The Stack Data Structure

1. The Stack Data Structure Mugurel Ionuț Andreica Spring 2012

2. 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

3. Stack - Example

4. 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; }

5. 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

6. 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; }

7. 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