import numpy as np

from collections import Counter

from sklearn import datasets, model$\_$selection

# No other libraries will be imported

# load the Iris Dataset, which contains $150$ samples.

# each sample has $4$ features.

# the dataset contains $3$ classes of $50$ instances each, where each class refers to a type of iris plant.

iris $=$ datasets.load$\_$iris$()$

X $=$ np$.$array$($iris$.$data$)$ # features, numeric attributes. $[$Sepal length, Sepal Width, Petal length, Petal width$]$

Y $=$ np$.$array$($iris$.$target$)$ # labels: class$-0,$ class$-1,$ class$-2$

X$\_$train, X$\_$test, Y$\_$train, Y$\_$test $=$ model$\_$selection.train$\_$test$\_$split$($X$,$ Y$,$ test$\_$size$=0\mathrm{.}25,$ random$\_$state$=0)$

print$("$Train Shape:", X$\_$train.shape$)$

print$("$Train Shape:", X$\_$test.shape$)$

$3.$ Calculate Information Gain for each attribute $($numeric$),$ and show the feature that should be used first when build a decision tree.

step$-1$: find the best cutpoint for each attribute. $($find value to split the data$)$

step$-2$: calculate the information gain for each attribute. $($decide the order of attributes when build DT$)$

#$--------------------$ Some helper functions $------------------------------$

# calculate Entropy for a given distribution H$($X$).$

def entropy$($probabilities: list$)->$ float:

return sum$([-$p $*$ np$.$log$2($p$)$ for p in probabilities if p$>0])$

# given a list of labels, return the probability for each class P$($Y$).$

def class$\_$probabilities$($labels: list$)->$ list:

total$\_$count $=$ len$($labels$)$

return $[$label$\_$count $/$ total$\_$count for label$\_$count in Counter$($labels$).$values$()]$

# calculate the Entropy H$($Y$)$ for a given list of labels.

def data$\_$entropy$($labels: list$)->$ float:

return entropy$($class$\_$probabilities$($labels$))$

# split data into two sub$-$groups $[$group$1,$ goup$2]$ based on attribute $[$feature$\_$idx$]$ and value $[$feature$\_$val$]$

# if sample$[$feature$\_$idx$]<$ feature$\_$val:

# group$1<-$ sample

# else:

# group$2<-$ sample

def split$\_$data$($data: np$.$array, feature$\_$idx: int, feature$\_$val: float$)->$ tuple:

mask$\_$below$\_$threshold $=$ data$[$:$,$ feature$\_$idx$]<$ feature$\_$val

group$1=$ data$[$mask$\_$below$\_$threshold$]$

group$2=$ data$[$~mask$\_$below$\_$threshold$]$

return group$1,$ group$2$

# calculate the entropy for current partition. H$($Y$|$X$=$feature$\_$val$)$

def partition$\_$entropy$($g$1\_$labels: list, g$2\_$labels:list$)->$ float:

total$\_$count $=$ len$($g$1\_$labels$)+$ len$($g$2\_$labels$)$

#weighted combination of conditional entropy in both group$1$ and group$2.$

return data$\_$entropy$($g$1\_$labels$)*($len$($g$1\_$labels$)/$total$\_$count$)+$ data$\_$entropy$($g$2\_$labels$)*($len$($g$2\_$labels$)/$total$\_$count$)$

#$-----------------------------------------------------------------------------------------$

#$----------------------------$ Examples to use the Helper functions $-----------------------$

# calculate the H$($Y$)$ for the train and test data:

print$($data$\_$entropy$($Y$\_$train$))$

print$($data$\_$entropy$($Y$\_$test$))$

## to split the data based on feature$\_$idx and feature$\_$val:

train$\_$data $=$ np$.$concatenate$(($X$\_$train, np$.$reshape$($Y$\_$train, $(-1,1))),$ axis$=1)$ # concatenate $[$X$\_$train, Y$\_$train$]$

print$($train$\_$data.shape$)$

# split the data into two subgroups

g$1,$ g$2=$ split$\_$data$($train$\_$data, feature$\_$idx$=1,$ feature$\_$val$=3)$

print$($g$1.$shape$)$

print$($g$2.$shape$)$

# calculate the weighted entropy for the current split.

print$($partition$\_$entropy$($g$1[$:$,-1],$ g$2[$:$,-1]))$

#$-----------------------------------------------------------------------------------------$

#$--------------------------------$ Your implementation $------------------------------------$

# Initialize variables to store the best cutpoint and information gain for each attribute

#$-----------------------------------------------------------------------------------------$

#$-----------------------------------$ Printing $--------------------------------------------$

#print the calculated cutpoint $[$feature$\_$val$]$ and information gain for each attribute.

# print the feature should be used first when build decision tree.

Please help me complete this code. The dataset is part of the question. Iris dataset is already embeded in python