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**The unorganized person’s data structure**

Stacks The unorganized person’s data structure stacks

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**Stack characteristics**

Entries are ordered in terms of access -- both insertion and removal take place at same spot (top of stack) Specialized type of container class; defining characteristic is insertion/removal order LIFO = last in, first out; entries are removed in reverse order of insertion stacks

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**Stack operations Push -- insert item on stack**

Pop -- remove item from stack Peek -- examine, but don’t remove item stacks

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Stack operations Important to know if stack is empty -- attempt to remove an item from an empty stack is an underflow error Depending on implementation, may be necessary to check if stack is full -- attempt to add item to a full stack is an overflow error stacks

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**Implementation of Stack ADT**

Stacks can be array based (static or dynamic) or linked list based Invariant for static array implementation: The number of items stored in the stack is found in member variable used Items are stored in member variable data, a static array with the stack bottom at data[0] and the stack top at data[used - 1] stacks

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**Stack class -- static array version**

template <class Item> class Stack { public: enum {CAPACITY = 64}; Stack ( ); // default constructor Item pop ( ); // removes top Item Item peek ( ) const; // reveals top Item . . . stacks

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Stack ADT continued void push (const Item & entry); // adds Item to stack size_t size ( ) const {return used;} bool is_empty ( ) const {return used == 0;} private: Item data[CAPACITY]; // the stack itself size_t used; // # of items stored in stack }; stacks

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**Stack function implementations: constructor**

// Postcondition: empty stack is created template <class Item> Stack<Item>::Stack( ) { used = 0; } stacks

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**Pop function // Precondition: stack is not empty**

// Postcondition: top item is removed template <class Item> Item Stack<Item>::pop ( ) { assert (!is_empty( )); used--; return data[used]; } stacks

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**Peek function // Precondition: stack is not empty**

// Postcondition: top item is revealed template <class Item> Item Stack<Item>::peek ( ) const { assert (!is_empty( )); return data[used - 1]; } stacks

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**Push function // Precondition: stack is not full**

// Postcondition: an item is inserted on stack template <class Item> void Stack<Item>::push(const Item& entry) { assert (size() < CAPACITY); data[used] = entry; used++; } stacks

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**Stack application examples**

Compilers use stacks for a variety of purposes: syntax analysis: matching brackets, parentheses, etc. activation records: structures associated with functions, keeping track of local variables, return address, etc. stacks

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**Example application: balanced parentheses**

Pseudocode algorithm: scan string left to right if ‘(‘ is encountered, push on stack if ‘)’ is encountered, and stack is not empty, pop one ‘(‘ -- if stack is empty, expression is unbalanced if stack is empty when entire string has been scanned and analyzed, expression is balanced stacks

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**A program to test for balanced parentheses**

int main( ) { String user_input; // uses String data type defined in ch. 4 - based on array cout << "Type a string with some parentheses and no white space:\n"; cin >> user_input; if (balanced_parentheses(user_input)) cout << "Those parentheses are balanced.\n"; else cout << "Those parentheses are not balanced.\n"; cout << "That ends this balancing act.\n"; return EXIT_SUCCESS; } stacks

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**balanced_parentheses function**

bool balanced_parentheses(const String& expression) // Library facilities used: assert.h, stack1.h, stdlib.h, mystring.h. { // Meaningful names for constants const char LEFT_PARENTHESIS = '('; const char RIGHT_PARENTHESIS = ')'; Stack<char> store; // Stack to store the left parentheses as they occur size_t i; // An index into the String char next; // The next character from the String char discard; // A char popped off the stack and thrown away bool failed = false; // Becomes true if a needed parenthesis is not found . . . stacks

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**balanced_parentheses continued**

for (i = 0; !failed && (i < expression.length( )); i++) { next = expression[i]; if (next == LEFT_PARENTHESIS) if (store.size( ) < store.CAPACITY); store.push(next); } else if ((next == RIGHT_PARENTHESIS) && (!store.is_empty( ))) discard = store.pop( ); else if ((next == RIGHT_PARENTHESIS) && (store.is_empty( ))) failed = true; return (store.is_empty( ) && !failed); stacks

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**Stack ADT as linked list**

Can make use of toolkit functions to simplify task Stack can grow & shrink as needed to accommodate data -- no fixed size Invariant: stack items are stored in a linked list member variable top is head pointer to list stacks

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**Class definition for new Stack**

template <class Item> class Stack { public: Stack( ) { top = NULL; } Stack(const Stack& source); ~Stack( ) { list_clear(top); } ... stacks

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**Stack definition continued**

void push(const Item& entry); Item pop( ); void operator =(const Stack& source); size_t size( ) const {return list_length(top);} bool is_empty( ) const {return top == NULL;} Item peek( ) const; private: Node<Item> *top; // Points to top of stack }; stacks

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**Push function template <class Item>**

void Stack<Item>::push(const Item& entry) { list_head_insert(top, entry); } stacks

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**Pop function template <class Item>**

Item Stack<Item>::pop( ) { assert(!is_empty( )); Item answer = top->data; list_head_remove(top); return answer; } stacks

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**Peek function template <class Item>**

Item Stack<Item>::peek( ) const { assert(!is_empty( )); return top->data; } stacks

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**Copy constructor template <class Item>**

Stack<Item>::Stack(const Stack<Item>& source) { list_copy(source.top, top); } stacks

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**Assignment operator template <class Item>**

void Stack<Item>::operator =(const Stack<Item>& source) { if (source.top== top) // Handle self-assignment return; list_clear(top); list_copy(source.top, top); } stacks

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**A stack-based calculator**

Input to program is a fully-parenthesized expression -- examples: ((5.3 * 1.2) / 3.1) (4 - 3) Two stacks are used -- one for operators, one for operands Right parenthesis is signal to pop the stacks and evaluate the expression stacks

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**Algorithm for expression evaluation**

Evaluate leftmost, innermost expression; continue evaluating, left to right Read each part of expression Push numbers on operand stack, operators on operator stack When right parenthesis is encountered, pop the stacks, evaluate, and push result on operand stack stacks

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**Code for stack calculator**

int main( ) { double answer; cout << "Type a fully parenthesized arithmetic expression:" << endl; answer = read_and_evaluate(cin); cout << "That evaluates to " << answer << endl; return EXIT_SUCCESS; } stacks

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**Code for stack calculator**

double read_and_evaluate(istream& ins) { const char DECIMAL = '.'; const char RIGHT_PARENTHESIS = ')'; Stack<double> numbers; Stack<char> operations; double number; char symbol; ... stacks

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**Code for stack calculator**

while (!ins.eof( ) && ins.peek( ) != '\n') { if (isdigit(ins.peek( )) || (ins.peek( ) == DECIMAL)) ins >> number; numbers.push(number); } … stacks

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**Code for stack calculator**

else if (strchr("+-*/", ins.peek( )) != NULL) { ins >> symbol; operations.push(symbol); } stacks

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**Code for stack calculator**

else if (ins.peek( ) == RIGHT_PARENTHESIS) { cin.ignore( ); evaluate_stack_tops(numbers, operations); } else } // end of while loop return numbers.pop( ); stacks

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**Code for stack calculator**

void evaluate_stack_tops(Stack<double>& numbers, Stack<char>& operations) { double operand1, operand2; operand2 = numbers.pop( ); operand1 = numbers.pop( ); ... stacks

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**Code for stack calculator**

switch (operations.pop( )) { case '+': numbers.push(operand1 + operand2); break; case '-': numbers.push(operand1 - operand2); ... stacks

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**Code for stack calculator**

4/12/2017 Code for stack calculator case '*': numbers.push(operand1 * operand2); break; case '/': numbers.push(operand1 / operand2); } // end switch statement } // end function stacks stacks

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