Can somebody hack my brute-forces solution ?

Revision en4, by SPyofgame, 2021-12-05 21:34:19

### The Statement

Here in this problem 1107D. Compression

Given an integer $n$ and a binary table $A[n][n]$

We are asked to find maximum $x$ that exist a binary table $B\left[\left \lceil \frac{n}{x} \right \rceil \right]\left[\left \lceil \frac{n}{x} \right \rceil \right]$

That this equation is satisfied $B\left[\left \lceil \frac{i}{x} \right \rceil \right]\left[\left \lceil \frac{j}{x} \right \rceil \right]$ $= A[i][j]\ \forall\ 1 \leq i, j \leq n$ (sorry but I dont know why the latex is broken like that)

### The solution

So my approach is to check for all $v | n$ if there is exist such table.

Let call a square $(lx, ly)$ is a subtable $A[lx..rx][ly..ry]$ for

$\begin{cases} 1 \leq lx \leq rx \leq n\\ 1 \leq ly \leq ry \leq n\\ rx - lx + 1 = v\\ ry - ly + 1 = v\\ v\ |\ rx\\ v\ |\ ry\\ \end{cases}$

So there are $\frac{n}{v} \times \frac{n}{v}$ such subtables

Binary Table $B[][]$ will exist if and only if $A[x][y] = A[u][v]$ for all subtables $(lx, ly)$ and $lx \leq x, u \leq rx$ and $ly \leq y, v \leq ry$

My solution is just check for all $x\ |\ n$ from $n$ downto $1$.

If $x$ is satisfied then just simply output it.

The checking can simply be done using partial sum matrix.

The complexity will be $\underset{x|n}{\Large \Sigma} \left(\frac{n}{x} \right)^2 = n^2 \times \underset{x|n}{\Large \Sigma} \left(\frac{1}{x}\right)^2 = n^2 \times \frac{\pi^2}{6} = O(n^2)$

This give us a simple solution that run in $373 ms$.

https://codeforces.com/contest/1107/submission/138112085

### My Hacking Question

For brute-force version, I check it by comparing each position one by one.

So the complexity seems to be at most $O(d(n) \times n^2)$ and atleast $O(n^2)$.

It should fail but it didnt, it passed in $1216 ms$

https://codeforces.com/contest/1107/submission/138111659

Can someone construct a test hack for it, since I failed to find such test that it will fail.

#### History

Revisions

Rev. Lang. By When Δ Comment
en4 SPyofgame 2021-12-05 21:34:19 2
en3 SPyofgame 2021-12-05 19:09:42 23
en2 SPyofgame 2021-12-05 19:08:41 368
en1 SPyofgame 2021-12-05 19:06:50 4652 Initial revision (published)