Math Number tricks

92. Multiply Strings

Medium

You are given two non-negative integers, num1 and num2, written as strings of decimal digits. Return their product, written the same way.

The numbers can be far longer than any built-in integer type holds. Work on the digits yourself: do not turn a whole string into a number, and do not use a big-number type such as BigInteger, BigInt or Python's int of the whole string.

The answer must not start with a zero, unless the product is zero, which is written as "0". Answers are shown in double quotes.

Example 1

Input: num1 = "308", num2 = "27"

Output: "8316"

Explanation: 308 × 27 = 8316.

Example 2

Input: num1 = "0", num2 = "98765"

Output: "0"

Explanation: The product is zero, which is written as "0", not as a run of zeros.

Example 3

Input: num1 = "99999999999999999999" num2 = "99999999999999999999"

Output: "9999999999999999999800000000000000000001"

Explanation: Each number has 20 digits, more than a 64-bit integer holds. Their product has 40 digits.

Check your understanding

Work out the answer for this input before you write any code.

num1 = "125", num2 = "40"

Constraints

1 ≤ num1.length, num2.length ≤ 2000
num1 and num2 hold only the digits 0 to 9
Neither num1 nor num2 starts with a zero, except the number 0 itself

Clarifying questions

What you would ask an interviewer before writing any code.