43. Multiply Strings

Given two non-negative integers num1 and num2 represented as strings, return the product of num1 and num2.

Note:

1. The length of both num1 and num2 is < 110.
2. Both num1 and num2 contains only digits 0-9.
3. Both num1 and num2 does not contain any leading zero.
4. You must not use any built-in BigInteger library or convert the inputs to integer directly.

Solution:

We can split this process to:

1. multiply num1.charAt(i) and num2.charAt(j). Put the result in product[i + j + 1].

2. calculate carry and complete the multiplication.

3. output



Code:

public class Solution {
    public String multiply(String num1, String num2) {
        int n1 = num1.length();
        int n2 = num2.length();
        int[] product = new int[n1 + n2];
        for (int i = n1 - 1; i >= 0; i--) {
            for (int j = n2 - 1; j >= 0; j--) {
                product[i + j + 1] += (num1.charAt(i) - '0') * (num2.charAt(j) - '0');
            }
        }
        int carry = 0;
        for (int i = n1 + n2 - 1; i >= 0; i--) {
            int sum = (product[i] + carry) % 10;
            carry = (product[i] + carry) / 10;
            product[i] = sum;
        }
        StringBuilder sb = new StringBuilder();
        for (int num : product) {
            sb.append(num);
        }
        while (sb.length() != 0 && sb.charAt(0) == '0') {
            sb.deleteCharAt(0);
        }
        return sb.length() == 0 ? "0" : sb.toString();
    }
}