$2.$ Convert the following infix expression to postfix notation using a stack:

$\backslash [$

$\backslash$mathrm$\{$A$\}+\backslash$mathrm$\{$B$\}*\backslash$mathrm$\{$C$\}*\backslash$mathrm$\{$D$\}-\backslash$mathrm$\{$E$\}$

$\backslash ]$

CSCI $2100$B

Note:

$(1).$ Show how the stack evolves as you process each token $($operator or operand$)$ in the infix expression.

$(2).$ Use the following operator precedence and associativity rules:

$-$ Operator precedence: $^($highest$),$ followed by $*$ and $/,$ followed by $+$ and $-.$

$-$ Associativity: $^$ is right$-$to$-$left; $*,/,+,$ and $-$ are left$-$to$-$right.

$(3).$ Assume all operands $($A$,$ B$,$ C$,$ etc.$)$ are single letters representing variables.

$($Hint: Operands will be output directly. Operators will be temporarily placed in the stack until a operator of equal or lower precedence is encountered, at which point they will be popped from the stack.$)$

The final result is