Transcript Lecture 4 - Al al

Lecture 4
1)
2)
3)
RECURSION
BACKTRACKING
LOOK AHEAD
Recursion
What is Recursion?
A recursive function is a function that calls itself.
EG: finding the factorial of a number:
non-recursive
long factorial (long n)
fact = 1;
for (i=1;i<=n;i++)
fact = fact*i;
return fact;
Recursive method
long factorial (long number)
{
if (number == 1) return 1;
else
return(number*factorial(number - 1));
}
main( ) - Next slide
Recursion
main()
{
int factnum;
cin>>num;
factnum = factorial(num);
cout<<factnum;
return 0;
}
If the number is 5 then process
will be
5 * Factorial (5-1)
4 * Factorial (4-1)
3 * Factorial (3-1)
2 * Factorial (2-1)
1
Recursion
• EG 2 : Sum of n Natural Numbers:
int sum(n)
int sum(n)
{ int i,sum;
{
for (i=1;i<=n;i++)
if (n==1)
return 1;
else
return( n+ sum(n-1));
}
sum = sum+i;
return sum;
}
Recursion
• Other Examples:
– Binary Search - searching for an element
– Towers of Hanoi
One Must Move the disks from the A to B with the following rules
1) a disk can be placed in any one , move one at a time
2) No large disk over a small disk
A
B
C
Binary Search
1
1
4
4
7
7
8
8
14
14
16
16
28
28
35
35
Back Tracking
What is BackTracking?
In this method the algorithm attempts to
complete a solution by constructing partial
solutions and then extends the partial solution
toward completion.
When an inconsistency occurs the algorithm
'backs up' by removing the most recent
construction and trys another possibility
(This is called backtracking).
Back Tracking
Example : 8 queens problem.
There is 8x8 Chess Board and there are 8
queens
All the 8 queens have to be placed on the
chess board so that no two queens are on the
same row,column and diagonal
(ie) no two attack each other
4 Queens Problem
Back Tracking
void AddQueen(void)
{ for (every unguarded position p on the board)
{
Place a queen in position p;
n ++;
if (n == 8) Print the configuration;
else
Addqueen();
Remove the queen from position p;
n--;
} }
Look Ahead
 In some games the advantage will always be
with the player who can think several moves
ahead.
• Thus this class of recursive algorithm
involves a look ahead procedure which findout possible future moves, evaluates them
and then selects the best before carrying out
the move.
Look Ahead
A general description might be:
Void LookAhead ()
{
Obtain a stack of possible moves
if recursion terminates (the base case) return one move and the value
else
{
for each move on the stack do
make the move and Lookahead
select the best value
return the move and value
}}
Look Ahead
 Try to apply this to the game of 8. The game consists of a
3x3 board containing numbers from 1 to 8 put randomly.
Therefore there is one space left for numbers to move. The
aim of the game is to move the numbers to rearrange them
in the following sequence:
123
456
78
A number is moveable if it is adjacent to the empty
square.