$2$ Editor Support

Solve and provide an implementation for Exercise $4\mathrm{.}19$ from the DSA$-$C$++$ Shaffer book.

A common problem for compilers and text editors is to determine if the parentheses or brackets in a string are balanced and properly nested. For example, the string $(([])[()])()$ contains properly

nested pairs of parentheses and brackets, but the string $)()($ and $[(])$ does not.

$3$

$1.$

$2.$

Give an algorithm that returns true if a string containing the characters$()[]$ is properly nested and balanced, and false otherwise.

Implement the function bool balanced$($std::string&$).$

Assume the string only contains the characters $(),$ we can of course use the same algorithm as in part $1.$ Can we do better? In this part, the best algorithm uses O$(1)$ memory and O$($n$)$ time.

Implement the function bool balanced unique$($std::string&$).$