void calculateProbabilities$($const std::vector& train, double probabilities$[$MAX$\_$CLASS$][$MAX$\_$COLS $-1][3],$ double classPriors$[$MAX$\_$CLASS$],$ double lambda$)\{$

int classCounts$[$MAX$\_$CLASS$]=\{0\}$;

for $($int c $=0$; c $<$ MAX$\_$CLASS; $++$c$)\{$

for $($int i $=0$; i $<$ MAX$\_$COLS $-1$; $++$i$)\{$

for $($int v $=0$; v $<3$; $++$v$)\{$

probabilities$[$c$][$i$][$v$]=$ lambda;

$\}$

$\}$

$\}$

for $($const auto& record : train$)\{$

classCounts$[$record$.$classLabel$]++$;

for $($size$\_$t i $=0$; i $<$ record.attributes.size$()$; $++$i$)\{$

if $($record$.$attributes$[$i$]!=$ MISSING$)\{$

probabilities$[$record$.$classLabel$][$i$][$record$.$attributes$[$i$]]++$;

$\}$

$\}$

$\}$

for $($int c $=0$; c $<$ MAX$\_$CLASS; $++$c$)\{$

classPriors$[$c$]=$ static$\_$cast$($classCounts$[$c$])/$ train.size$()$;

for $($int i $=0$; i $<$ MAX$\_$COLS $-1$; $++$i$)\{$

double total $=$ classCounts$[$c$]+3*$ lambda;

for $($int v $=0$; v $<3$; $++$v$)\{$

probabilities$[$c$][$i$][$v$]/=$ total;

$\}$

$\}$

$\}$

$\}$

ClassLabel naiveBayesPredict$($const Record& record, const double probabilities$[$MAX$\_$CLASS$][$MAX$\_$COLS $-1][3],$ const double classPriors$[$MAX$\_$CLASS$])\{$

double logProbs$[$MAX$\_$CLASS$]=\{$ std::log$($classPriors$[$DEMOCRAT$]),$ std::log$($classPriors$[$REPUBLICAN$])\}$;

for $($int c $=0$; c $<$ MAX$\_$CLASS; $++$c$)\{$

for $($size$\_$t i $=0$; i $<$ record.attributes.size$()$; $++$i$)\{$

if $($record$.$attributes$[$i$]!=$ MISSING$)\{$

logProbs$[$c$]+=$ std::log$($probabilities$[$c$][$i$][$record$.$attributes$[$i$]])$;

$\}$

$\}$

$\}$

if $($logProbs$[$DEMOCRAT$]>$ logProbs$[$REPUBLICAN$])\{$

return DEMOCRAT;

$\}$

else $\{$

return REPUBLICAN;

$\}$

$\}$

void evaluateModel$($const std::vector& data, const double probabilities$[$MAX$\_$CLASS$][$MAX$\_$COLS $-1][3],$ const double classPriors$[$MAX$\_$CLASS$],$ double& accuracy$)\{$

int correct $=0$;

for $($const auto& record : data$)\{$

if $($naiveBayesPredict$($record$,$ probabilities, classPriors$)==$ record.classLabel$)\{$

correct$++$;

$\}$

$\}$

accuracy $=$ static$\_$cast$($correct$)/$ data.size$()$;

$\}$

void crossValidate$($const std::vector& records, double lambda, double& averageAccuracy, double& stdDev, std::vector& foldAccuracies$)\{$

size$\_$t foldSize $=$ records.size$()/10$;

foldAccuracies.clear$()$;

for $($int i $=0$; i $<10$; $++$i$)\{$

std::vector train, test;

for $($size$\_$t j $=0$; j $<$ records.size$()$; $++$j$)\{$

if $($j $>=$ i $*$ foldSize && j $<($i $+1)*$ foldSize$)\{$

test.push$\_$back$($records$[$j$])$;

$\}$

else $\{$

train.push$\_$back$($records$[$j$])$;

$\}$

$\}$

double probabilities$[$MAX$\_$CLASS$][$MAX$\_$COLS $-1][3]=\{\}$;

double classPriors$[$MAX$\_$CLASS$]=\{\}$;

calculateProbabilities$($train$,$ probabilities, classPriors, lambda$)$;

double foldAccuracy;

evaluateModel$($test$,$ probabilities, classPriors, foldAccuracy$)$;

foldAccuracies.push$\_$back$($foldAccuracy$)$;

$\}$

double sum $=0\mathrm{.}0$;

for $($size$\_$t i $=0$; i $<$ foldAccuracies.size$()$; $++$i$)\{$

sum $+=$ foldAccuracies$[$i$]$;

$\}$

double mean $=$ sum $/$ foldAccuracies.size$()$;

double sqSum $=0\mathrm{.}0$;

for $($size$\_$t i $=0$; i $<$ foldAccuracies.size$()$; $++$i$)\{$

sqSum $+=($foldAccuracies$[$i$]-$ mean$)*($foldAccuracies$[$i$]-$ mean$)$;

$\}$

stdDev $=$ std::sqrt$($sqSum $/$ foldAccuracies.size$())$;

averageAccuracy $=$ mean;

$\}$

Optimize this C$++$ code for Naive Bayes Classification of republicans and democrats dataset. Can you make it more understandable and clear, and to be connected? In this particular code is implemented naive bayes with Laplas and logarithm for handling the unexpected errors and deviations