## 11029 - Leading and Trailing

All about problems in Volume 110. If there is a thread about your problem, please use it. If not, create one with its number in the subject.

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trulo17
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### 11029 - Leading and Trailing

how to get the first tree digits? Can this be done in O(logn), i mean, is it realted with modular exponentiation?
kp
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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
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and how about the three last digits ???
kp
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A^B mod 1000
trulo17
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kp: thx very much for helping.
jan holmes:for last 3 digits you can use logarithmic exponentiation.
helloneo
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Can anybody check this out..?
I'm getting WA..

Code: Select all

CUT AFTER AC
Last edited by helloneo on Sat May 13, 2006 8:31 pm, edited 1 time in total.
kp
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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
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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
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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
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I'm using this method,but I got WA... Please Help :

Code: Select all

AC...ed :D
Thx...
Last edited by jan_holmes on Sun May 14, 2006 7:34 am, edited 3 times in total.
kp
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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)

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search(a,b)
jan_holmes
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Thx kp,but I still got WA... Please give me critical I/O... thx...
kp
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2100000056 67333

982...016

983...016

...

see my third post at this topic
helloneo
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jan_holmes wrote:I'm using this method,but I got WA... Please Help :

Code: Select all

...
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.. ~
Last edited by helloneo on Sun May 14, 2006 7:50 am, edited 1 time in total.
mamun
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