#include

#include

#include

#include

using namespace std;

$//$function that calculates the error

$//$A:the starting index of the subarray "points"

$//$B:the ending index of the subarray "points"

double findTheError$($const vector& Pnts$,$ int A$,$ int B$)\{$

$/*$here the vector ins a constant

so that the values of the vector cannot be changed within the function$*/$

$//$calculating the average

double sum$=0$;

for $($int i $=$ A; i $<=$ B; i$++)\{$

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

$\}$

double avg$=0$;

avg $=$ sum $/($B $-$ A $+1)$; $//$B $-$ A: difference between starting and ending

$//$ by adding $1$ we include the A itself

$//$the sum of squared differences from the average

double error $=0$;

for $($int i $=$ A; i $<=$ B; $++$i$)\{$

error $+=$ pow$($Pnts$[$i$]-$ avg, $2)$; $//$the given equation from the task that finds the error

$\}$

return error; $//$returns the error that it found

$\}$

$//$function that calculates the partition error

$//$ n: number of points

$//$ N: number of groups

double minError$($const vector& Pnts$,$ int n$,$ int N$)\{$

if $($n $==0$ && N $==0)\{//$if there are no points or groups

return $0$;

$\}$

double result $=$ INT$\_$MAX; $//$initializing the result with the largest$/$max value so thats why i included the climits library

$//$the loop goes through possible ending positions

$//$from the last group and

$//$it keeps updating the error result.

for $($int p $=$ n $-1$; p $>=0$; $--$p$)\{$

$//$ calculating the current error

double currentError$=$ minError$($Pnts$,$ p$,$ N $-1)+$ findTheError$($Pnts$,$ p$,$ n $-1)$;

$//$ update result

if $($currentError $<$ result$)\{$

result$=$ currentError;

$\}$

$\}$

return result;

$\}$

$//$a function that prints the groups

void Grps$($const vector& Pnts$,$ const vector& Groups$)\{$

int A $=0$;

for $($int i$=0$;i$>$ N;

vector Pnts $=\{1,2,3,6,8,12,13,15\}$; $//$initializing the vector with the examole's points

vector Groups $=\{2,4,2\}$; $//$Example of the groups with the best error beacause i couldntt figure out how to find the groups that have the $8\mathrm{.}66667$ error

$//$printing the groups

cout$<<$ "The groups are:" $<$