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Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.



You are a beetle scientist and you have to identify the species of a lot of male beetles in your research.
Currently, you can easily identify these beetles after they are fully grown up.
However, in your research, you want to identify the species of the male beetles while they are still pupae.

You had already done a one-dimensional decision tree to separate the pupae:
However, the paper got rejected because the result is not significant enough.
You decide to include more features to see if you can improve the accuracy of the decision tree.

Before you start this puzzle, it is highly recommended to finish the first one,
since we will follow the same entropy algorithm.

You will have PN pupae with their index, species, and features.

This time, instead of using only horn length as the separator,
you are given FN features and you will want to select FM features that will have the lowest entropy.
If 2 different sets of features can have the same entropy, we will choose those features with a smaller index.
The output features index should be in numerical order.

The index of features are from 1 to FN.

For example:

You have 4 pupae each with 3 features, (PN and FN)
and you need to select the 2 best features. (FM)
Pupa-0 is species 1 and has feature values 1, 1, 2
Pupa-1 is species 1 and has feature values 1, 2, 1
Pupa-2 is species 2 and has feature values 1, 2, 2
Pupa-3 is species 2 and has feature values 1, 2, 2

By selecting feature 1 and 2, we scan through both features with the method in the previous puzzle.
The best separator will be pupa-1's feature 2,
and can separate the pupae into [(0), (1, 2, 3)] with entropy 0.6887.
After that, we are not able to find any other separator to decrease the entropy.

By selecting feature 1 and 3, we get similar result as get entropy 0.6887.

By selecting feature 2 and 3, we first separate pupae into [(0), (1, 2, 3)] with pupa-1's feature 2.
And then further separate pupa-1,2,3 into [(1), (2, 3)] with pupa-2's feature 3.
The tree at the end will be [(0), [(1), (2, 3)]], with entropy 0.

Therefore, the output should be 2 and 3.

P.S. pupa index is not used in this puzzle
Line 1: An integer PN for the number of pupae
Line 2: An integer FN for the number of given features
Line 3: An integer FM for the number of features to be select
Next PN Lines: Space separated parameters in the order of
pupa index, species id, FN number of features
Line 1: Space separated parameters FM number of feature ids
2 <= PN <= 20
2 <= FN <= 8
1 <= FM <= 4
0 <= index < 20
0 <= feature value <= 100
1 <= species ID <= 4
0 1 1 1
1 2 1 2

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