multiplyingTwoStrings.java

public class Solution {
    public String multiply(String num1, String num2) {
        int n1 = num1.length(), n2 = num2.length();
        int[] products = new int[n1 + n2];
        for (int i = n1 - 1; i >= 0; i--) {
            for (int j = n2 - 1; j >= 0; j--) {
                int d1 = num1.charAt(i) - '0';
                int d2 = num2.charAt(j) - '0';
                products[i + j + 1] += d1 * d2;
            }
        }
        int carry = 0;
        for (int i = products.length - 1; i >= 0; i--) {
            int tmp = (products[i] + carry) % 10;
            carry = (products[i] + carry) / 10;
            products[i] = tmp;
        }
        StringBuilder sb = new StringBuilder();
        for (int num : products) sb.append(num);
        while (sb.length() != 0 && sb.charAt(0) == '0') sb.deleteCharAt(0);
        return sb.length() == 0 ? "0" : sb.toString();
    }
}

/*
(e.g. 99 * 99 cannot be five digit)
1. The product of two numbers cannot exceed the sum of the two lengths. (e.g. 99 * 99 cannot be five digit)

2.
int d1 = num1.charAt(i) - '0';
int d2 = num2.charAt(j) - '0';
products[i + j + 1] += d1 * d2;
*/