To write mathematical equations we used 3 types of parenthesis: (), [], {} and these were always hierarchical like this: {[()]}, always in this order. And to go even further we would reuse the curly braces like this { { { [ ( ) ] } } }. It's like Matryoshka doll from Russia. :)
An example would be: {(4 + 1) * { 5 * [( 5 ^ 2 - 4 ^ 2 ) * 2 ]}} / 2. (where 5^2 means 5 to the power of 2).
We need an application that would take a mathematical equation as string for input and return a boolean response representing the validity of the parenthesis ordering.
Some valid equations for which the application would return true:
- 5 * 5
- (4 + 1) * 2
- (4 + 1) * [(2 - 4) / (2 + 2)]
- {(4 + 1) * { 5 * [( 5 ^ 2 - 4 ^ 2 ) * 2 ]}} / 2
Some invalid equations for which the application would return false:
- (4 + 1) * 2)
- [4 + 1] * 2
- 4 * ([2 - 4] / [2 + 2])
- 4 * {(2 - 4) / (2 + 2)}
- ([4 * [1 + 2] - 1])