The stack data structure
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The Stack Data Structure. Mugurel Ionu ț Andreica Spring 2012. Operations. push(x) Adds the element x at the top of the stack pop() Removes the element from the top of the stack and returns it Returns an error if the stack is empty peek()

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The Stack Data Structure

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The stack data structure

The Stack Data Structure

Mugurel Ionuț Andreica

Spring 2012


Operations

Operations

  • push(x)

    • Adds the element x at the top of the stack

  • pop()

    • Removes the element from the top of the stack and returns it

    • Returns an error if the stack is empty

  • peek()

    • Returns (but does not remove) the element at the top of the stack

  • isEmpty()

    • Returns 1 if the stack is empty and 0 otherwise

  • The axioms are given implicitly – they determine the expected behavior of the stack for a given sequence of operations

    • See the examples on the upcoming slides


Stack example

Stack - Example


Stack array based implementation

Stack – Array-based Implementation

T peek() {

if (isEmpty()) {

fprintf(stderr, "Error 103 - The stack is empty!\n");

T x;

return x;

}

return stackArray[topLevel];}

int isEmpty() {

return (topLevel < 0);}

Stack() { // constructor

topLevel = -1; } // the stack is empty in the beginning

};

int main() {

Stack<int> s;

s.push(7);s.push(3);s.push(10);s.push(13);s.push(20);

s.push(9);s.push(1);printf("%d\n", s.pop());

printf("%d\n", s.peek());printf("%d\n", s.peek());

printf("%d\n", s.pop());printf("%d\n", s.peek());

s.push(100); printf("%d\n", s.pop());

return 0;

}

#include <stdio.h>

#define NMAX 100

template<typename T> class Stack {

private:

T stackArray[NMAX];

int topLevel;

public:

void push(T x) {

if (topLevel >= NMAX - 1) {

fprintf(stderr, "Error 101 - The stack is full!\n");

return;

}

topLevel++;

stackArray[topLevel] = x;

}

T pop() {

if (isEmpty()) {

fprintf(stderr, "Error 102 - The stack is empty!\n");

T x;

return x;

}

T x = stackArray[topLevel];

topLevel--;

return x;

}


Paranthesis checking

Paranthesis Checking

  • Given a string S composed of the characters ‘(‘, ‘)’, ‘[‘, ‘]’, ‘{‘, ‘}’ (round bracket, square bracket and curly bracket), determine if the parantheses are correctly balanced

  • S=“([()[{([]()){}}[[]]]{}])[]({})” is correctly balanced

  • S1=“([]({)})”, S2=“[{{}(())([]{“, S3=“[(){}]]” are not correctly balanced

  • Algorithm

    • We use a stack

    • We traverse the string from left to right

      • We push on the stack every open bracket

      • For every closed bracket, the bracket at the top of the stack must be an open bracket of the same type (and the stack must not be empty) => then we pop the open bracket from the stack

      • In the end, the stack must be empty


Paranthesis checking implementation

Paranthesis Checking - Implementation

#include <stdio.h>

#include <string.h>

// copy & paste the definition of the Stack class

char s[200]="([{()[]}(()[{}()])])(){}[{{()[]}()}]";

int error = 0;

int main(){

Stack<char> stk;

for (int i = 0; i < strlen(s); i++){

if (s[i] == '(' || s[i] == '[' || s[i] == '{')

stk.push(s[i]);

elseif (stk.isEmpty()){

fprintf(stderr, "Error 201 - Empty stack\n");

error = 1;

break;

}

else{

if ((s[i] == ')' && stk.peek() != '(') ||

(s[i] == ']' && stk.peek() != '[') ||

(s[i] == '}' && stk.peek() != '{')){

fprintf(stderr, "Error 202 -Wrongparanthesis\n");

error = 1;

break;

}

stk.pop();

}

}

if (!error && !stk.isEmpty())

fprintf(stderr, "Error 203 - The stack is not empty at the end\n");

elseif (!error)

printf("OK\n");

return 0;

}


Header with the stack class definition

Header with the Stack Class Definition

  • Definition of the Stack class must be copy-pasted in every program in which it is used => annoying + prone to mistakes (maybe we do not copy-paste everything, or we copy-paste more than we need)

  • Elegant solution: define the Stack class in a header file (e.g. mystack.h)

  • Any program that uses the Stack class will include the header file

    • #include “mystack.h” (or #include <mystack.h>)

    • we will proceed similarly for the upcoming data structures


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