1. Stack Applications Lecture 29 Thu, Apr 5, 2007 2/23/2019

2. Infix Expressions
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
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3. Postfix Expressions
A postfix expression with one (binary) operator is written in the order: left-operand, right-operand, operator.
For example, to add 3 and 4, we write
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4. Prefix Expressions
A prefix expression with one binary operator is written in the order: operator, left-operand, right-operand.
For example, to add 3 and 4, we write
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5. Postfix Expression Evaluation
In expression with several operators, each operand is a subexpression
Example: *
Left operand of * is 3 4 +
Right operand of * is 5 6 +
Parentheses are never needed!
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6. Postfix Expression Evaluation
Rewrite the infix expression
((1 + 2)*3 – 4/(5 + 6 – 7*8))*9
as a postfix expression.
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7. Postfix Expression Evaluation
Rewrite the infix expression
((1 + 2)*3 – 4/(5 + 6 – 7*8))*9
as a postfix expression.
1 2 +
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8. Postfix Expression Evaluation
Rewrite the infix expression
((1 + 2)*3 – 4/(5 + 6 – 7*8))*9
as a postfix expression. *
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9. Postfix Expression Evaluation
Rewrite the infix expression
((1 + 2)*3 – 4/(5 + 6 – 7*8))*9
as a postfix expression.
* 4
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10. Postfix Expression Evaluation
Rewrite the infix expression
((1 + 2)*3 – 4/(5 + 6 – 7*8))*9
as a postfix expression. *
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11. Postfix Expression Evaluation
Rewrite the infix expression
((1 + 2)*3 – 4/(5 + 6 – 7*8))*9
as a postfix expression.
* *
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12. Postfix Expression Evaluation
Rewrite the infix expression
((1 + 2)*3 – 4/(5 + 6 – 7*8))*9
as a postfix expression.
* * –
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13. Postfix Expression Evaluation
Rewrite the infix expression
((1 + 2)*3 – 4/(5 + 6 – 7*8))*9
as a postfix expression.
* * – /
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14. Postfix Expression Evaluation
Rewrite the infix expression
((1 + 2)*3 – 4/(5 + 6 – 7*8))*9
as a postfix expression.
* * – / –
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15. Postfix Expression Evaluation
Rewrite the infix expression
((1 + 2)*3 – 4/(5 + 6 – 7*8))*9
as a postfix expression.
* * – / – 9 *
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16. Postfix Expression Evaluation
Begin with an empty stack.
Each number or operator is a token.
Process the tokens in the postfix expression from left to right.
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17. Postfix Expression Evaluation
If the token is a number,
Push it onto the stack.
If the token is a binary operator,
Pop two numbers off the stack.
Combine them under the operator.
Push the result onto the stack.
The single remaining value on the stack is the value of the expression.
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18. Postfix Expression Evaluation
Evaluate *
Read 3: Push 3
Read 4: Push 4
Read +: Pop 4, pop 3, compute = 7, push 7
Read 5: Push 5
Read 6: Push 6
Read +: Pop 6, pop 5, compute = 11, push 11
Read *: Pop 11, pop 7, compute 7 * 11 = 77, push 77
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19. PostfixEvaluator.cpp
PostfixEvaluator.cpp
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20. 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.
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21. Handling Function Calls
When a function returns, the program
Pops (and discards) the values of the local variables.
Pops the return address (and stores it in the IP register).
Branches to the return address.
Pops the parameters.
The stack has now been returned to its previous state.
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22. The Restaurant Triangle Puzzle
While waiting for your order in a restaurant, you pick up and play the Triangle Puzzle.
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23. The Restaurant Triangle Puzzle
There are fifteen holes.
One hole is empty.
The other 14 holes have pegs in them.
You make moves by jumping, as in checkers.
One peg jumps an adjacent peg, landing in an empty hole.
Remove the jumped peg.
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24. The Restaurant Triangle Puzzle
The goal is to remove all but one peg.
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25. The Restaurant Triangle Puzzle
There are 18 possible moves, each in either of 2 directions.
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26. The Restaurant Triangle Puzzle
Six moves in each direction along this diagonal.
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27. The Restaurant Triangle Puzzle
Six moves in each direction along this diagonal.
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28. The Restaurant Triangle Puzzle
Six moves in each direction along this diagonal.
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29. The Restaurant Triangle Puzzle
Six moves in each direction along this diagonal.
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30. The Restaurant Triangle Puzzle
Six moves in each direction horizontally.
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31. The Restaurant Triangle Puzzle
Six moves in each direction horizontally.
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32. The Restaurant Triangle Puzzle
List the 36 possible moves in a particular order.
The program will systematically try the moves until it finds a valid move.
Then it will
Make that move.
Push that move onto the stack.
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33. The Restaurant Triangle Puzzle
If no move if possible, then it will
Pop the last move off the stack.
Continue through the list of possible moves until it finds a legal move.
Make that move and continue as before.
When a single peg remains, the contents of the stack is a winning sequence of moves.
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34. The Restaurant Triangle Puzzle
TrianglePuzzle.cpp
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35. Solving a Maze
A computer program can solve a maze by using trial and error.
Systematically try each open path.
When a dead-end is reached, back up to the most recent alternative path.
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36. Solving a Maze Push the starting square onto the stack.
For the square on top of the stack, attempt to move to an adjacent square.
Test the adjacent squares in the following order. Up
Down
Left
Right
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37. Solving a Maze When a move is possible,
Push the new square onto the stack.
When no move is possible (dead-end),
Repeatedly pop squares off the stack until an untried alternate move is available.
When the final square is reached, the stack contains the path (in reverse order) from start to finish.
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