Appleby Contest '19 P3 - A Recursion Problem

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Points: 5 (partial)
Time limit: 2.0s
Memory limit: 128M

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Problem type

There are many ways to represent arithmetic expressions.

We commonly use infix notation where operations are put in between values (i.e. 1+2 \times 3=7), but another less well-known method is prefix notation. This is where operations are put before values. For example, if we want to add two numbers we would write + x y instead of x + y. Furthermore, brackets are used to enforce order of evaluation.

The formal definition of prefix notation we will be using is as any one of the following options:

  • x, where x is an integer
  • (+ x y), where x and y are valid prefix notation expressions. The result of this expression is x+y.

Your objective today is to evaluate prefix notation expressions that only involve addition.

Input Specification

The first and only line of input contains a valid prefix notation expression. You can expect the expression to only consist of the following characters: 0123456789()+ (and the space: )

Output Specification

The value of that expression.

Input Constraints

Any integer x in the given expression will satisfy the following inequality: -10^4 \le x \le 10^4.

1 \le |s| \le 10^5

|s| denotes the length of the prefix notation expression.

Sample Input

(+ 1 (+ (+ (+ 3 4) -2) 5))

Sample Output

11

Sample Explanation

Here is the sample input being simplified:

  • (+ 1 (+ (+ (+ 3 4) -2) 5))
  • (+ 1 (+ (+ 7 -2) 5))
  • (+ 1 (+ 5 5))
  • (+ 1 10)
  • (11)
  • 11

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