10633 - Rare Easy Problem

[windows2k]

I thought it is an easy problem.
But get WA all the time.
What's wrong with my input/output
input

Code: Select all

911
99999
4110
7774


output

Code: Select all

1012
111109 111110
4566
8637


Or someone could give some tricky input/output, thx

[rotoZOOM]

Check trailing spaces in output.
You should use unsigned long long instead of signed long long.

Input:
1000000000000000000

Output:
1111111111111111111

[prince56k]

i don't think that u should use unsigned long long. i used only long long.
if n=9 output 10
and if u use 10*n/9 then u will face overflow problem if n is 18 digit
Hope, it will help u

[Eduard]

Maybe 10^18 is not so big,but i use big numbers and got AC at one's.
I don't know how in C++ may be long long is bigger than 10^18 but in Pascal i don't think that INT64 is bigger than 10^18.That why i use big numbers.

[PdR]

With some care no overflow will ever ocur in a 64 bit signed integer.

[mlvahe]

In Pascal INT64 type can store integers, less than 2^63-1>10^18. So you could fill free to use int64.

10*a/9 = a + a/9.
if you write this way you won't meet any overflowing.

P.S. This is realy very easy problem.

[Sajid]

How can we detemine about the multiple answer...?
(we can find out a number easily by the formula)

[shamim]

The other answers lie (+-) 10 of the number calculated using formula.

[Sajid]

hmm, I guess, I did simple mistake in the contest. I checked only previous ten number of the calculated number....
anyway, got AC now

[Larry]

Actually, there's an easier way to check if a number is capable of multiple numbers..

[Sajid]

Larry,
Can you explain the ways?

[Larry]

I'm not a good math prover, but either prove to yourself or believe that the most number of ways is 2.

Knowing this, most numbers will have only one solution. Try to find that special case where there are two.

Hope it helps without giving too much away.. =)

[soyoja]

Just I'm so curious that why maximum answers are only two.
Of course, I think it's very natural, but I want to know the reason.

[soyoja]

Here is general idea of this problem ^^

A = original number
B = Sample input

A - A/10 = B ( by problem description )
therefore , (10A - A)/10 = B, 9A = 10B, A = 10/9 * B
So we can find one answer.
And minus value is always made by ( A/10 ),
so another answer's range is - 10 ~ + 10 at original answer.
You can find that number by small range searching.

[Larry]

soyoja:

sorry, as I said, I'm not a good math prover, and it was just an intuition (that worked), so I don't know why this is the case.