Write an algorithm using Stack Data structure to test if a mathematical expression

has balanced and matching parentheses. This algorithm will accept an expression character

by character as input along with a stack. The expression can use one of the following

parenthesis : $[,],(,),\{,\}$

The input expressions can also have variables and operators, which must be ignored from

processing. For example, an expression $[$a $+\{$c $*$ d$\}($e$+$d$)]$ has matching parenthesis leaving

out the variables and operators. That is$,$ the parenthesis sequence $[\{\}()],$ ignoring the

variables and operators, is a valid sequence. Further, the expression $[$a $+($c $*$ d $\}\{$e$+$d$)]$ do not

have matching parenthesis as in the corresponding parenthesis sequence $[(\}\{)],$ the curly

braces does not match.