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Add Two Signed Decimal Character Arrays

ByteDanceSoftware Engineer · Technical Screen
EasySoftware EngineerTechnical ScreenCoding & Algorithms

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This problem tests string manipulation, handling of sign logic, and carrying operations for large integer arithmetic without utilizing large integer libraries.

Problem Statement

Implement a function that adds two signed decimal integers represented as strings. You cannot convert the strings to full integer types (e.g., int(), long()) because the inputs might exceed the capacity of standard primitive types. You must handle signs (+ or -) and potential leading zeros.

Function Signature

def add_signed_strings(num1: str, num2: str) -> str:

Constraints

  • The strings consist of digits, and optionally a single leading + or - sign.
  • The length of the strings can be up to 10,000 characters.
  • The result should be a string representation of the sum.

Examples

Example 1:

  • Input: num1 = "-123", num2 = "45"
  • Output: "-78"

Example 2:

  • Input: num1 = "999", num2 = "1"
  • Output: "1000"

Edge Cases

  • Zero handling ("0", "-0", "+0").
  • Mismatched signs (subtraction logic vs. addition logic).
  • Large carries resulting in a longer string.

Hints

Hint 1

Determine the sign of the result first, and if the signs are different, decide whether to perform addition or subtraction based on the absolute values.

Hint 2

For subtraction, always subtract the smaller absolute value from the larger one and prepend the appropriate sign.

Hint 3

Use a two-pointer approach starting from the end of the strings and carry over the remainder to the next position.

Follow-up questions

  • How would your approach change if you were asked to perform multiplication instead of addition?
  • What modifications are needed to handle decimals/floating-point numbers provided as strings?
  • How can you optimize the space complexity if you are allowed to modify one of the input strings (if they were lists of characters)?