Stack Applications. Lecture 27 Sections Robb T. Koether. Hampden-Sydney College. Wed, Mar 29, 2017

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1 Stack Applications Lecture 27 Sections Robb T. Koether Hampden-Sydney College Wed, Mar 29, 2017 Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

2 1 Function Calls 2 Infix, Postfix, and Prefix Notation 3 Infix Expression Evaluation 4 Postfix Expressions 5 Assignment Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

3 Outline 1 Function Calls 2 Infix, Postfix, and Prefix Notation 3 Infix Expression Evaluation 4 Postfix Expressions 5 Assignment Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

4 Handling Function Calls When a function is called, the program Pushes the values of the parameters. Pushes the address of the next instruction to which the function should return later). Allocates space on the stack for the local variables. Branches to the first line in the function. Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

5 Handling Function Calls The Stack Other Stuff Begin with the current stack Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

6 Handling Function Calls The Stack Other Stuff Function Parameters Push the function parameters Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

7 Handling Function Calls The Stack Other Stuff Function Parameters Return Address Push the return address Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

8 Handling Function Calls The Stack Other Stuff Function Parameters Return Address Local Variables Push the local variables Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

9 Handling Function Calls When a function returns, the program Pops the values of the local variables. Pops the return address and stores it in the IP register. Pops the parameters. The stack has now been returned to its previous state. Execution continues with the instruction in the IP register. Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

10 Handling Function Calls The Stack Other Stuff Function Parameters Return Address Pop the local variables Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

11 Handling Function Calls The Stack Other Stuff Function Parameters Pop the return address Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

12 Handling Function Calls The Stack Other Stuff Pop the function parameters Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

13 Outline 1 Function Calls 2 Infix, Postfix, and Prefix Notation 3 Infix Expression Evaluation 4 Postfix Expressions 5 Assignment Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

14 Infix Notation An infix expression is an arithmetic expression in which the binary operators are written in between the operands. For example, to add 3 and 4, we write Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

15 Postfix Expressions In a postfix expression, the operator is written after the operands. For example, to add 3 and 4, we write The infix expression would be written as in postfix notation. Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

16 Prefix Expressions In a prefix expression, the operator is written before the operands. For example, to add 3 and 4, we write The infix expression would be written as in prefix notation. Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

17 Outline 1 Function Calls 2 Infix, Postfix, and Prefix Notation 3 Infix Expression Evaluation 4 Postfix Expressions 5 Assignment Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

18 Fully Parenthesized Infix Expressions With infix expressions, the operations are not necessarily performed from left to right. Infix expressions may require parentheses to specify the order of operation. Precedence and associativity rules allow us to omit some of the parentheses. A fully parenthesized expression assumes no precedence or associativity rules. In a fully parenthesized expression, there is a pair of parentheses for every operator. Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

19 Examples The expression would be fully parenthesized as )). The expression /5 6 would be fully parenthesized as 2 3) + 4/5)) 6). Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

20 Infix Expression Evaluation We may use a pair of stacks to evaluate a fully parenthesized infix expression. The expression contains four types of token: Left parenthesis Right parenthesis ) Number, e.g., 123 Operator +,,, / Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

21 Infix Expression Evaluation To evaluate the expression we need a stack of numbers and a stack of operators. Read the tokens from left to right and process them as follows: Token Left parenthesis Number Operator Right Parenthesis Action No action Push the number onto the number stack Push the operator onto the operator stack 1. Pop two numbers off the number stack 2. Pop one operator off the operator stack 3. Perform the operation on the numbers 4. Push the result onto the number stack Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

22 Example Use the algorithm to evaluate the expression 2 5) + 6/3)) 8) Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

23 Example Robb T. Koether Hampden-Sydney College) Stack caption Applications Wed, Mar 29, / 27 Token Number Stack Operator Stack Begin with an empty stack

24 Robb T. Koether Hampden-Sydney College) Stack caption Applications Wed, Mar 29, / 27 Example Token Number Stack Operator Stack 2 5) + 6/3)) 8)

25 Robb T. Koether Hampden-Sydney College) Stack caption Applications Wed, Mar 29, / 27 Example Token Number Stack Operator Stack 2 5) + 6/3)) 8)

26 Robb T. Koether Hampden-Sydney College) Stack caption Applications Wed, Mar 29, / 27 Example Token Number Stack Operator Stack 2 5) + 6/3)) 8)

27 Robb T. Koether Hampden-Sydney College) Stack caption Applications Wed, Mar 29, / 27 Example Token Number Stack Operator Stack ) + 6/3)) 8)

28 Robb T. Koether Hampden-Sydney College) Stack caption Applications Wed, Mar 29, / 27 Example Token Number Stack Operator Stack ) + 6/3)) 8)

29 Robb T. Koether Hampden-Sydney College) Stack caption Applications Wed, Mar 29, / 27 Example Token Number Stack Operator Stack ) + 6/3)) 8)

30 Robb T. Koether Hampden-Sydney College) Stack caption Applications Wed, Mar 29, / 27 Example Token Number Stack Operator Stack ) ) + 6/3)) 8)

31 Robb T. Koether Hampden-Sydney College) Stack caption Applications Wed, Mar 29, / 27 Example Token Number Stack Operator Stack ) ) + 6/3)) 8)

32 Robb T. Koether Hampden-Sydney College) Stack caption Applications Wed, Mar 29, / 27 Example Token Number Stack Operator Stack ) ) + 6/3)) 8)

33 Robb T. Koether Hampden-Sydney College) Stack caption Applications Wed, Mar 29, / 27 Example Token Number Stack Operator Stack ) ) + 6/3)) 8)

34 Robb T. Koether Hampden-Sydney College) Stack caption Applications Wed, Mar 29, / 27 Example Token Number Stack Operator Stack ) / / 2 5) + 6/3)) 8)

35 Robb T. Koether Hampden-Sydney College) Stack caption Applications Wed, Mar 29, / 27 Example Token Number Stack Operator Stack ) / / / 2 5) + 6/3)) 8)

36 Robb T. Koether Hampden-Sydney College) Stack caption Applications Wed, Mar 29, / 27 Example Token Number Stack Operator Stack ) / / / ) ) + 6/3)) 8)

37 Robb T. Koether Hampden-Sydney College) Stack caption Applications Wed, Mar 29, / 27 Example Token Number Stack Operator Stack ) / / / ) ) ) + 6/3)) 8)

38 Robb T. Koether Hampden-Sydney College) Stack caption Applications Wed, Mar 29, / 27 Example Token Number Stack Operator Stack ) / / / ) ) ) + 6/3)) 8)

39 Robb T. Koether Hampden-Sydney College) Stack caption Applications Wed, Mar 29, / 27 Example Token Number Stack Operator Stack ) / / / ) ) ) + 6/3)) 8)

40 Robb T. Koether Hampden-Sydney College) Stack caption Applications Wed, Mar 29, / 27 Example Token Number Stack Operator Stack ) / / / ) ) ) 4 2 5) + 6/3)) 8)

41 Infix Expression Evaluation Run the program InfixEvalFullParen.cpp. Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

42 Outline 1 Function Calls 2 Infix, Postfix, and Prefix Notation 3 Infix Expression Evaluation 4 Postfix Expressions 5 Assignment Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

43 Postfix Expression Evaluation Example Postfix Expressions) Expression: Left operand of is Right operand of is In postfix expressions, parentheses are never needed! Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

44 Postfix Expression Evaluation To evaluate a postfix expression we need a stack of numbers. Read the tokens from left to right and process them as follows: Token Number Operator Action Push the number onto the number stack 1. Pop two numbers off the number stack 2. Pop one operator off the operator stack 3. Perform the operation on the numbers 4. Push the result onto the number stack Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

45 Postfix Expression Evaluation Example Postfix Expressions) The fully parenthesized infix expression 2 5) + 6/3)) 8) can be written as /3 8 As a postfix expression, it is / + 8 Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

46 Example Token 2 2 Number Stack / + 8 Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

47 Example Token Number Stack / + 8 Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

48 Example Token Number Stack / + 8 Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

49 Example Token Number Stack / + 8 Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

50 Example Token Number Stack / + 8 Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

51 Example Token Number Stack / / + 8 Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

52 Example Token Number Stack / / + 8 Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

53 Example Token Number Stack / / + 8 Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

54 Example Token Number Stack / / + 8 Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

55 Postfix Expression Evaluation Run the program PostfixEvaluator.cpp. Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

56 Outline 1 Function Calls 2 Infix, Postfix, and Prefix Notation 3 Infix Expression Evaluation 4 Postfix Expressions 5 Assignment Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

57 Assignment Assignment Read Sections Robb T. Koether Hampden-Sydney College) Stack Applications Wed, Mar 29, / 27

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