Prefix notation (also known as polish notation) is an alternative to the more familier infix notation.
In infix notation, operators(add,multiply,etc) are written between their operands(number, variables, or sub-expression).
- In prefix notation, operators are written before their operands Some examples follow of expression in infix notation and their equivalents in prefix notation. In this example the operator is + and its operands are 1 and 2:
Infix expression: 1 + 2
Prefix expression: + 1 2
Value: 3
In this example, the sub-expression + 1 2 is the first operand of the + operator
Infix expression: (1+2) * 3
Prefix expression: * + 1 2 3
Value: 9
Sometimes there are multiple sub-expressions:
Infix expression: ((1 + 2) *3)-4
Prefix expression: - * + 1 2 3 4
value: 5
Sub-expressions can be nested arbitrarily deeply:
Infix expression: 6 + (( 4 - (2 + 3 ) ) * 8 )
Prefix expression: + 6 * - 4 + 2 3 8
value: -2
So far we have only considered numbers as our operands for the prefix expression. For this test, we would like your function to also support variables withing the expression.
For example:
expression: + 10 x
variables {"x":3}
value: 13
Implement a function CalculateExpression(expression,variables) that takes as inputs:
- expression, a string containing an expression in prefix notiation that might contain variables
- variables, a JSON objeect containing the values for each variable in the expression and returns:
- the result of the expression for the given values
- throw exception the expression is invalid or if the expression does not have any valid result
The syntax supports 4 operators: +, -, *, and /. These are the standard artihmetic operators.
- Note: / denotes integer division, that is / 7 2 evaluates to 3, not 3.5.
The only accepted numeric operands aer positive integers in base 10 (e.g 1,22, 85 are valid, -1,0x43, 0 are not valid).
A valid variable name is any sequence of characters that doesn't include whitespaces(spaces,tabs, newlines, etc).
Expression: + 1 5
variables: {}
result: 6
Expression: + 1 2 3
variables: {}
result: 6
Expression: + 1
variables: {}
result: exception
Expression: 9
variables: {}
result: 9
Expression: * + 1 2 3
variables: {}
result: 9
Although, negative numeric operands are invalid in expression, intermediate and final results may be negative
Expression: + 6 * - 4 + 2 3 8
variables: {}
result: -2
Operators and operrands must be seperated by one or more white spaces:
Expression: -+1 5 3
variables: {}
result: exception
Expression: +1 2
variables: {}
result: 3
Expression containing variables:
Expression: * + 2 x y
variables: {"x":1,"y":3}
result: 9
