Implement precise string-based decimal addition
Problem Description
Implement a function that accepts two non-empty strings, each representing a decimal number, and returns their exact sum as a string.
The implementation must adhere to the following constraints:
- No Floating-Point Arithmetic: You cannot use native floating-point types (e.g.,
float,double) or any language-provided big-number libraries. - Precision Loss Prevention: The sum must be exact, with no loss of precision.
- Input Format:
- Inputs are non-empty strings like "123.456" or "6234.42432".
- They may contain leading/trailing zeros and decimal points.
- They will not contain scientific notation.
- Total number of digits (before and after the decimal) can be very large, up to 10^5 digits.
- Output Requirements:
- Describe your approach for aligning fractional parts.
- Explain how carries are propagated, especially across the decimal point.
- Detail the normalization process for the output string (e.g., removing unnecessary leading/trailing zeros, but preserving a fractional zero if it's the only digit after the decimal, like "123.0").
- State the time and space complexity of your solution.
- Provide test cases covering edge scenarios such as:
- Different fractional lengths.
- One operand lacking a fractional part (e.g., "123" + "0.45").
- All-zero values (e.g., "0.00" + "0").
- Very large inputs (up to 10^5 digits).
AI interview prep
Core dilemma
Managing arbitrary precision decimal arithmetic using only string manipulation, specifically handling alignment, carry propagation across the decimal point, and robust output normalization for potentially very large numbers.
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Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Implement precise string-based decimal addition
Problem Description
Implement a function that accepts two non-empty strings, each representing a decimal number, and returns their exact sum as a string.
The implementation must adhere to the following constraints:
- No Floating-Point Arithmetic: You cannot use native floating-point types (e.g.,
float,double) or any language-provided big-number libraries. - Precision Loss Prevention: The sum must be exact, with no loss of precision.
- Input Format:
- Inputs are non-empty strings like "123.456" or "6234.42432".
- They may contain leading/trailing zeros and decimal points.
- They will not contain scientific notation.
- Total number of digits (before and after the decimal) can be very large, up to 10^5 digits.
- Output Requirements:
- Describe your approach for aligning fractional parts.
- Explain how carries are propagated, especially across the decimal point.
- Detail the normalization process for the output string (e.g., removing unnecessary leading/trailing zeros, but preserving a fractional zero if it's the only digit after the decimal, like "123.0").
- State the time and space complexity of your solution.
- Provide test cases covering edge scenarios such as:
- Different fractional lengths.
- One operand lacking a fractional part (e.g., "123" + "0.45").
- All-zero values (e.g., "0.00" + "0").
- Very large inputs (up to 10^5 digits).