11029 - Leading and Trailing

[jan_holmes]

AC.... Finally Thx to kp,mamun,helloneo...

[C]

Let C = A^B,

lg(C) = B*lg(A), lg - decimal logarithm lg(x) = ln(X)/ln(10).
First three digits of C are first three digits of mantissa of lg(C).

That's how I got AC (not sure about mathematical correctness).

kp: I really don't understand,why first three digits of C are first three digits of mantissa of lg(C)?? For example,
lg(123456)= 5.091512... where is 123 ???
or can someone else explain it to me ??

[mamun]

It's actually antilog of first 3 digits of mantissa of log(c).

[vinay]

Let C = A^B,

lg(C) = B*lg(A), lg - decimal logarithm lg(x) = ln(X)/ln(10).
First three digits of C are first three digits of mantissa of lg(C).

That's how I got AC (not sure about mathematical correctness).

how do u calulate mantissa in c++?

[mamun]

It's not a question of C++. It's simple maths.

Of a number, say 12.589, .589 is the mantissa. So you can calculate mantissa of a vlaue, x

mantissa(x) = x - floor(x)

You can use frexp() function in C/C++.

[little joey]

I also calculated the first three digits using <math.h> and got accepted, but I still have some doubts about precision.
How can we be sure that a 100-million digit number that starts off "123999999999999999999999999..." is not printed as "124..." without doing bigint calculus?

[vinay]

ohhhh. Sorry for the silly question

[vinay]

one last question
How to calculate this antilog?

[mamun]

If you do log calculation in base 10 ie. log10() then use pow(10,x) for antilog and if base is e ie. log(), then use exp().

[vinay]

thanks

[vinay]

I need some help for the leading part..
what is the problem with the following code snippet :

double dd=(double)k*log(mm);
char buf1[30];
sprintf(buf1,"%.Lf",exp(dd));

I have got WA

[Darko]

I did the first three with fast exponentiation, I just kept moving the decimal point so it wouldn't go into infinity. Never occured to me that I could've used logs

[C]

Please help me,I have read all posts here, but have no idea..
My code is:

Code: Select all

AC ed..

[Cho]

I also calculated the first three digits using <math.h> and got accepted, but I still have some doubts about precision.
How can we be sure that a 100-million digit number that starts off "123999999999999999999999999..." is not printed as "124..." without doing bigint calculus?

I think the 4th to 15th digit can be considered as some sort of pseudo-random number, then the probability that all these digits being 9 is exponentially small.

[vinay]

I did the first three with fast exponentiation, I just kept moving the decimal point so it wouldn't go into infinity.

For the trailing part I used the Square-and-multiply method .
How to use the same for the leading .. I really can't understand