exercise2_2.py

import numpy 
import matplotlib.pyplot as plt 
import random
import os
import re

# embedded the data in the file 

iris = [
    [5.1, 3.5, 1.4, 0.2, 'Iris-setosa'],
    [4.9, 3.0, 1.4, 0.2, 'Iris-setosa'],
    [4.7, 3.2, 1.3, 0.2, 'Iris-setosa'],
    [4.6, 3.1, 1.5, 0.2, 'Iris-setosa'],
    [5.0, 3.6, 1.4, 0.2, 'Iris-setosa'],
    [5.4, 3.9, 1.7, 0.4, 'Iris-setosa'],
    [4.6, 3.4, 1.4, 0.3, 'Iris-setosa'],
    [5.0, 3.4, 1.5, 0.2, 'Iris-setosa'],
    [4.4, 2.9, 1.4, 0.2, 'Iris-setosa'],
    [4.9, 3.1, 1.5, 0.1, 'Iris-setosa'],
    [5.4, 3.7, 1.5, 0.2, 'Iris-setosa'],
    [4.8, 3.4, 1.6, 0.2, 'Iris-setosa'],
    [4.8, 3.0, 1.4, 0.1, 'Iris-setosa'],
    [4.3, 3.0, 1.1, 0.1, 'Iris-setosa'],
    [5.8, 4.0, 1.2, 0.2, 'Iris-setosa'],
    [5.7, 4.4, 1.5, 0.4, 'Iris-setosa'],
    [5.4, 3.9, 1.3, 0.4, 'Iris-setosa'],
    [5.1, 3.5, 1.4, 0.3, 'Iris-setosa'],
    [5.7, 3.8, 1.7, 0.3, 'Iris-setosa'],
    [5.1, 3.8, 1.5, 0.3, 'Iris-setosa'],
    [5.4, 3.4, 1.7, 0.2, 'Iris-setosa'],
    [5.1, 3.7, 1.5, 0.4, 'Iris-setosa'],
    [4.6, 3.6, 1.0, 0.2, 'Iris-setosa'],
    [5.1, 3.3, 1.7, 0.5, 'Iris-setosa'],
    [4.8, 3.4, 1.9, 0.2, 'Iris-setosa'],
    [5.0, 3.0, 1.6, 0.2, 'Iris-setosa'],
    [5.0, 3.4, 1.6, 0.4, 'Iris-setosa'],
    [5.2, 3.5, 1.5, 0.2, 'Iris-setosa'],
    [5.2, 3.4, 1.4, 0.2, 'Iris-setosa'],
    [4.7, 3.2, 1.6, 0.2, 'Iris-setosa'],
    [4.8, 3.1, 1.6, 0.2, 'Iris-setosa'],
    [5.4, 3.4, 1.5, 0.4, 'Iris-setosa'],
    [5.2, 4.1, 1.5, 0.1, 'Iris-setosa'],
    [5.5, 4.2, 1.4, 0.2, 'Iris-setosa'],
    [4.9, 3.1, 1.5, 0.1, 'Iris-setosa'],
    [5.0, 3.2, 1.2, 0.2, 'Iris-setosa'],
    [5.5, 3.5, 1.3, 0.2, 'Iris-setosa'],
    [4.9, 3.1, 1.5, 0.1, 'Iris-setosa'],
    [4.4, 3.0, 1.3, 0.2, 'Iris-setosa'],
    [5.1, 3.4, 1.5, 0.2, 'Iris-setosa'],
    [5.0, 3.5, 1.3, 0.3, 'Iris-setosa'],
    [4.5, 2.3, 1.3, 0.3, 'Iris-setosa'],
    [4.4, 3.2, 1.3, 0.2, 'Iris-setosa'],
    [5.0, 3.5, 1.6, 0.6, 'Iris-setosa'],
    [5.1, 3.8, 1.9, 0.4, 'Iris-setosa'],
    [4.8, 3.0, 1.4, 0.3, 'Iris-setosa'],
    [5.1, 3.8, 1.6, 0.2, 'Iris-setosa'],
    [4.6, 3.2, 1.4, 0.2, 'Iris-setosa'],
    [5.3, 3.7, 1.5, 0.2, 'Iris-setosa'],
    [5.0, 3.3, 1.4, 0.2, 'Iris-setosa'],
    [7.0, 3.2, 4.7, 1.4, 'Iris-versicolor'],
    [6.4, 3.2, 4.5, 1.5, 'Iris-versicolor'],
    [6.9, 3.1, 4.9, 1.5, 'Iris-versicolor'],
    [5.5, 2.3, 4.0, 1.3, 'Iris-versicolor'],
    [6.5, 2.8, 4.6, 1.5, 'Iris-versicolor'],
    [5.7, 2.8, 4.5, 1.3, 'Iris-versicolor'],
    [6.3, 3.3, 4.7, 1.6, 'Iris-versicolor'],
    [4.9, 2.4, 3.3, 1.0, 'Iris-versicolor'],
    [6.6, 2.9, 4.6, 1.3, 'Iris-versicolor'],
    [5.2, 2.7, 3.9, 1.4, 'Iris-versicolor'],
    [5.0, 2.0, 3.5, 1.0, 'Iris-versicolor'],
    [5.9, 3.0, 4.2, 1.5, 'Iris-versicolor'],
    [6.0, 2.2, 4.0, 1.0, 'Iris-versicolor'],
    [6.1, 2.9, 4.7, 1.4, 'Iris-versicolor'],
    [5.6, 2.9, 3.6, 1.3, 'Iris-versicolor'],
    [6.7, 3.1, 4.4, 1.4, 'Iris-versicolor'],
    [5.6, 3.0, 4.5, 1.5, 'Iris-versicolor'],
    [5.8, 2.7, 4.1, 1.0, 'Iris-versicolor'],
    [6.2, 2.2, 4.5, 1.5, 'Iris-versicolor'],
    [5.6, 2.5, 3.9, 1.1, 'Iris-versicolor'],
    [5.9, 3.2, 4.8, 1.8, 'Iris-versicolor'],
    [6.1, 2.8, 4.0, 1.3, 'Iris-versicolor'],
    [6.3, 2.5, 4.9, 1.5, 'Iris-versicolor'],
    [6.1, 2.8, 4.7, 1.2, 'Iris-versicolor'],
    [6.4, 2.9, 4.3, 1.3, 'Iris-versicolor'],
    [6.6, 3.0, 4.4, 1.4, 'Iris-versicolor'],
    [6.8, 2.8, 4.8, 1.4, 'Iris-versicolor'],
    [6.7, 3.0, 5.0, 1.7, 'Iris-versicolor'],
    [6.0, 2.9, 4.5, 1.5, 'Iris-versicolor'],
    [5.7, 2.6, 3.5, 1.0, 'Iris-versicolor'],
    [5.5, 2.4, 3.8, 1.1, 'Iris-versicolor'],
    [5.5, 2.4, 3.7, 1.0, 'Iris-versicolor'],
    [5.8, 2.7, 3.9, 1.2, 'Iris-versicolor'],
    [6.0, 2.7, 5.1, 1.6, 'Iris-versicolor'],
    [5.4, 3.0, 4.5, 1.5, 'Iris-versicolor'],
    [6.0, 3.4, 4.5, 1.6, 'Iris-versicolor'],
    [6.7, 3.1, 4.7, 1.5, 'Iris-versicolor'],
    [6.3, 2.3, 4.4, 1.3, 'Iris-versicolor'],
    [5.6, 3.0, 4.1, 1.3, 'Iris-versicolor'],
    [5.5, 2.5, 4.0, 1.3, 'Iris-versicolor'],
    [5.5, 2.6, 4.4, 1.2, 'Iris-versicolor'],
    [6.1, 3.0, 4.6, 1.4, 'Iris-versicolor'],
    [5.8, 2.6, 4.0, 1.2, 'Iris-versicolor'],
    [5.0, 2.3, 3.3, 1.0, 'Iris-versicolor'],
    [5.6, 2.7, 4.2, 1.3, 'Iris-versicolor'],
    [5.7, 3.0, 4.2, 1.2, 'Iris-versicolor'],
    [5.7, 2.9, 4.2, 1.3, 'Iris-versicolor'],
    [6.2, 2.9, 4.3, 1.3, 'Iris-versicolor'],
    [5.1, 2.5, 3.0, 1.1, 'Iris-versicolor'],
    [5.7, 2.8, 4.1, 1.3, 'Iris-versicolor'],
    [6.3, 3.3, 6.0, 2.5, 'Iris-virginica'],
    [5.8, 2.7, 5.1, 1.9, 'Iris-virginica'],
    [7.1, 3.0, 5.9, 2.1, 'Iris-virginica'],
    [6.3, 2.9, 5.6, 1.8, 'Iris-virginica'],
    [6.5, 3.0, 5.8, 2.2, 'Iris-virginica'],
    [7.6, 3.0, 6.6, 2.1, 'Iris-virginica'],
    [4.9, 2.5, 4.5, 1.7, 'Iris-virginica'],
    [7.3, 2.9, 6.3, 1.8, 'Iris-virginica'],
    [6.7, 2.5, 5.8, 1.8, 'Iris-virginica'],
    [7.2, 3.6, 6.1, 2.5, 'Iris-virginica'],
    [6.5, 3.2, 5.1, 2.0, 'Iris-virginica'],
    [6.4, 2.7, 5.3, 1.9, 'Iris-virginica'],
    [6.8, 3.0, 5.5, 2.1, 'Iris-virginica'],
    [5.7, 2.5, 5.0, 2.0, 'Iris-virginica'],
    [5.8, 2.8, 5.1, 2.4, 'Iris-virginica'],
    [6.4, 3.2, 5.3, 2.3, 'Iris-virginica'],
    [6.5, 3.0, 5.5, 1.8, 'Iris-virginica'],
    [7.7, 3.8, 6.7, 2.2, 'Iris-virginica'],
    [7.7, 2.6, 6.9, 2.3, 'Iris-virginica'],
    [6.0, 2.2, 5.0, 1.5, 'Iris-virginica'],
    [6.9, 3.2, 5.7, 2.3, 'Iris-virginica'],
    [5.6, 2.8, 4.9, 2.0, 'Iris-virginica'],
    [7.7, 2.8, 6.7, 2.0, 'Iris-virginica'],
    [6.3, 2.7, 4.9, 1.8, 'Iris-virginica'],
    [6.7, 3.3, 5.7, 2.1, 'Iris-virginica'],
    [7.2, 3.2, 6.0, 1.8, 'Iris-virginica'],
    [6.2, 2.8, 4.8, 1.8, 'Iris-virginica'],
    [6.1, 3.0, 4.9, 1.8, 'Iris-virginica'],
    [6.4, 2.8, 5.6, 2.1, 'Iris-virginica'],
    [7.2, 3.0, 5.8, 1.6, 'Iris-virginica'],
    [7.4, 2.8, 6.1, 1.9, 'Iris-virginica'],
    [7.9, 3.8, 6.4, 2.0, 'Iris-virginica'],
    [6.4, 2.8, 5.6, 2.2, 'Iris-virginica'],
    [6.3, 2.8, 5.1, 1.5, 'Iris-virginica'],
    [6.1, 2.6, 5.6, 1.4, 'Iris-virginica'],
    [7.7, 3.0, 6.1, 2.3, 'Iris-virginica'],
    [6.3, 3.4, 5.6, 2.4, 'Iris-virginica'],
    [6.4, 3.1, 5.5, 1.8, 'Iris-virginica'],
    [6.0, 3.0, 4.8, 1.8, 'Iris-virginica'],
    [6.9, 3.1, 5.4, 2.1, 'Iris-virginica'],
    [6.7, 3.1, 5.6, 2.4, 'Iris-virginica'],
    [6.9, 3.1, 5.1, 2.3, 'Iris-virginica'],
    [5.8, 2.7, 5.1, 1.9, 'Iris-virginica'],
    [6.8, 3.2, 5.9, 2.3, 'Iris-virginica'],
    [6.7, 3.3, 5.7, 2.5, 'Iris-virginica'],
    [6.7, 3.0, 5.2, 2.3, 'Iris-virginica'],
    [6.3, 2.5, 5.0, 1.9, 'Iris-virginica'],
    [6.5, 3.0, 5.2, 2.0, 'Iris-virginica'],
    [6.2, 3.4, 5.4, 2.3, 'Iris-virginica'],
    [5.9, 3.0, 5.1, 1.8, 'Iris-virginica']
] 

pima = [
    [6.0, 148.0, 72.0, 35.0, 0.0, 33.6, 0.627, 50.0, 1],
    [1.0, 85.0, 66.0, 29.0, 0.0, 26.6, 0.351, 31.0, 0],
    [8.0, 183.0, 64.0, 0.0, 0.0, 23.3, 0.672, 32.0, 1],
    [1.0, 89.0, 66.0, 23.0, 94.0, 28.1, 0.167, 21.0, 0],
    [0.0, 137.0, 40.0, 35.0, 168.0, 43.1, 2.288, 33.0, 1],
    [5.0, 116.0, 74.0, 0.0, 0.0, 25.6, 0.201, 30.0, 0],
    [3.0, 78.0, 50.0, 32.0, 88.0, 31.0, 0.248, 26.0, 1],
    [10.0, 115.0, 0.0, 0.0, 0.0, 35.3, 0.134, 29.0, 0],
    [2.0, 197.0, 70.0, 45.0, 543.0, 30.5, 0.158, 53.0, 1],
    [8.0, 125.0, 96.0, 0.0, 0.0, 0.0, 0.232, 54.0, 1],
    [4.0, 110.0, 92.0, 0.0, 0.0, 37.6, 0.191, 30.0, 0],
    [10.0, 168.0, 74.0, 0.0, 0.0, 38.0, 0.537, 34.0, 1],
    [10.0, 139.0, 80.0, 0.0, 0.0, 27.1, 1.441, 57.0, 0],
    [1.0, 189.0, 60.0, 23.0, 846.0, 30.1, 0.398, 59.0, 1],
    [5.0, 166.0, 72.0, 19.0, 175.0, 25.8, 0.587, 51.0, 1],
    [7.0, 100.0, 0.0, 0.0, 0.0, 30.0, 0.484, 32.0, 1],
    [0.0, 118.0, 84.0, 47.0, 230.0, 45.8, 0.551, 31.0, 1],
    [7.0, 107.0, 74.0, 0.0, 0.0, 29.6, 0.254, 31.0, 1],
    [1.0, 103.0, 30.0, 38.0, 83.0, 43.3, 0.183, 33.0, 0],
    [1.0, 115.0, 70.0, 30.0, 96.0, 34.6, 0.529, 32.0, 1],
    [3.0, 126.0, 88.0, 41.0, 235.0, 39.3, 0.704, 27.0, 0],
    [8.0, 99.0, 84.0, 0.0, 0.0, 35.4, 0.388, 50.0, 0],
    [7.0, 196.0, 90.0, 0.0, 0.0, 39.8, 0.451, 41.0, 1],
    [9.0, 119.0, 80.0, 35.0, 0.0, 29.0, 0.263, 29.0, 1],
    [11.0, 143.0, 94.0, 33.0, 146.0, 36.6, 0.254, 51.0, 1],
    [10.0, 125.0, 70.0, 26.0, 115.0, 31.1, 0.205, 41.0, 1],
    [7.0, 147.0, 76.0, 0.0, 0.0, 39.4, 0.257, 43.0, 1],
    [1.0, 97.0, 66.0, 15.0, 140.0, 23.2, 0.487, 22.0, 0],
    [13.0, 145.0, 82.0, 19.0, 110.0, 22.2, 0.245, 57.0, 0],
    [5.0, 117.0, 92.0, 0.0, 0.0, 34.1, 0.337, 38.0, 0],
    [5.0, 109.0, 75.0, 26.0, 0.0, 36.0, 0.546, 60.0, 0],
    [3.0, 158.0, 76.0, 36.0, 245.0, 31.6, 0.851, 28.0, 1],
    [3.0, 88.0, 58.0, 11.0, 54.0, 24.8, 0.267, 22.0, 0],
    [6.0, 92.0, 92.0, 0.0, 0.0, 19.9, 0.188, 28.0, 0],
    [10.0, 122.0, 78.0, 31.0, 0.0, 27.6, 0.512, 45.0, 0],
    [4.0, 103.0, 60.0, 33.0, 192.0, 24.0, 0.966, 33.0, 0],
    [11.0, 138.0, 76.0, 0.0, 0.0, 33.2, 0.42, 35.0, 0],
    [9.0, 102.0, 76.0, 37.0, 0.0, 32.9, 0.665, 46.0, 1],
    [2.0, 90.0, 68.0, 42.0, 0.0, 38.2, 0.503, 27.0, 1],
    [4.0, 111.0, 72.0, 47.0, 207.0, 37.1, 1.39, 56.0, 1],
    [3.0, 180.0, 64.0, 25.0, 70.0, 34.0, 0.271, 26.0, 0],
    [7.0, 133.0, 84.0, 0.0, 0.0, 40.2, 0.696, 37.0, 0],
    [7.0, 106.0, 92.0, 18.0, 0.0, 22.7, 0.235, 48.0, 0],
    [9.0, 171.0, 110.0, 24.0, 240.0, 45.4, 0.721, 54.0, 1],
    [7.0, 159.0, 64.0, 0.0, 0.0, 27.4, 0.294, 40.0, 0],
    [0.0, 180.0, 66.0, 39.0, 0.0, 42.0, 1.893, 25.0, 1],
    [1.0, 146.0, 56.0, 0.0, 0.0, 29.7, 0.564, 29.0, 0],
    [2.0, 71.0, 70.0, 27.0, 0.0, 28.0, 0.586, 22.0, 0],
    [7.0, 103.0, 66.0, 32.0, 0.0, 39.1, 0.344, 31.0, 1],
    [7.0, 105.0, 0.0, 0.0, 0.0, 0.0, 0.305, 24.0, 0],
    [1.0, 103.0, 80.0, 11.0, 82.0, 19.4, 0.491, 22.0, 0],
    [1.0, 101.0, 50.0, 15.0, 36.0, 24.2, 0.526, 26.0, 0],
    [5.0, 88.0, 66.0, 21.0, 23.0, 24.4, 0.342, 30.0, 0],
    [8.0, 176.0, 90.0, 34.0, 300.0, 33.7, 0.467, 58.0, 1],
    [7.0, 150.0, 66.0, 42.0, 342.0, 34.7, 0.718, 42.0, 0],
    [1.0, 73.0, 50.0, 10.0, 0.0, 23.0, 0.248, 21.0, 0],
    [7.0, 187.0, 68.0, 39.0, 304.0, 37.7, 0.254, 41.0, 1],
    [0.0, 100.0, 88.0, 60.0, 110.0, 46.8, 0.962, 31.0, 0],
    [0.0, 146.0, 82.0, 0.0, 0.0, 40.5, 1.781, 44.0, 0],
    [0.0, 105.0, 64.0, 41.0, 142.0, 41.5, 0.173, 22.0, 0],
    [2.0, 84.0, 0.0, 0.0, 0.0, 0.0, 0.304, 21.0, 0],
    [8.0, 133.0, 72.0, 0.0, 0.0, 32.9, 0.27, 39.0, 1],
    [5.0, 44.0, 62.0, 0.0, 0.0, 25.0, 0.587, 36.0, 0],
    [2.0, 141.0, 58.0, 34.0, 128.0, 25.4, 0.699, 24.0, 0],
    [7.0, 114.0, 66.0, 0.0, 0.0, 32.8, 0.258, 42.0, 1],
    [5.0, 99.0, 74.0, 27.0, 0.0, 29.0, 0.203, 32.0, 0],
    [0.0, 109.0, 88.0, 30.0, 0.0, 32.5, 0.855, 38.0, 1],
    [2.0, 109.0, 92.0, 0.0, 0.0, 42.7, 0.845, 54.0, 0],
    [1.0, 95.0, 66.0, 13.0, 38.0, 19.6, 0.334, 25.0, 0],
    [4.0, 146.0, 85.0, 27.0, 100.0, 28.9, 0.189, 27.0, 0],
    [2.0, 100.0, 66.0, 20.0, 90.0, 32.9, 0.867, 28.0, 1],
    [5.0, 139.0, 64.0, 35.0, 140.0, 28.6, 0.411, 26.0, 0],
    [13.0, 126.0, 90.0, 0.0, 0.0, 43.4, 0.583, 42.0, 1],
    [4.0, 129.0, 86.0, 20.0, 270.0, 35.1, 0.231, 23.0, 0],
    [1.0, 79.0, 75.0, 30.0, 0.0, 32.0, 0.396, 22.0, 0],
    [1.0, 0.0, 48.0, 20.0, 0.0, 24.7, 0.14, 22.0, 0],
    [7.0, 62.0, 78.0, 0.0, 0.0, 32.6, 0.391, 41.0, 0],
    [5.0, 95.0, 72.0, 33.0, 0.0, 37.7, 0.37, 27.0, 0],
    [0.0, 131.0, 0.0, 0.0, 0.0, 43.2, 0.27, 26.0, 1],
    [2.0, 112.0, 66.0, 22.0, 0.0, 25.0, 0.307, 24.0, 0],
    [3.0, 113.0, 44.0, 13.0, 0.0, 22.4, 0.14, 22.0, 0],
    [2.0, 74.0, 0.0, 0.0, 0.0, 0.0, 0.102, 22.0, 0],
    [7.0, 83.0, 78.0, 26.0, 71.0, 29.3, 0.767, 36.0, 0],
    [0.0, 101.0, 65.0, 28.0, 0.0, 24.6, 0.237, 22.0, 0],
    [5.0, 137.0, 108.0, 0.0, 0.0, 48.8, 0.227, 37.0, 1],
    [2.0, 110.0, 74.0, 29.0, 125.0, 32.4, 0.698, 27.0, 0],
    [13.0, 106.0, 72.0, 54.0, 0.0, 36.6, 0.178, 45.0, 0],
    [2.0, 100.0, 68.0, 25.0, 71.0, 38.5, 0.324, 26.0, 0],
    [15.0, 136.0, 70.0, 32.0, 110.0, 37.1, 0.153, 43.0, 1],
    [1.0, 107.0, 68.0, 19.0, 0.0, 26.5, 0.165, 24.0, 0],
    [1.0, 80.0, 55.0, 0.0, 0.0, 19.1, 0.258, 21.0, 0],
    [4.0, 123.0, 80.0, 15.0, 176.0, 32.0, 0.443, 34.0, 0],
    [7.0, 81.0, 78.0, 40.0, 48.0, 46.7, 0.261, 42.0, 0],
    [4.0, 134.0, 72.0, 0.0, 0.0, 23.8, 0.277, 60.0, 1],
    [2.0, 142.0, 82.0, 18.0, 64.0, 24.7, 0.761, 21.0, 0],
    [6.0, 144.0, 72.0, 27.0, 228.0, 33.9, 0.255, 40.0, 0],
    [2.0, 92.0, 62.0, 28.0, 0.0, 31.6, 0.13, 24.0, 0],
    [1.0, 71.0, 48.0, 18.0, 76.0, 20.4, 0.323, 22.0, 0],
    [6.0, 93.0, 50.0, 30.0, 64.0, 28.7, 0.356, 23.0, 0],
    [1.0, 122.0, 90.0, 51.0, 220.0, 49.7, 0.325, 31.0, 1],
    [1.0, 163.0, 72.0, 0.0, 0.0, 39.0, 1.222, 33.0, 1],
    [1.0, 151.0, 60.0, 0.0, 0.0, 26.1, 0.179, 22.0, 0],
    [0.0, 125.0, 96.0, 0.0, 0.0, 22.5, 0.262, 21.0, 0],
    [1.0, 81.0, 72.0, 18.0, 40.0, 26.6, 0.283, 24.0, 0],
    [2.0, 85.0, 65.0, 0.0, 0.0, 39.6, 0.93, 27.0, 0],
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    [1.0, 109.0, 58.0, 18.0, 116.0, 28.5, 0.219, 22.0, 0],
    [9.0, 140.0, 94.0, 0.0, 0.0, 32.7, 0.734, 45.0, 1],
    [13.0, 153.0, 88.0, 37.0, 140.0, 40.6, 1.174, 39.0, 0],
    [12.0, 100.0, 84.0, 33.0, 105.0, 30.0, 0.488, 46.0, 0],
    [1.0, 147.0, 94.0, 41.0, 0.0, 49.3, 0.358, 27.0, 1],
    [1.0, 81.0, 74.0, 41.0, 57.0, 46.3, 1.096, 32.0, 0],
    [3.0, 187.0, 70.0, 22.0, 200.0, 36.4, 0.408, 36.0, 1],
    [6.0, 162.0, 62.0, 0.0, 0.0, 24.3, 0.178, 50.0, 1],
    [4.0, 136.0, 70.0, 0.0, 0.0, 31.2, 1.182, 22.0, 1],
    [1.0, 121.0, 78.0, 39.0, 74.0, 39.0, 0.261, 28.0, 0],
    [3.0, 108.0, 62.0, 24.0, 0.0, 26.0, 0.223, 25.0, 0],
    [0.0, 181.0, 88.0, 44.0, 510.0, 43.3, 0.222, 26.0, 1],
    [8.0, 154.0, 78.0, 32.0, 0.0, 32.4, 0.443, 45.0, 1],
    [1.0, 128.0, 88.0, 39.0, 110.0, 36.5, 1.057, 37.0, 1],
    [7.0, 137.0, 90.0, 41.0, 0.0, 32.0, 0.391, 39.0, 0],
    [0.0, 123.0, 72.0, 0.0, 0.0, 36.3, 0.258, 52.0, 1],
    [1.0, 106.0, 76.0, 0.0, 0.0, 37.5, 0.197, 26.0, 0],
    [6.0, 190.0, 92.0, 0.0, 0.0, 35.5, 0.278, 66.0, 1],
    [2.0, 88.0, 58.0, 26.0, 16.0, 28.4, 0.766, 22.0, 0],
    [9.0, 170.0, 74.0, 31.0, 0.0, 44.0, 0.403, 43.0, 1],
    [9.0, 89.0, 62.0, 0.0, 0.0, 22.5, 0.142, 33.0, 0],
    [10.0, 101.0, 76.0, 48.0, 180.0, 32.9, 0.171, 63.0, 0],
    [2.0, 122.0, 70.0, 27.0, 0.0, 36.8, 0.34, 27.0, 0],
    [5.0, 121.0, 72.0, 23.0, 112.0, 26.2, 0.245, 30.0, 0],
    [1.0, 126.0, 60.0, 0.0, 0.0, 30.1, 0.349, 47.0, 1],
    [1.0, 93.0, 70.0, 31.0, 0.0, 30.4, 0.315, 23.0, 0]
]

def column(matrix, i):
    return [row[i] for row in matrix]

def slice_2d_columns(matrix, i_start, i_end): 
    return [matrix[i][i_start : i_end] for i in range(0, matrix.__len__())]

def most_frequent(List): 
    return max(set(List), key = List.count) 

def group_by_class(training, n_classes):    
    matrix = []
    
    for i in range(0, n_classes.__len__()):
        matrix.append([])
        for j in range(0, training.__len__()):
            if (training[j][training[j].__len__() - 1] == n_classes[i]):
                matrix[i].append(training[j])
                
    return matrix

def multiplication(v1, M, v2):
    result = numpy.dot(numpy.dot(numpy.transpose(v1), numpy.linalg.inv(M)), v2)
    return result

def discrimination_function(x, m1, m2, cov1, cov2, p1, p2):
    x = x[0 : x.__len__() - 1]
    
    quadratic_term = 1/2 * (multiplication(x, cov2, x) - multiplication(x, cov1, x))
    linear_term = multiplication(m1, cov1, x) - multiplication(m2, cov2, x)
    det_cov1 = numpy.linalg.det(cov1)
    det_cov2 = numpy.linalg.det(cov2)
    constant = -1/2 * multiplication(m1, cov1, m1) + 1/2 * multiplication(m2, cov2, m2) + numpy.log(p1/p2) + 1/2 * numpy.log(det_cov2/det_cov1)
    g_x = quadratic_term + linear_term + constant

    return g_x

def bayes_classifier_2classes(x, training_set):
    
    #training
    n_classes = numpy.unique(column(training_set, training_set[0].__len__() - 1))

    classes = group_by_class(training_set, n_classes)
    class_0 = classes[0]
    class_1 = classes[1]
    # calculation of prior probabilities
    p_0 = (classes[0].__len__())/training_set.__len__()
    p_1 = (classes[1].__len__())/training_set.__len__()
    
    # Gaussian distribution parameters 
    
    # calculations of means and variances  per columns per class
    m_0 = []
    m_1 = []

    for i in range(0, class_0[0].__len__() - 1):        
        m_0.append(numpy.mean(column(class_0, i)))
        m_1.append(numpy.mean(column(class_1, i)))   
    
    # calculation of covariances(multiplication by (N-1)/N because numpy.cov calculates variance dividing by N-1)  
    training_0 = slice_2d_columns(classes[0], 0, classes[0][0].__len__() - 1)
    training_1 = slice_2d_columns(classes[1], 0, classes[1][0].__len__() - 1)

    training_0_t = numpy.transpose(training_0)
    covariance_0 = numpy.cov(training_0_t)*((training_0.__len__() - 1)/training_0.__len__())
    
    training_1_t = numpy.transpose(training_1)
    covariance_1 = numpy.cov(training_1_t)*((training_1.__len__() - 1)/training_1.__len__())
    
    # Discrimination Function 
    result = discrimination_function(x, m_0, m_1, covariance_0, covariance_1, p_0, p_1)
        
    return n_classes[0] if result > 0 else n_classes[1]
        
 
def cross_validation_leave_one_out(training_set):
    
    right_guesses = 0
    wrong_guesses = 0

    for i in range(0, training_set.__len__()):
        result = bayes_classifier_2classes(training_set[i], [x for j, x in enumerate(training_set) if j != i])
        if (result == training_set[i][training_set[i].__len__() - 1]):
            right_guesses = right_guesses + 1
        else:
            wrong_guesses = wrong_guesses + 1
            
    frequency_right = (right_guesses/training_set.__len__())*100
    frequency_wrong = (wrong_guesses/training_set.__len__())*100
    
    return [frequency_right, frequency_wrong]


def exercise2_2():
        
    classification_percent_pima = cross_validation_leave_one_out(pima)
    
    frequency_right_pima =  classification_percent_pima[0]
    frequency_wrong_pima =  classification_percent_pima[1]
    
    print(frequency_right_pima)
    print(frequency_wrong_pima)

   
    

exercise2_2()