### Problem Statement

You must write a class Calculate, with a method calc, which takes a String expression, where expression is a mathematical expression. You should calculate the value of the expression, using the standard order of operations:
• Always evaluate expressions in parentheses first.
• Exponentiation next.
• Multiplication and division next.
• Addition and subtraction last.
Operators with the same precedence should be evaluated from left to right. So 2^3^2 = (2^3)^2 = 64, and 3-2+1 = (3-2)+1 = 2

Thus, if expression = "1+2*3^(1+1)-2", we first calculate (1+1), and get "1+2*3^2-2". Next we apply exponentiation and get "1+2*9-2". Then multiplication and division gives us "1+18-2". Last, addition and subtraction, left to right, gives 17.

Furthermore, you will be given a String[] variables each of whose elements represents a variable which may be used in expression. Each element of variables will be formatted as "<variable> <value>", where <variable> is a sequence of 1 or more letters ('a'-'z' and 'A'-'Z'), and <value> is an integer. For example, if variables = {"x 1", "y 11"}, and expression = "x*y+3*x", we substitute the values for the variables to get 1*11+3*1 = 14.

The expression will conform to the following grammar:
• <expression> ::= (<expression>) | <expression><op><expression> | <val>
• <op>::= '+'|'-'|'/'|'*'|'^'
• <val>::= a sequence of 1 or more digits or a <variable> from variables

### Definition

 Class: Calculate Method: calc Parameters: String, String[] Returns: int Method signature: int calc(String expression, String[] variables) (be sure your method is public)

### Notes

-All of the intermediate and final results of both division and exponentiation will be integers between -2^31 and 2^31 - 1, inclusive. (see constraints)
-Variable names are case sensitive.

### Constraints

-expression will include only the characters '0' to '9', '+', '-', '*', '/', '^', '(', and ')' and letters ('a'-'z' and 'A'-'Z').
-expression will be well-formed, conforming to the grammar in the problem statement.
-The final result, and all intermediate results will be integers in the range -2^31 to 2^31-1, inclusive. This includes all numbers and variables, so "0*10000000000" is not allowed, nor is "0*a", {"a 10000000000"}.
-expression will not result in division by 0 or 0^x, for x less than or equal to 0.
-variables will have between 0 and 50 elements, inclusive.
-Each element of variables will be formatted as "<variable> <value>", where <variable> is a sequence of 1 or more letters ('a'-'z' and 'A'-'Z'), and <value> is an integer between -2^32 and 2^32-1, inclusive (possibly with leading zeros).
-No two elements of variables will have the same <variable>.
-Each variable in expression will be found in variables.
-expression will contain between 1 and 50 characters, inclusive.
-Each element of variables will contain between 3 and 50 characters, inclusive.

### Examples

0)

 `"x*y+3*x"` `{"x 1", "y 11"}`
`Returns: 14`
 The example from the problem statement.
1)

 `"x^p*2^(2^p)/t^p^t+xx*n^v"` `{"x 53", "xx 32", "p 3","t 2","n -1","v -21"}`
`Returns: 595476`
2)

 `"t^003^t"` `{"t 00000000000002","a 999999999"}`
`Returns: 64`
 Substituting, we get 2^3^2 = 8^2 = 64.
3)

 `"(8*(Aa^(aA-1230))-aA^2+((00)))*(0-1)"` `{"aA 01234","Aa 98"}`
`Returns: -736371772`
4)

 `"0-2+t^30+t^30+1"` `{"t 2"}`
`Returns: 2147483647`
 The largest possible result.
5)

 `"1+(0-t)^31-1"` `{"t 2"}`
`Returns: -2147483648`
 The smallest possible result.
6)

 `"((5-x+1^x))"` `{"x -100"}`
`Returns: 106`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=1019

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=4703&pm=1019

lars2520

String Parsing