43

class Solution {
    public String multiply(String num1, String num2) {
        //用num1的每一位去乘num2的每一位
        int i = num1.length() - 1;
        String res = "";
        int carry = 0;
        while(i >= 0){
            StringBuilder temp = new StringBuilder("");
            //再每次循环的时候在后面填上对应的0
            for(int k = 0; k < num1.length() - 1 - i; k++){
                temp.append("0");
            }
            int n1 = num1.charAt(i) - '0';
            carry = 0;
            for(int j = num2.length() - 1; j >= 0; j--){
                int n2 = num2.charAt(j) - '0';
                int sum = n1 * n2 + carry;
                carry = sum / 10;
                sum = sum % 10;
                temp.append(sum);
            }
            if(carry > 0){
                temp.append(carry);
            }
            res = addSum(temp.reverse().toString(), res);
            i--;
        }
        //去掉多余的前缀0
        while(res.length() > 1 && res.charAt(0) == '0'){
            res = res.substring(1);
        }
        return res;

    }
//下面的方法引用了415题的代码  https://www.cnblogs.com/zhaijiayu/p/11525566.html
    private String addSum(String num1, String num2){
        int i = num1.length() - 1;
        int j = num2.length() - 1;
        int carry  = 0;
        StringBuilder res = new StringBuilder("");
        while(i >= 0 || j >= 0){
            int n1 = i >= 0 ? num1.charAt(i) - '0' : 0;
            int n2 = j >= 0 ? num2.charAt(j) - '0' : 0;
            int sum = n1 + n2 + carry;
            carry = sum / 10;
            sum = sum % 10;
            res.append(sum);
            i--;
            j--;
        }
        if(1 == carry){
            res.append("1");
        }

        return res.reverse().toString();
    }
}