43-字符串相乘

public String multiply(String num1, String num2) {
    int[] jiShu = new int[num1.length() + num2.length()];   //基数数组
    int[] jinWei = new int[num1.length() + num2.length()];  //进位数组
    for (int i = 0; i < num1.length(); i++) {
        for (int j = 0; j < num2.length(); j++) {
            int bit1 = num1.charAt(i) - '0';
            int bit2 = num2.charAt(j) - '0';
            int add = bit1 * bit2 + jiShu[i + j + 1];
            jiShu[i + j + 1] = add % 10;                //关键步骤
            jinWei[i + j] = add / 10 + jinWei[i + j];   //关键步骤
        }
    }
    //将基数和进位从低位向高位相加得出最终结果
    int[] res = new int[jinWei.length];
    for (int i = jinWei.length - 1; i >= 0; i--) {
        int num = jiShu[i] + jinWei[i] + res[i];
        res[i] = num % 10;
        if (i - 1 < 0) break;
        res[i - 1] += num / 10;
    }
    //转换成字符串，注意开头为0和全0情况
    StringBuilder sb = new StringBuilder();
    boolean flag = false;   //遇到开头不为0时才能插入
    for (int i = 0; i < res.length; i++) {
        if (res[i] != 0) flag = true;
        if (flag) sb.append(res[i]);
    }
    return "".equals(sb.toString()) ? "0" : sb.toString();
}