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The constraint is what makes this annoying.
Simulate grade-school multiplication digit by digit, storing intermediate results in an array where each position accumulates the product of corresponding digits. After processing all digit pairs, handle carries to produce the final string, ensuring no leading zeros except for the result '0'.
Pro tip: Mention that this approach is O(m*n) time and O(m+n) space, and note that it's the same algorithm used in arbitrary-precision arithmetic libraries, showing you understand the trade-offs and real-world applications.
Confirm that inputs are non-negative, may be very large, and that the result should be a string. Discuss edge cases like '0' and '1'.
Use an integer array of size m+n to store intermediate results. Simulate multiplication from least significant digit to most significant.
Iterate over each digit of the first number and second number, compute the product, and add it to the appropriate position in the array, handling carries.
After all multiplications, process carries from right to left, then build the result string by skipping leading zeros.
Walk through examples like '123' * '456' and edge cases like '0' * '0' to ensure correctness.
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