Basic Calculator IV

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Given an expression such as expression = “e + 8 – a + 5” and an evaluation map such as {“e”: 1} (given in terms of evalvars = [“e”] and evalints = [1]), return a list of tokens representing the simplified expression, such as [“-1*a”,”14″]

- An expression alternates chunks and symbols, with a space separating each chunk and symbol.
- A chunk is either an expression in parentheses, a variable, or a non-negative integer.
- A variable is a string of lowercase letters (not including digits.) Note that variables can be multiple letters, and note that variables never have a leading coefficient or unary operator like “2x” or “-x”.

Expressions are evaluated in the usual order: brackets first, then multiplication, then addition and subtraction. For example, expression = “1 + 2 * 3” has an answer of [“7”].

The format of the output is as follows:

- For each term of free variables with non-zero coefficient, we write the free variables within a term in sorted order lexicographically. For example, we would never write a term like “b*a*c”, only “a*b*c”.
- Terms have degree equal to the number of free variables being multiplied, counting multiplicity. (For example, “a*a*b*c” has degree 4.) We write the largest degree terms of our answer first, breaking ties by lexicographic order ignoring the leading coefficient of the term.
- The leading coefficient of the term is placed directly to the left with an asterisk separating it from the variables (if they exist.) A leading coefficient of 1 is still printed.
- An example of a well formatted answer is [“-2*a*a*a”, “3*a*a*b”, “3*b*b”, “4*a”, “5*c”, “-6”]
- Terms (including constant terms) with coefficient 0 are not included. For example, an expression of “0” has an output of [].

Examples:

Input: expression = "e + 8 - a + 5", evalvars = ["e"], evalints = [1] Output: ["-1*a","14"] Input: expression = "e - 8 + temperature - pressure", evalvars = ["e", "temperature"], evalints = [1, 12] Output: ["-1*pressure","5"] Input: expression = "(e + 8) * (e - 8)", evalvars = [], evalints = [] Output: ["1*e*e","-64"] Input: expression = "7 - 7", evalvars = [], evalints = [] Output: [] Input: expression = "a * b * c + b * a * c * 4", evalvars = [], evalints = [] Output: ["5*a*b*c"] Input: expression = "((a - b) * (b - c) + (c - a)) * ((a - b) + (b - c) * (c - a))", evalvars = [], evalints = [] Output: ["-1*a*a*b*b","2*a*a*b*c","-1*a*a*c*c","1*a*b*b*b","-1*a*b*b*c","-1*a*b*c*c","1*a*c*c*c","-1*b*b*b*c","2*b*b*c*c","-1*b*c*c*c","2*a*a*b","-2*a*a*c","-2*a*b*b","2*a*c*c","1*b*b*b","-1*b*b*c","1*b*c*c","-1*c*c*c","-1*a*a","1*a*b","1*a*c","-1*b*c"]

Note:

- expression will have length in range [1, 250].
- evalvars, evalints will have equal lengths in range [0, 100].

Github: code.dennyzhang.com

Credits To: leetcode.com

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**General Thinkings:**

**Key Observations:**

**Walk Through Testdata**

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