# CS 136 - Lecture 18

## Applications of stacks

### Running mazes

• Keep cells on path from start on a stack. Mark cells when they're visited.

public void runMaze()
{
success = false;                 // No solution yet

current = start;                 // Initialize current to start
current.visit();

path = new StackList();          // Create new path
path.push(current);              // with start on it

while (!path.empty() && !success)
{                              // Search until success or run out of cells
current = nextUnvisited();  // Get new cell to visit

if (current != null) {      // If unvisited cell,
current.visit();         // move to it &
path.push(current);      // push it onto path
success = current.equals(finish); // Done yet?
}
else        // No neighbors to visit so back up
{           // Pop off last cell visited
current = (Position)path.pop();
if (!path.empty())      // If path non-empty take last
//  visited as new current
current = (Position)path.peek();
}
}
}

### Evaluation of arithmetic expressions

Some machines have stack based machine language instructions.

Example. PUSH, POP, ADD (pop off top two elements from stack, add them and push result back onto stack), SUB, MULT, DIV, etc.

Ex. Translate X * Y + Z * W to:

```    PUSH X
PUSH Y
MULT
PUSH Z
PUSH W
MULT
```
Trace result if X = 2, Y = 7, Z = 3, W = 4.

How do you generate this code?

Write expression in postfix form: operator after operands

E.g. 2 + 3 -> 2 3 +

Representing arithmetic expressions:

• infix notation (e.g. (2 + 3) * 4 - 5)
• (Polish) postfix notation (e.g. 2 3 + 4 * 5 -)
• (Polish) prefix notation (e.g.  - * + 2 3 4 5)
General algorithm to convert to postfix notation:
1. Write expression fully parenthesized.
2. Recursively move operator after operands, dropping parentheses when done.
E.g.

X * Y + Z * W -> (X * Y) + (Z * W) -> (X Y *) (Z W *) + -> X Y * Z W * +

Note: in Polish notation parentheses no longer needed. Corresponds to reverse Polish calculator.

Once in postfix, easy to generate code as follows:

• If operand, generate PUSH command
• If operator, generate command to do operation.
Above expression compiled as shown earlier: PUSH X, PUSH Y, MULT, ...

Straightforward to write a computer program using stacks to use these instructions (or even the original postfix expression) to calculate values of arithmetic expressions.

Interestingly, algorithm to convert expression to postfix form can either be done recursively (as above) or using a stack.

Notice all operands appear in same order as started - only operations move. Commands to transform above expression (working on it from left to right):

```    OUTPUT X
PUSH *
OUTPUT Y
POP and OUTPUT operator
PUSH +
OUTPUT Z
PUSH *
OUTPUT W
POP and OUTPUT operator
POP and OUTPUT operator
```
Other rules - "(" is always pushed onto stack, ")" causes operators to be popped and output until pop off topmost "(" on stack. )

Big question: When do you push one operator on top of another and when do you pop off topmost operator before pushing on new one?

Answer:     given in terms of precedence of operators!

### Run-time stacks on computers

All computers use a run-time stack in order to keep track of procedure, function, or method invocations.

Programs that use stacks can often be rewritten to simply use recursion (since recursion deals with an implicit stack. Hence the maze-running program can be rewritten as follows, where caller is responsible for setting success to false and current to start originally:

```public static void runMaze()
{
Position origCurrent = current;     // Save orig value
current.visit();
success = current.equals(finish);   // Are we finished?

while (current != null && !success)
{                   // Search until success or run out of cells
current = nextUnvisited();  // Find new cell to visit
if (current != null)
{
runMaze();  // Try solving maze from new current
current = origCurrent;      // reset to try again
}
}
}

```