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.

解决方案如下：

Remember how we do multiplication?

Start from right to left, perform multiplication on every pair of digits, and add them together. Let's draw the process! From the following draft, we can immediately conclude:

 `num1[i] * num2[j]` will be placed at indices `[i + j`, `i + j + 1]` 

代码如下：

public class MultiplyStrings {public static void main(String[] args) {System.out.println(multiply("123","456"));}public static String multiply(String num1,String num2){int m = num1.length(),n = num2.length();int[] pos = new int[m+n];for(int i=m-1;i>=0;i--){for(int j=n-1;j>=0;j--){int mul = (num1.charAt(i)-'0')*(num2.charAt(j)-'0');int p1 = i+j , p2 = i+j+1;int sum = mul +pos[p2];//注意加上上一步的结果System.out.println(pos[p1]+"__"+pos[p2]);pos[p1] += sum/10;pos[p2] = sum%10;}}StringBuilder sb = new StringBuilder();for(int p : pos){if(!(sb.length() == 0 && p==0))sb.append(p);}return sb.length() == 0 ? "0" : sb.toString();}}