# A virus gone viral 2

In a laboratory housed in kotebe micro-organisms were arranged in a $$n\times n$$ grid for studying purpose. By accident one of the laboratory technicians spills an infectious virus on some of the organism.This virus has the ability to infect the organism located immediately (east, west, north and south) of its already infected organism in $$3$$ microseconds.

To mitigate the rapid spread of this deadly virus some of the grid indices were left empty. How many microseconds does it take for all the organisms to be infected for the $$19\times 19$$ grid shown below. were $$0$$ means infected and $$1$$ means normal and - means empty.

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 1,-,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 1,1,-,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 1,1,1,-,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 1,0,1,1,-,1,1,1,1,1,1,1,1,1,1,1,1,1,1 1,1,1,1,1,-,1,1,1,1,1,1,1,1,1,1,1,1,1 

Details and Assumptions

-Explicit example, If the virus was spilled on a $$3\times 3$$ grid.

$\begin{pmatrix} 1 & 1 & 1 \\ 1 & - & 1 \\ 0 & 1 & - \end{pmatrix}\overset { 3\mu s }{ \longrightarrow } \begin{pmatrix} 1 & 1 & 1 \\ 0 & - & 1 \\ 0 & 0 & - \end{pmatrix}\overset { 3\mu s }{ \longrightarrow } \begin{pmatrix} 0 & 1 & 1 \\ 0 & - & 1 \\ 0 & 0 & - \end{pmatrix}\cdots \begin{pmatrix} 0 & 0 & 0 \\ 0 & - & 0 \\ 0 & 0 & - \end{pmatrix}$

For a total of 15 microseconds.

The organism will quickly start infecting other organisms after being infected.

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