StackStackMobile Game ProgrammingMobile Game Programming

jintaeks@gmail.comDivision of Digital Contents, Dongseo Univ.

September 8, 2016

Presentation Outline ADT Data Structure Stack Implementation of a stack

– KStack– template KStack

Algorithms with stack– Base conversion of numeral system– Evaluation of postfix notation– Conversion from infix to postfix notation

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Abstract Data Type(ADT) an abstract data type (ADT) is a mathematical model

 for data types where a data type is defined by its behavior (semantics) from the point of view of a user of the data.

possible values, possible operations on data of this type, and the behavior of these operations.

Example: integers– Values …, -2, -1, 0, 1, 2, …– Operations

• Addition• Subtraction• Multiplication• Division• Greater than, etc…

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ADT examples Some common ADTs, which have proved useful in a

great variety of applications, are:– Container, List, Set, Multiset– Map, Multimap, Graph, Stack– Queue, Priority queue– Double-ended queue– Double-ended priority queue

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Data Structure(s) a data structure is a particular way of organizing data in

a computer so that it can be used efficiently. Data Structures implement one or more particular 

abstract data types (ADT). Data Structure is a concrete implementation of the

contract provided by an ADT. Examples:

– Array, Stack, List– Associative array, Record(struct)– Union– Set– Graph, Tree– Class– …

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Stack an abstract data type that serves as a collection of

elements. two principal operations:

– push, which adds an element to the collection.– pop, which removes the most recently added element that was

not yet removed. LIFO (for last in, first out) the push and pop operations occur only at one end of

the structure, referred to as the top of the stack. may be implemented to have a bounded capacity. Overflow

– when the stack is full and does not contain enough space to accept an entity to be pushed.

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Stack runtime Simple representation of a stack runtime.

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Hardware stacks#include "stdafx.h"

void Test( int i ){ i = 4;}void main(){ int i; int j; i = 3; j = i; Test( i ); printf( "%d\r\n", i );}

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Stack Settings in Visual Studio 2013 Property pageLinkerSystemStack Reserve Size

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Working Example#include <stdio.h>void Swap(int a, int b) {

int t=a;a=b;b=t;

}//Swapvoid main() {

int a=2;int b=3;Swap(a,b);printf("%d,%d\n",a,b);

}//main

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#include <stdio.h>void Swap(int a, int b) {

int t=a;a=b;b=t;

}//Swapvoid main() {

int a=2;int b=3;Swap(a,b);printf("%d,%d\n",a,b);

}//main

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#include <stdio.h>void Swap(int a, int b) {

int t=a;a=b;b=t;

}//Swapvoid main() {

int a=2;int b=3;Swap(a,b);printf("%d,%d\n",a,b);

}//main

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#include <stdio.h>void Swap(int a, int b) {

int t=a;a=b;b=t;

}//Swapvoid main() {

int a=2;int b=3;Swap(a,b);printf("%d,%d\n",a,b);

}//main

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Revised working example#include <stdio.h>void Swap(int *a,int *b) {

int t=*a;//assigns the contents of a to t*a=*b;//assigns the contents of b to the location of contents of a.*b=t;//assigns the t to the location of contents of b

}//Swapvoid main() {

int a=2,b=3;Swap(&a,&b);//pass addresses of a and bprintf("%d,%d\n",a,b);

}//main

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#include <stdio.h>void Swap(int *a,int *b) {

int t=*a;//assigns the contents of a to t*a=*b;//assigns the contents of b to the location of contents of a.*b=t;//assigns the t to the location of contents of b

}//Swapvoid main() {

int a=2,b=3;Swap(&a,&b);//pass addresses of a and bprintf("%d,%d\n",a,b);

}//main

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#include <stdio.h>void Swap(int *a,int *b) {

int t=*a;//assigns the contents of a to t*a=*b;//assigns the contents of b to the location of contents of a.*b=t;//assigns the t to the location of contents of b

}//Swapvoid main() {

int a=2,b=3;Swap(&a,&b);//pass addresses of a and bprintf("%d,%d\n",a,b);

}//main

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#include <stdio.h>void Swap(int *a,int *b) {

int t=*a;//assigns the contents of a to t*a=*b;//assigns the contents of b to the location of contents of a.*b=t;//assigns the t to the location of contents of b

}//Swapvoid main() {

int a=2,b=3;Swap(&a,&b);//pass addresses of a and bprintf("%d,%d\n",a,b);

}//main

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#include <stdio.h>void Swap(int *a,int *b) {

int t=*a;//assigns the contents of a to t*a=*b;//assigns the contents of b to the location of contents of a.*b=t;//assigns the t to the location of contents of b

}//Swapvoid main() {

int a=2,b=3;Swap(&a,&b);//pass addresses of a and bprintf("%d,%d\n",a,b);

}//main

C++ implementations of a stackclass KStack{public: KStack() : m_sp( 0 ) { } void Push( int data_ ); bool Pop( int& outData_ ); bool IsEmpty() const;private: int m_sp; int m_data[ 100 ];};//class KStack

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void KStack::Push( int data_ ){ m_data[ m_sp ] = data_; m_sp += 1;}bool KStack::Pop( int& outData_ ){ if( m_sp <= 0 ) return false; m_sp -= 1; outData_ = m_data[ m_sp ]; return true;}bool KStack::IsEmpty() const{ return m_sp == 0;}

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Template KStacktemplate<typename T, int STACK_SIZE>class KStack{public: KStack() : m_sp( 0 ) { } void Push( T data_ ); bool Pop( T& outData_ ); bool IsEmpty() const;private: int m_sp; T m_data[ STACK_SIZE ];};//class KStack

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template<typename T, int STACK_SIZE>void KStack<T,STACK_SIZE>::Push( T data_ ){ m_data[ m_sp ] = data_; m_sp += 1;}template<typename T, int STACK_SIZE>bool KStack<T, STACK_SIZE>::Pop( T& outData_ ){ if( m_sp <= 0 ) return false; m_sp -= 1; outData_ = m_data[ m_sp ]; return true;}

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void main(){ KStack<int,100> s; s.Push( 3 ); s.Push( 5 ); int data; const bool bIsPop = s.Pop( data ); printf( "%d\r\n", data );}

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Actual usage of stack in C++ std::stack

template<    class T,    class Container = std::deque<T>

> class stack;

a container adapter that gives the programmer the functionality of a stack - specifically, a LIFO (last-in, first-out) data structure.

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#include <stack>

void main(){ std::stack<int> s; int n;

printf( "Enter decimal digit:" ); scanf( "%d", &n ); while( n >= 5 ) { s.push( n % 5 ); n /= 5; }//while

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printf( "Equivalent Quintett is %d", n );

while( s.empty() == false ) { n = s.top(); printf( "%d", n ); s.pop(); }//while}//main

Algorithms with Stack Convert Decimal Number to Pentamal Number Reverse Polish Notation: Evaluating Postfix Notation Conversion from Infix to Postfix Notation

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Convert Decimal Number to Pentamal Number divide the number by 5. write quotient and remainder.

now quotient is dividend, continue till dividend is less than 5.

the reverse order of the remainder is a pentamal number.

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void main(){ KStack<int, 100> s; int n;

printf( "Enter decimal number:" ); scanf( "%d", &n ); while( n >= 5 ) { s.Push( n % 5 ); n /= 5; }//while printf( "Equivalent pentamal is ", n ); while( s.Pop( n ) ) printf( "%d", n );}//main

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Practice Write a class that convert decimal number to n-ary

number.– binary– trimal– tetramal– pentamal– hexamal– heptamal– octal– nonamal

there must a getter that gets the converted number in string.

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Reverse Polish Notation: Postfix Notation the operators follow their operands; for instance, to add 3 and 4, one would write "3 4 +"

rather than "3 + 4". "3 − 4 + 5“ "3 4 − 5 +"

– if there are multiple operations, the operator is given immediately after its second operand.

it removes the need for parentheses that are required by infix.

"3 − (4 × 5)“ is quite different from "(3 − 4) × 5". In postfix, it could be written "3 4 5 × −", which

unambiguously means "3 (4 5 ×) −" which reduces to "3 20 −“.

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Evaluation postfix expression While there are input tokens left

– Read the next token from input.– If the token is a value

• Push it onto the stack.– Otherwise, the token is an operator (operator here includes both

operators and functions). • It is known a priori that the operator takes n arguments.• If there are fewer than n values on the stack

– (Error) The user has not input sufficient values in the expression.• Else, Pop the top n values from the stack.• Evaluate the operator, with the values as arguments.• Push the returned results, if any, back onto the stack.

If there is only one value in the stack – That value is the result of the calculation.

Otherwise, there are more values in the stack – (Error) The user input has too many values.

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example: "5 + ((1 + 2) × 4) − 3“ 5 1 2 + 4 × + 3 −

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Input Operation Stack Comment5 Push 5　

1Push 1

　5

2

Push 2

　1

5

+Add 3

Pop two values (1, 2) and push result (3)5

4

Push 4

　3

5

×Multiply 12

Pop two values (3, 4) and push result (12)5

+ Add 17Pop two values (5, 12) and push result (17)

3Push value 3

　17

− Subtract 14Pop two values (17, 3) and push result (14)

　 Result 14　

Practice Write a class that evaluates a postfix notation.

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Conversion from Infix to Postfix NotationWhile there are tokens to be read:•Read a token.•If the token is a number, then add it to the output queue.•If the token is an operator, o1, then:

• while there is an operator token o2, at the top of the operator stack and either

• o1 is left-associative and its precedence is less than or equal to that of o2, or

• o1 is right associative, and has precedence less than that of o2,• pop o2 off the operator stack, onto the output queue;

• at the end of iteration push o1 onto the operator stack.•If the token is a left parenthesis (i.e. "("), then push it onto the stack.

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• If the token is a left parenthesis (i.e. "("), then push it onto the stack.

• If the token is a right parenthesis (i.e. ")"):• Until the token at the top of the stack is a left parenthesis, pop

operators off the stack onto the output queue.• Pop the left parenthesis from the stack, but not onto the output

queue.• If the stack runs out without finding a left parenthesis, then there

are mismatched parentheses.When there are no more tokens to read:• While there are still operator tokens in the stack:

• If the operator token on the top of the stack is a parenthesis, then there are mismatched parentheses.

• Pop the operator onto the output queue.Exit.

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Detailed example: 3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3 predefined operator properties table.

How can we implement this properties table?

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Detailed example: 3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3

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Detailed example: 3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3

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Practice Write a class that converts Infix notation to Postfix

notation. Expand the features of existing class(written in previous

learning).

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int priority( char a ) { int temp = 0;

if( a == '^' ) temp = 4; else if( a == '*' || a == '/' ) temp = 3; else if( a == '+' || a == '-' ) temp = 2; return temp;}

int main() { std::string infix; infix = "3+4*2/(1-5)^2^3";

std::stack<char> operator_stack; std::string postfix;

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for( unsigned i = 0; i < infix.length(); i++ ) { if( infix[ i ] == '+' || infix[ i ] == '-' || infix[ i ] == '*' || infix[ i ] == '/' ) { // } else if( infix[ i ] == '^' ) { // } else if( infix[ i ] == '(' ) { operator_stack.push( infix[ i ] ); } else if( infix[ i ] == ')' ) { while( operator_stack.top() != '(' ) { postfix += operator_stack.top(); operator_stack.pop(); } operator_stack.pop(); } else { postfix += infix[ i ]; } }

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if( infix[ i ] == '+' || infix[ i ] == '-' || infix[ i ] == '*' || infix[ i ] == '/' ) { while( !operator_stack.empty() && priority( infix[ i ] ) <= priority( operator_stack.top() ) ) { postfix += operator_stack.top(); operator_stack.pop(); } operator_stack.push( infix[ i ] ); } else if( infix[ i ] == '^' ) { while( !operator_stack.empty() && priority( infix[ i ] ) < priority( operator_stack.top() ) ) { postfix += operator_stack.top(); operator_stack.pop(); } operator_stack.push( infix[ i ] ); } else if( infix[ i ] == '(' ) {

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while( !operator_stack.empty() ) { postfix += operator_stack.top(); operator_stack.pop(); }//while

std::cout << postfix << std::endl;

return 0;}

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Actual usage of equation evaluation in C++ boost::math boost::spirit

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End https://en.wikipedia.org/wiki/Abstract_data_type https://en.wikipedia.org/wiki/Reverse_Polish_notation https://en.wikipedia.org/wiki/Shunting-yard_algorithm http://www.cplusplus.com/forum/beginner/16722/

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