11029 - Leading and Trailing

trulo17 · Post by **trulo17** » Sat May 13, 2006 5:55 pm

how to get the first tree digits? Can this be done in O(logn), i mean, is it realted with modular exponentiation?

kp · Post by kp » Sat May 13, 2006 6:19 pm

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).

jan_holmes · Post by **jan_holmes** » Sat May 13, 2006 6:26 pm

and how about the three last digits ???

kp · Post by kp » Sat May 13, 2006 7:03 pm

A^B mod 1000

trulo17 · Post by **trulo17** » Sat May 13, 2006 7:05 pm

kp: thx very much for helping.
jan holmes:for last 3 digits you can use logarithmic exponentiation.

helloneo · Post by **helloneo** » Sat May 13, 2006 7:05 pm

Can anybody check this out..?
I'm getting WA..
Please help .. ㅠ_ㅠ

Code: Select all

CUT AFTER AC

kp · Post by kp » Sat May 13, 2006 7:25 pm

Try to replace your part:

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  temp1 = temp1 - temp2 + 4.0; 
  temp3 = pow(10.0, temp1); 
  sprintf(buf1, "%.0Lf", temp3);

with this:

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  temp1 = temp1 - temp2; 
  temp3 = pow(10.0, temp1); 
  while (temp3<1000.0) temp3 *= 10.0;
  int tmp = floor(temp3);
  while (tmp>999) tmp /= 10;
  sprintf(buf1, "%d", tmp);

lonelyone · Post by **lonelyone** » Sat May 13, 2006 7:36 pm

I don't think so, all of yours are right.
I think the bug of helloneo's code is in finding last three digits.
Did you know logarithm of finding n^k algorithm?
If you have no idea, you could reference it in Intro. to Algorithm.

Similar idea in UVa374, if you solved this problem.
You could use same thought to solve logarithm of it.

Hope this helps.

Lonely ^^

helloneo · Post by **helloneo** » Sat May 13, 2006 8:39 pm

kp and lonelyone ..
Thanks for help.. I got AC..

Actually I already solved the problem 374 ..
but didn't notice this is about big mod .. ^_^;

jan_holmes · Post by **jan_holmes** » Sat May 13, 2006 9:26 pm

I'm using this method,but I got WA... Please Help :

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AC...ed :D

Thx...

kp · Post by kp » Sat May 13, 2006 10:25 pm

It's because of overflow

Replace

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return (pangkat(search(a,b/2))%1000*a%1000)%1000;

with

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return (pangkat(search(a,b/2))%1000*(a%1000))%1000;

or

in the main program use

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search(a%1000,b)

instead of

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search(a,b)

jan_holmes · Post by **jan_holmes** » Sat May 13, 2006 10:40 pm

Thx kp,but I still got WA... Please give me critical I/O... thx...

kp · Post by kp » Sat May 13, 2006 10:49 pm

2100000056 67333

answer should be

982...016

your program get
983...016

...

see my third post at this topic

helloneo · Post by **helloneo** » Sun May 14, 2006 5:29 am

jan_holmes wrote:I'm using this method,but I got WA... Please Help :
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...
Thx...

Hello..~
I got WA with that code too..
Don't know why it doesn't work.. possibly precision error..
Replace that part with what kp suggested.. ~

mamun · Post by **mamun** » Sun May 14, 2006 6:50 am

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temp1 = temp1-temp2+4.0;

You can increase this constant 4.0 to say, 5.0.