The X$-$Raly sensor is producing continuous measurements with a frequency of approximately $1800$ Hz $($the

measurement frequency isn't precise, values are read with a period from $\frac{1}{2000}$ of a second to $\frac{1}{1500}$ of a

second$).$

Whenever a density measurement is ready the following callback function is called.

void MeasureDensityReady $($int densitiy, int time$\_$us$)$;

The variable density contains the single measurement and time$\_$uS express the time difference elapsedfrom

the start of the program to time the actual measurement was taken, in microseconds.

The position sensor detects the position of the board with a frequency of approximately $500$ Hz $($the

measurement frequency isn't precise; values are read with a period from $\frac{1}{400}$ of a second to $1/600$ of a

second$).$

Whenever a position measurement is ready the following callback function is called:

void MeasurePositionReady$($int position$\_$m$,$ int time$\_$u$3)$;

The variable position$\_$mm contains the position of the board when is measured from the X$-$Ray sensor$.$

time$\_$uS express the fime difference elapsed from the start of the program to time the actual measurement

was taken, in microseconds.

An asynchrony thread should calculate a couple of values in a given length intervall of the board with

following function:

void CaleulateDensityValues $($int min$\_$pos$\_$mm$,$ int max$\_$pos$\_$mm$,$

int $*$mean$\_$density, int $*$min$\_$density, int $*$median$\_$density$)$;

This function should calculate following values in the length interval from min$\_$pos$\_$mm to max$\_$pos$\_$mm of

the board:

Mean density

Minimal density

Median of the density

Only the last $5$ seconds of the measured data are of interest. That means the calculation thread can ask

only for the last $5$ seconds of measured data.

Implement the $3$ function concerning the efficiency of calculations and optimization of the memory usage.

The implementation of the main function where these $3$ functions are called is not asked, pretending this

function is already existing.

Try to comment the most complex part of the $3$ functions. Take into account time and memory complexity. Try to reduce it at maxium.