Containers: Stack Jordi Cortadella and Jordi Petit Department of Computer Science
The Stack ADT A stack is a list of objects in which insertions and deletions can only be performed at the top of the list. Also known as LIFO (Last In, First Out) push (insert an element at the top) pop (delete the most recently inserted element) 8 3 5 1 6 top (the most recently inserted element) empty (is there any element?) Note: pop and top generate an error on an empty stack Containers: Stacks Dept. CS, UPC 2
The Stack ADT template <typename T> class Stack { public: // Default constructor Stack() { private: vector<t> data; ; The definition can handle generic stacks of any type T. The default constructor does not need to do anything: a zero-sized vector is constructed by default. Containers: Stacks Dept. CS, UPC 3
template <typename T> class Stack { public: bool empty() const { return data.size() == 0; The Stack ADT const T& top() const { // Returns a const reference assert (not empty()); return data.back(); T& top() { // Returns a reference assert (not empty()); return data.back(); void pop() { assert (not empty()); data.pop_back(); ; void push(const T& x) { data.push_back(x); Containers: Stacks Dept. CS, UPC 4
Balancing symbols Balancing symbols: check for syntax errors when expressions have opening/closing symbols, e.g., () [] { Correct: [(){()[()]()] Incorrect: [(){( Algorithm (linear): read all chars until end of file. For each char, do the following: If the char is opening, push it onto the stack. If the char is closing and stack is empty error, otherwise pop a symbol from the stack and check they match. If not error. At the end of the file, check the stack is empty. Exercise: implement and try the above examples. Containers: Stacks Dept. CS, UPC 5
Evaluation of postfix expressions This is an infix expression. What s his value? 42 or 968? 8 * 3 10 2 * 4 It depends on the operator precedence. For scientific calculators, * has precedence over. Postfix (reverse Polish notation) has no ambiguity: 8 3 * 10 2 4 * Postfix expressions can be evaluated using a stack: each time an operand is read, it is pushed on the stack each time an operator is read, the two top values are popped and operated. The result is push onto the stack Containers: Stacks Dept. CS, UPC 6
Evaluation of postfix expressions: example 6 5 2 3 8 * 3 * 3 2 5 6 5 5 6 8 5 5 6 40 5 6 45 6 3 45 6 48 6 288 push(6) push(5) push(2) push(3) push(8) * push(3) * Containers: Stacks Dept. CS, UPC 7
From infix to postfix a b * c ( d * e f ) * g a b c * d e * f g * Algorithm: When an operand is read, write it to the output. If we read a right parenthesis, pop the stack writing symbols until we encounter the left parenthesis. For any other symbol (, *, (), pop entries and write them until we find an entry with lower priority. After popping, push the symbol onto the stack. Exception: ( can only be removed when finding a ). When the end of the input is reached, all symbols in the stack are popped and written onto the output. Containers: Stacks Dept. CS, UPC 8
From infix to postfix a b * c ( d * e f ) * g Output a a a b Containers: Stacks Dept. CS, UPC 9
From infix to postfix a b * c ( d * e f ) * g * a b * a b c a b c * ( a b c * Containers: Stacks Dept. CS, UPC 10
From infix to postfix a b * c ( d * e f ) * g ( * ( a b c * d a b c * d * ( ( a b c * d e a b c * d e * Containers: Stacks Dept. CS, UPC 11
From infix to postfix a b * c ( d * e f ) * g ( a b c * d e * f a b c * d e * f * a b c * d e * f * a b c * d e * f g Containers: Stacks Dept. CS, UPC 12
From infix to postfix a b * c ( d * e f ) * g a b c * d e * f g * Complexity: O(n) Suggested exercise: Add substraction (same priority as addition) and division (same priority as multiplication). Containers: Stacks Dept. CS, UPC 13
The Stack ADT with pointers head top A B C push(x) head top X A B C head (empty stack) Containers: Stacks Dept. CS, UPC 14
The Stack ADT with pointers template <typename Type> class Stack { private: // The internal cell to represent a node struct Node { Type elem; // Data Node* next; // pointer to the next element ; ; Node* head; // Pointer to the top of the stack int n; // Number of elements Containers: Stacks Dept. CS, UPC 15
The Stack ADT with pointers public: int size() const { return n; bool empty() const { return size() == 0; // or also head == nullptr void push(const Type& x) { head = new Node{x, head; n; void pop() { assert(not empty()); Node* old = head; head = head->next; delete old; --n; // Returns a copy Type top() const { assert(not empty()); return head->elem; // Returns a reference Type& top() { assert(not empty()); return head->elem; // Returns a const reference const Type& top() const { assert(not empty()); return head->elem; Containers: Stacks Dept. CS, UPC 16
The Stack ADT with pointers: usage Stack<Person> S; // Empty stack Person p( MyName, myage); S.push(p); Person q1 = S.top(); // Makes a copy Person& q2 = S.top(); // Ref to the top const Person& q3 = S.top(); // Const ref to the top q1.name = newname ; // Only local copy modified q2.name = newname ; // Top of the stack modified q3.name = newname ; // Illegal (q3 is const) q2 = q1; // Illegal: references cannot be modified Containers: Stacks Dept. CS, UPC 17
The Stack ADT with pointers private: // Recursive copy of the elements. // Exercise: design an iterative version. Node* copy(node* p) { if (p) return new Node{p->elem, copy(p->next); else return nullptr; // Recursive deallocation of the elements void free(node* p) { if (p) { free(p->next); delete p; Containers: Stacks Dept. CS, UPC 18
The Stack ADT with pointers public: // Default constructor (empty stack) Stack() : head(nullptr), n(0) { // Copy constructor Stack(const Stack& s) : head(copy(s.head)), n(s.n) { // Assignment constructor Stack& operator= (const Stack& s) { if (&s!= this) { // Make a new copy only if different free(head); head = copy(s.head); n = s.n; return *this; // Must return a ref to the object // Destructor ~Stack() { free(head); Containers: Stacks Dept. CS, UPC 19
Assertions vs. error handling Assertions: Runtime checks of properties (e.g., invariants, pre-/post-conditions). Useful to detect internal errors. They should always hold in a bug-free program. They should give meaningful error messages to the programmers. Error handling: Detect improper use of the program (e.g., incorrect input data). The program should not halt unexpectedly. They should give meaningful error messages to the users. Containers: Stacks Dept. CS, UPC 20
Assertions vs. error handling assert (x >= 0); double y = sqrt(x); assert (i >= 0 and i < A.size()); int v = A[i]; assert (p!= nullptr); int n = p->number; string id; cin >> id; if (isdigit(name[0])) { cerr << Invalid identifier << endl; return false; Containers: Stacks Dept. CS, UPC 21