43. Multiply Strings

Given two non-negative integers num1 and num2 represented as strings, return the product of num1 and num2.
Note:
The length of both num1 and num2 is < 110.
Both num1 and num2 contains only digits 0-9.
Both num1 and num2 does not contain any leading zero.
You must not use any built-in BigInteger library or convert the inputs to integer directly.

Solution：模拟乘法计算，对应位结果加到结果数组pos

Time Complexity: O(m * n) Space Complexity: O(m + n)

屏幕快照 2017-08-31 下午9.18.03.png

Solution Code：

class Solution {
    public String multiply(String num1, String num2) {
        int m = num1.length(), n = num2.length();
        int[] pos = new int[m + n];

        for(int j = n - 1; j >= 0; j--) {
            for(int i = m - 1; i >= 0; i--) {
                int mul = (num1.charAt(i) - '0') * (num2.charAt(j) - '0'); 
                int p1 = i + j, p2 = i + j + 1;
                int sum = mul + pos[p2];

                pos[p1] += sum / 10;
                pos[p2] = (sum) % 10;
            }
        }  

        // prepare the result
        StringBuilder sb = new StringBuilder();
        for(int p : pos) 
            if(!(sb.length() == 0 && p == 0)) sb.append(p);
        return sb.length() == 0 ? "0" : sb.toString();
    }
}