corrupting others

  • Recursion and Function Implementation


    Shared physical memory

    0x0000FFFF

    Process 3

    stack

    stack

    stack

    Process 2

    Physical

    memory

    Process 1

    0x00000000

    Shared Physical Memory

    OS Kernel

    Recursion and Function Implementation


    Questions1

    Questions?

    Recursion and Function Implementation


    The stack summary
    The Stack(summary)

    • The stack gives each function call its own, private place to work

      • Separate from all other calls to same function

      • Separate from all calls to other functions

      • Place for automatic variables, parameters, results

    Recursion and Function Implementation


    The stack continued1
    The Stack(continued)

    • Originally intended to support recursion

      • Mostly for computer scientists

      • Compiler writers, etc.

  • Powerful enabling concept

    • Allows function to be shared among multiple running programs

    • Shared libraries

    • Concurrent activities within a process

  • Recursion and Function Implementation


    Questions2

    Questions?

    Recursion and Function Implementation


    ad