CSC 202 Analysis and Design of Algorithms Lecture 06: CSC 202 Analysis and Design of Algorithms Lecture 06: Analysis of Algorithm using List, Stack and Queues Asst.Prof.Dr.Surasak Mungsing Sep-151

9/17/ Stacks

9/17/ Stack Operation: Push

9/17/ Stack Operation: Pop

9/17/ Stack Operation: Top

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7Stacks  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

9/17/ Stack represented by Linked list

9/17/ Stack represented by Linked list

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9/17/ Stack Operation: Push

9/17/ Stack Operation: Destroy

9/17/ Operations พื้นฐานของ Stack ที่สร้างด้วย Linked 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

9/17/ Stack Applications: Balancing Symbols

9/17/ Stack Applications: Infix to Postfix conversion The conversion time is O(n)

9/17/ Postfix expression evaluation The evaluation time is O(n)

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. Sep-15 17

9/17/ Stack Applications: Backtracking

9/17/ Stack Applications: Backtracking

9/17/ Print path to goal Algorithm seekGoal (val map ) This algorithm determines the path to a desired goal. Prea graph containing the path Postpath 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 Running time is O(|E|+|V|)

9/17/ Stack Applications: Backtracking

9/17/ Stack Applications: Backtracking

9/17/ Eight queens problem Algorithm queen8 (boardSize ) 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)

9/17/ /** * 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 recursion 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.

9/17/ 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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9/17/ 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

9/17/ The Queue concept

9/17/ Operation Enqueue

9/17/ Operation Dequeue

9/17/ Operation QueueFront

9/17/ Operation QueueRear

9/17/ Queue Operations

9/17/ Queue implemented by Array

9/17/ Is queue full?

9/17/ Circular Queue

9/17/ Queue implemented by linked list

9/17/ Queue data structure

9/17/ 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

9/17/ Create and enqueue

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9/17/ Applications of Queue  Queue simulation  Categorizing Data

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