将非常大的二进制数字表示形式转换为十进制表示形式的最快方法是什么？

Question

I've got very big number stored in binary representation and I need to output it in decimal representation:

struct BigInteger {
    int *parts; // one part stores 12 bits of number, range: 0 to 0xfff
    int parts_n;
};

void convertToDecString( BigInteger *in, std::string &out );

I can't find any approach, that would do it in linear time.

For demostration you can chose any order for parts. I've got it ordered in way, that [0] is lowest value, and [n-1] is the highest value.

Answer 1

I am afraid it cannot be done in linear time, because every read bit affects all digits of the decimal representation. The longer the digit, the longer every new read bit takes.