11581 - Grid Successors

[f74956227]

I think this problem can't be a cycle...but why??? Can someone give me a proof please

[Jan]

Check the first sample..

Code: Select all

111
100
001

Its f0(g). We can find f1(g) easily.

f1(g) = f( f0(g) )

This way we can construct all.

So,

Code: Select all

f0(g) =
    111
    100
    001

f1(g) =
    001
    100
    110

f2(g) =
    110
    101
    011

f3(g) =
    010
    101
    010

f4(g) =
    000
    000
    000

f5(g) =
    000
    000
    000

...

fI(g) = f4(g). Here 'I' stands for infinity. So, 3 is the highest index for which the result is finite. So, the result is 3. Hope it helps.

[f74956227]

Thank you!! I think this problem will always convergence to the zero matrix (3x3) for every grid, but i can't prove this. Actually my AC program shows the
feature.

[priorm]

Hey all, having trouble getting WA and tried some rudimentary test cases. Formatting looks good. Any hints?

DELETED - missed the new line at the very end =/

[brianfry713]

Use class Main

[priorm]

Sorry. Edited my response - (I modify my code to conform to the java submission instructions just prior to submitting)

[brianfry713]

Print a newline char at the end of the last line.

[priorm]

ugh, thanks!

[uDebug]

Jan,
Thanks for the explanation. That really helped see things in perspective.

Also, I've uploaded input I found useful during testing / debugging on uDebug.