CSE 221/ICT221
Analysis and Design of Algorithms
Lecture 06:
Analysis of Algorithm using List, Stack
and Queues
Dr.Surasak Mungsing
E-mail: Surasak.mu@spu.ac.th
Apr-15
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Stacks
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Stack Operation: Push
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Stack Operation: Pop
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Stack Operation: Top
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Stacks
 Stack operation is LIFO (Last-In, First-Out)
 Basic operations of Stack
- Adding an element to Stack (Push)
- Removing an element from Stack (Pop)
- Using an element of Stack (Top)
 Creating a Stack
- using an array to represent a stack
- using a Linked list to represent a Stack
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Stack represented by Linked list
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Stack represented by Linked list
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Stack Operation: Push
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Stack Operation: Destroy
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Operations
1.
2.
3.
4.
5.
6.
7.
8.
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พืน้ ฐานของ Stack ที่สร้ างด้ วย Linked list
Create stack:
Push stack:
Pop stack:
Stack top:
Empty stack:
Full stack:
Stack count:
Destroy stack:
allocate memory for stack head node
add an element to a stack
remove an element from a stack
using the value on the top of stack
check whether the stack is empty
check whether the stack is full
return number of elements in stack
return all nodes of stack to system
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Stack Applications: Balancing Symbols
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Stack Applications:
Infix to Postfix
conversion
The conversion time is O(n)
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Postfix expression evaluation
The evaluation time is O(n)
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Backtracking
 backtracking is a general algorithm for finding all (or
some) solutions to some computational problem, that
incrementally builds candidates to the solutions, and
abandons each partial candidate c ("backtracks") as
soon as it determines that c cannot possibly be
completed to a valid solution.
 classic example of the use of backtracking is the eight
queens puzzle, that asks for all arrangements of eight
queens on a standard chessboard so that no queen
attacks any other.
 an important tool for solving constraint satisfaction
problems, such as crosswords, verbal arithmetic,
Sudoku, and many other puzzles.
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Stack Applications: Backtracking
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Stack Applications: Backtracking
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Print path
to goal
Running time is O(|E|+|V|)
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Algorithm seekGoal (val map <linked list>)
This algorithm determines the path to a desired goal.
Pre a graph containing the path
Post path printed
1 Stack=createStack
2 pMap= pMap
3 loop (pMap not null AND goalNotFound)
1 if (pMap is goal)
1 set goalNoFound to false
2 else
1 pushStack (stack,pMap)
2 if (pMapis a branch point)
1 loop (more branch point)
1 create branchPoint node
2 pushStack (stack, branchPoint)
3 advance to next node
4 if (emptyStack (stack))
1 print (There is no path to your goal)
5 else
1 print (The path to your goal is: )
2 loop (not emptyStack (stack))
1 popStack (stack, pMap)
2 if (pMap notbranchPoint)
1 print (pMAp->nodeName)
3 print (End of File)
6 destroyStack (stack)
end seekGoal
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Stack Applications: Backtracking
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Stack Applications: Backtracking
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Eight queens problem
Algorithm queen8 (boardSize <integer>)
Position chess queens on a game board so that no queen can capture any other
queen.
Pre boardSize is number of rows & collumns on board
Post Queen’ position pointed
createStack (stack)
Set row to 1
Set col to 0
loop (row <= boardSize)
loop (col <= boardSize AND row <= boardSize)
add 1 to col
if (not garded (row, col))
place queen at board [row] [col]
pushStack (stack, [row, col])
add 1 to row
set col to 0
loop (col >= boardSize)
popStack (stack, [row, col])
remove queen at board[row] [col]
printBoard (stack)
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Tail Recursion: bad use of recursion
/**
* Print List from ListNode p onwards.
*/
Public static void printlist (ListNode p)
{
/* 1*/
if (p== nul)
/* 2*/
return;
/* 3*/
system.out.println(p.element);
/* 4*/
printList(p.next);
}
If the list contains 20,000 elements to print, there will be a stack of
20,000 activation records representing the nested calls of line 4.
Activation records are typically large, so the program is likely to run
out of stack space.
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Printing a list without recursion
/**
* Print List from ListNode p onward
*/
Public static void printList (ListNode p)
{
while (true)
{
if (p== null)
return;
system.out.println (p.element);
p = p.next;
{
}
Removal of tal recursion is so simple that some compilers do it
automatically.
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Queue
 Queue uses FIFO (First-In, First-Out)
 Basic operations of Queue
- Enqueue :adding an element to Queue ()
- Dequeue: removing an element from Queue ()
- QueueFront: Returns a reference to the value
at the front of a non-empty queue
- QueueRear: Returns a reference to the value
at the rear of a non-empty queue
Implementing a Queue
- by an Array
- by Linked list
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The Queue concept
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Operation Enqueue
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Operation Dequeue
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Operation QueueFront
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Operation QueueRear
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Queue
Operations
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Queue implemented by Array
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Is queue full?
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Circular Queue
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Queue implemented by linked list
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Queue data structure
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Operation algorithms on Queue
1. Create queue: create queue head based on dynamic memory
2. Enqueue:
add an element on queue
3. Dequeue:
remove an element from queue
4. Queue front: return an element at the front of queue
5. Queue rear: return an element at the rear of queue
6. Empty queue: returns true if queue is empty, else returns false
7. Full queue:
returns true if queue is full, else returns false
8. Queue count: returns number of elements in queue
9. Destroy queue: returns memory allocated to queue to system
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Create and enqueue
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Applications of Queue
 Queue simulation
 Categorizing Data
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