Recursion, a programming concept with implentation view of "Tower of Hanoi"

1. Fundamentals Of Programming in C
Presented By:
saket kr Pathak
M.sc. nt & M
aMIty InstItute Of InfOrMatIOn
technOlOgy
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2. Recursion
Recursion is said as a mathematical concept which states that an
expression such that each term is generated by repeating a particular
mathematical operation. Here repeating is the iterative manner to
perform same operation.
As the approach of the programming language C, it can be performed
and are in practice within the definition part of functions. Syntactically
language provides the freedom to call function within it’s body
defined.
Definition of ‘Recursion’ as the logical prospective view states simply
the iterative manner to perform any code snippet in C, but we always
need a terminating condition to control the going on iterations. In the
following sections we will discuss the iterative manner of recursion
and the terminating condition in bit expanded form.
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3. Recursive Functions
Recursive functions are not different from the syntactical structure of
the general functions that we had discussed in previous sections.
They have same return type, function name, parameters enclosed
within parenthesis.
Declaration:
int Think_and_ Play (int, char);
We had discussed the syntactical view of the function, where return
type is ‘int’, function name is ‘Think_and_Play’ and within the
parenthesis we had defined the parameters as of data type integer
with another one that is of data type character.
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4. Now let us manipulate the definition of the our function, that we had
declared in the previous slide from the general aspect of definition
we had practiced till now.
Definition:
int _iFlag =0, _iTerminate = 0;
int Think_and_Play(int _iBat, char _chBall)
{
if (_iFlag ==0)
printf(“This is game cricket going on.”);
_iFlag++;
if(_iTerminate < 6)
{
printf(“Hit the Ball with the Bat.”);
++ _iTerminate;
Think_and_Play(1, ‘0’);
return 1;
}
}
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5. As in sequence of explanation, this snippet code has few syntactical
statements. In the very first the program counter encounters with the
Variables of type integer that are global to the function.
Then it encounters the return type of the function following with the
function name, and the parameters defined. All of these has the
considerable part in function definition structure of C language that
we had discussed in the previous sections of declaration.
As encounter with the right curly braces comes into just next
statement, it considers the following structure is for definition.
In the definition part, the first if condition is doing its formal
responsibility to control the execution of print function where the
defined condition will be true i.e. when the value of the variable
‘_iFlag’ is strictly equal to 0.
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6. The next statement is simply incrementing the value stored in the
memory location termed as ‘_iFlag’ (the variable name).
Then our point of consideration comes into picture in the execution
of second ‘if’ structure. Here in this ‘if’ structure program counter
will execute the statements defined within ‘if’ body, if and only if
the condition gets true. It means whenever the condition defined
with the if statements returns ‘Boolean True’ value then the further
body will execute. So we can consider the controlling system of the
execution of ‘if-body’ is properly controlled through the condition
defined there in if statement.
Now within the body concerned, we have a print function that
supports its definition with two arguments defined as ‘String type’
and another is ‘Variable Length Argument’ (i.e. null in the snippet).
Function performs the role successfully and control passes further.
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7. The followed statement says to increment the value stored in the
memory location corresponds to the variable name ‘_iTerminate’.
Here logically this increasing value of ‘_iTerminate’ and the if
condition defined above will cause the terminating condition.
At the near end of the body, we have a function call as
‘Think_and_Play(…, …)’. Since here we are calling the same
function that is executing, is said as recursion. Therefore, calling of
the function from its own body forms a loop like execution pattern
and is said as recursion. It is also considered as the alternative
programming pattern of looping structure (i.e. of ‘for loop’ and
‘while loop’).
The end statement says to return the value to the calling function as
‘return 1’, that declares the successful completion of all other
statements defined above.
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8. Discussion
Typically, recursion is quite elegant and requires fewer variables to
make the same calculation as iterative looping structural programs.
It take care of its assigned records by maintaining the stack of
arguments and variables for each invocation. It has been calculated
in some machines a simple recursive program call with snippet
defining one integer argument can be requires 8 32-bit words on the
stack.
Let us consider a snippet code of fibonacci sequence and calculate
it’s efficiency in the following section.
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9. Snippet-Code:
int fibonacci (int _iNam)
{
if (_iNam <= 1)
return _iNam;
else
return (fibonacci(_iNam-1)+fibonacci(_iNam-2)) }
Through ‘main()’ call the ‘fibonacci()’ with the index value to next generate
recursive value.
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10. Dissection of ‘fibonacci’ Program:
 int fibonacci (int _iNam)
Here in the above statement the function name ‘fibonacci’
has the parameter type defined as ‘integer’ having the return type as
‘integrer’. The right braces comes as the starting point of the snippet
code.
 if (_iNam <= 1)
return _iNam;
Here in the above two statements the condition followed by
‘if’, is establised as the terminating point if condition gets it
satisfied. On the satisfactory mode of ‘if’ statement the value
stored in _iNam return back to the calling.
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11.  else
return (fibonacci(_iNam -1) + fibonacci(_iNam - 2));
In the else part of the consecutive ‘if’ statement the return value
is a bit complex. At first the recursion takes place for the first part
from left and returns 1 decremented value i.e. ‘-1’ to the previous
value, simultaneously it maintains a stack of all the new variables
and concern values for each invocation. That will be come in use
for the next recursive call. The next recursive call initializes the
variable with the decremented value as ‘-2’. At the end when
function call completes then the respective sum of the value
returns back to the calling statement in ‘main()’.
The left braces shows the termination of the code snippet.
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12. As in the following we have the table showing 10 number of
function calls in simultaneous recursion.
Value of _iNam Return Value of Number of Function calls in recursive
fibonacci(_iNam) computation.
0 0 1
1 1 1
2 1 3
3 2 5
4 3 9
5 5 15
6 8 25
7 13 41
8 21 67
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13. As in the above table describes, the value passed through the
parameter, the value that the function returns and the number of
recursive steps a function can perform up to 9 sequential calls.
Cons:
Recursive programs typically use a large amount of computer
memory and the greater the recursion, the more memory used.
Recursive programs can be confusing to develop and
extremely complicated to debug.
Pros:
Recursion is a natural fit for some types of problems as
‘Tower of Hanoi’.
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14. Practice ‘Towers of Hanoi’
Problem:
The Classical Towers of Hanoi - an initial position of all disks is on
post 'A‘.
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15. The target solution of the puzzle is to build the tower on post 'C'.
The number of discs can vary, but there are only three towers.
The goal is to transfer the discs from one tower another tower.
However you can move only one disk at a time and you can never
place a bigger disc over a smaller disk.
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16. Algorithm to solve the above problem:
Move the top 3 disks from Source to Auxiliary tower,
Move the 4th disk from Source to Destination tower,
Move the 3 disks from Auxiliary tower to Destination tower.
Transfer the top 3 disks from Source to Auxiliary tower can again
be thought as a fresh problem and can be solve in the same manner.
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17. Let us do it step by step:
 At first move the ‘Disc1’ to ‘B’ and ‘Disc2’ to ‘C’ as in
following figure:
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18. Move the ‘Disc1’ to the top of the ‘Disc2’ at ‘C’ and ‘Disc3’ at
‘B’.
 Move the ‘Disc1’ to ‘A’ at the top of ‘Disc4’ and ‘Disc2’ at ‘B’ to the top
of ‘Disc3’.
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19.  Move the ‘Disc1’ at ‘B’ to the top of ‘Disc2’ and ‘Disc4’ at ‘A’.
 Move the ‘Disc1’ at ‘C’ to the top of ‘Disc4’ and ‘Disc2’ at ‘A’.
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20.  Move the ‘Disc1’ at ‘A’ to the top of ‘Disc2’ and ‘Disc3’ to the top of
‘disc4’ at ‘A’.
 Move the ‘Disc1’ at ‘B’ and ‘Disc2’ at ‘B’ to the top of ‘Disc3’.
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21.  Move the ‘Disc1’ at the top of ‘Disc2’ at ‘C’.
Congratulations you got your answer. Code implementation is up to
you people as hint use the concept of stack and just follow the steps
Above described.
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22. /
***********************************************************//
/Here in the following Program, towers are considered as character A, B
//and C and disks are considered as integral numbers.
/***********************************************************/
#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
#include <string.h>
#include <math.h>
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23. void generate_moves_toh(int i_disk_num, char from_peg,
char to_peg, char aux_peg)
{
/* If only 1 disk, make the move and return */
if(i_disk_num == 1)
{
printf("nMove disk 1 from peg %c to peg
%c", from_peg, to_peg);
return;
}
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24. /*Move top n-1 disks from A to B, using C as auxiliary
*/
generate_moves_toh(i_disk_num-1, from_peg,
aux_peg, to_peg);
printf("nMove disk %d from peg %c to peg %c",
i_disk_num, from_peg, to_peg);
/* Move n-1 disks from B to C using A as auxiliary */
generate_moves_toh(i_disk_num-1, aux_peg, to_peg,
from_peg);
}
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25. void gen_tow_of_honoi()
{
printf("WAP to display the steps required in
solving 'Tower of Hanoi' for 'n' number of disks.");
printf("nLimitation: nt-> Disks are
represented as integral numbers in assending order.");
printf("nnn");
int i_num_disk;
printf("Enter the number of disks : ");
scanf("%d",&i_num_disk);
printf("The Tower of Hanoi involves the moves
:nn");
generate_moves_toh(i_num_disk, 'A', 'C', 'B');
}
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26. int main()
{
gen_tow_of_honoi();
printf("nnn");
getch();
return 0;
}
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27. •The C Programming Language (by Dennis M. Ritchie and Brain W.
Kernighan).
•A book on C (by Al Kelley and Ira Pohl).
•Let us C (by Yashavant Kanetkar).
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