Plus-Minus Calculator With Brackets

Hard

The string expr is a valid arithmetic expression made of non-negative integers, the signs + and -, round brackets and spaces. Evaluate it and return the result. A minus may be unary: -7 and -(1 + 2) are allowed. A plus is never unary, and two signs never stand next to each other. Spaces may appear anywhere between numbers and signs. Do not use anything built in that evaluates a string as an expression (such as eval): parse the string yourself.

Example 1

expr="12 - (4 + 3) + 1" → 6

The bracket gives 7, then 12 - 7 + 1 = 6.

Example 2

expr="-(8 - (2 + 9))" → 3

Inside it is 8 - 11 = -3, and the minus in front of the bracket flips it to 3.

Example 3

expr=" 40 " → 40

Constraints

1 ≤ len(expr) ≤ 10⁶
expr consists of digits, +, -, (, ) and spaces
expr is a valid expression
Every number, every bracket value and the result fit in a signed 32-bit integer

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Topics

Stack Recursion Math String

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Input

expr="12 - (4 + 3) + 1"

Expected

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