Expression assessment

Question

I run an expression evaluation program like. My problem is that I cannot figure out how to handle operation priorities. I used recursion to find the innermost pair of parentheses and, when I found, resolve the expression inside them, for example:

Evaluate("2 + (3 * 5)")

will repeat the call this way:

Evaluate("3 * 5")

now, since there are no brackets, it calculates the result and calls itself at another time:

Evaluate("2 + 15")

Well, the return value is 17, as expected. But if I call Evaluate("2 + 3 * 5"), the result will be as follows:

Evaluate("2 + 3 * 5")
Evaluate("5 * 5")

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Answer 1

, . , + *, * aaaa * bbbb aaaa * bbbb. , +.

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Answer 2

, , , Antlr .net.

http://www.codeproject.com/KB/recipes/sota_expression_evaluator.aspx

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. '+' '*'

additiveExpression: multiplicativeExpression '+' multiplicativeExpression
multiplicativeExpression: number '*' number

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Answer 3

-, , : http://en.wikipedia.org/wiki/Polish_notation#Computer_programming. .

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, . "2 + 3 * 5":

2 + 3 * 5
b = 3 * 5
    -convert b-
b = * 3 5
2 + b
    -convert expression-
+ 2 b
    -expand b-
+ 2 * 3 5

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Answer 4

. , +, . , , .

2 + 3 * 5 2 + (3 * 5).