CSC 202CSC 202Analysis and Design of AlgorithmsAnalysis and Design of Algorithms

Lecture 06:Lecture 06:Analysis of Algorithm using List, Stack and Queues

Asst.Prof.Dr.Surasak MungsingAsst.Prof.Dr.Surasak MungsingE-mail: surasak.mu@spu.ac.th

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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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StacksStacks

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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OperationsOperations พื้��นฐานของพื้��นฐานของ StackStack ที่��สร้�างด้�วยที่��สร้�างด้�วย Linked listLinked list

1.     Create stack: allocate memory for stack head node

2.     Push stack: add an element to a stack

3.     Pop stack: remove an element from a stack

4.     Stack top: using the value on the top of stack

5.     Empty stack: check whether the stack is empty

6.     Full stack: check whether the stack is full 7.     Stack count: return number of elements in stack

8.     Destroy 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)

BacktrackingBacktracking

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 Print path to goalto goal

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=createStack2 pMap= pMap3 loop (pMap not null AND goalNotFound)

1 if (pMap is goal) 1 set goalNoFound to false2 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

Running time is O(|E|+|V|)

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Stack Applications: Backtracking

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Stack Applications: Backtracking

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Eight queens problemEight 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 boardPost Queen’ position pointed

createStack (stack)Set row to 1Set col to 0loop (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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/** * 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);

}

Tail Recursion: bad use of Tail Recursion: bad use of recursionrecursion

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 recursionPrinting 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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QueueQueue 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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QueueOperations

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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 Applications of Queue Queue

Queue simulation

Categorizing Data

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