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9.8 KiB
9.8 KiB
id, title, challengeType, forumTopicId, dashedName
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5e44414f903586ffb414c950 | 概率计算器 | 23 | 462364 | probability-calculator |
--description--
假设有一顶帽子，里面有 5 个蓝球、4 个红球和 2 个绿球。 随机抽取的 4 个球中至少包含 1 个红球和 2 个绿球的概率是多少？ 虽然可以使用高等数学来计算概率，但更简单的方法是编写一个程序来执行大量实验来估计近似概率。
对于这个项目，你将编写一个程序来确定从帽子中随机抽取某些球的大致概率。
First, create a Hat class in main.py. 该类应该采用可变数量的参数来指定帽子中每种颜色的球数。 例如，可以通过以下任何一种方式创建类对象：
hat1 = Hat(yellow=3, blue=2, green=6)
hat2 = Hat(red=5, orange=4)
hat3 = Hat(red=5, orange=4, black=1, blue=0, pink=2, striped=9)
一顶帽子总是至少有一个球。 创建时传递给 hat 对象的参数应转换为 contents 实例变量。 contents 应该是一个字符串列表，其中包含帽子中每个球的一个项目。 列表中的每一项都应该是一个颜色名称，代表该颜色的单个球。 例如，如果你的帽子是 {"red": 2, "blue": 1}，contents 应该是 ["red", "red", "blue"]。
Hat 类应该有一个 draw 方法，该方法接受一个参数，该参数指示要从帽子中抽取的球数。 此方法应该从 contents 中随机删除球，并将这些球作为字符串列表返回。 在抽取过程中球不应回到帽子中，类似于没有放回的黑盒实验。 如果要抽的球数量超过可用数量，则返回所有球。
Next, create an experiment function in main.py (not inside the Hat class). 此函数应接受以下参数：
hat：一个包含球的帽子对象，应该在函数内复制。expected_balls：一个对象，指示尝试从帽子中抽取的确切球组以进行实验。 例如，要确定从帽子中抽取 2 个蓝球和 1 个红球的概率，将expected_balls设置为{"blue":2, "red":1}。num_balls_drawn：每次实验中从帽子中抽出的球数。num_experiments：要执行的实验数量。 （进行的实验越多，近似概率就越准确。）
experiment 函数应该返回一个概率。
例如，如果你想确定当你从一个包含 6 个黑球、4 个红球和 3 个绿球的帽子中抽出 5 个球时，至少得到 2 个红球和 1 个绿球的概率， 你将进行 N 次实验，记录其中你至少得到 2 个红球和 1 个绿球的次数 M，并估计概率为 M/N。 每个实验都包括从一个装有指定球的帽子开始，抽出几个球，并检查你是否抽到了你试图抽出的球。
以下是基于上面的示例调用 experiment 函数的方法，其中包含 2000 个实验：
hat = Hat(black=6, red=4, green=3)
probability = experiment(hat=hat,
expected_balls={"red":2,"green":1},
num_balls_drawn=5,
num_experiments=2000)
The output would be something like this:
0.356
由于这是基于随机抽取的，因此每次运行代码时概率会略有不同。
Hint: Consider using the modules that are already imported at the top. Do not initialize random seed within the file.
--hints--
Creation of hat object should add correct contents.
({
test: () => {
pyodide.FS.writeFile("/home/pyodide/probability_calculator.py", code);
pyodide.FS.writeFile(
"/home/pyodide/test_module.py",
`
import unittest
import probability_calculator
from importlib import reload
reload(probability_calculator)
probability_calculator.random.seed(95)
class UnitTests(unittest.TestCase):
maxDiff = None
def test_hat_class_contents(self):
hat = probability_calculator.Hat(red=3,blue=2)
actual = hat.contents
expected = ["red","red","red","blue","blue"]
self.assertEqual(actual, expected, 'Expected creation of hat object to add correct contents.')
`
);
const testCode = `
from unittest import main
import test_module
from importlib import reload
reload(test_module)
t = main(module='test_module', exit=False)
t.result.wasSuccessful()
`;
const out = runPython(testCode);
assert(out);
},
});
The draw method in hat class should reduce number of items in contents.
({
test: () => {
pyodide.FS.writeFile("/home/pyodide/probability_calculator.py", code);
pyodide.FS.writeFile(
"/home/pyodide/test_module.py",
`
import unittest
import probability_calculator
from importlib import reload
reload(probability_calculator)
probability_calculator.random.seed(95)
class UnitTests(unittest.TestCase):
maxDiff = None
def test_hat_draw(self):
hat = probability_calculator.Hat(red=5,blue=2)
actual = hat.draw(2)
expected = ['blue', 'red']
self.assertEqual(actual, expected, 'Expected hat draw to return two random items from hat contents.')
actual = len(hat.contents)
expected = 5
self.assertEqual(actual, expected, 'Expected hat draw to reduce number of items in contents.')
`
);
const testCode = `
from unittest import main
import test_module
from importlib import reload
reload(test_module)
t = main(module='test_module', exit=False)
t.result.wasSuccessful()
`;
const out = runPython(testCode);
assert(out);
},
});
The draw method should behave correctly when the number of balls to extract is bigger than the number of balls in the hat.
({
test: () => {
pyodide.FS.writeFile("/home/pyodide/probability_calculator.py", code);
pyodide.FS.writeFile(
"/home/pyodide/test_module.py",
`
import unittest
import probability_calculator
from importlib import reload
reload(probability_calculator)
probability_calculator.random.seed(95)
class UnitTests(unittest.TestCase):
maxDiff = None
def test_hat_draw_2(self):
hat = probability_calculator.Hat(yellow=5,red=1,green=3,blue=9,test=1)
actual = hat.draw(20)
expected = ['yellow', 'yellow', 'yellow', 'yellow', 'yellow', 'red', 'green', 'green', 'green', 'blue', 'blue', 'blue', 'blue', 'blue', 'blue', 'blue', 'blue', 'blue', 'test']
self.assertEqual(actual, expected, 'Expected hat draw to return all items from hat contents.')
actual = len(hat.contents)
expected = 0
self.assertEqual(actual, expected, 'Expected hat draw to leave no items in contents.')
`
);
const testCode = `
from unittest import main
import test_module
from importlib import reload
reload(test_module)
t = main(module='test_module', exit=False)
t.result.wasSuccessful()
`;
const out = runPython(testCode);
assert(out);
},
});
The experiment method should return a different probability.
({
test: () => {
pyodide.FS.writeFile("/home/pyodide/probability_calculator.py", code);
pyodide.FS.writeFile(
"/home/pyodide/test_module.py",
`
import unittest
import probability_calculator
from importlib import reload
reload(probability_calculator)
probability_calculator.random.seed(95)
class UnitTests(unittest.TestCase):
maxDiff = None
def test_prob_experiment(self):
hat = probability_calculator.Hat(blue=3,red=2,green=6)
probability = probability_calculator.experiment(hat=hat, expected_balls={"blue":2,"green":1}, num_balls_drawn=4, num_experiments=1000)
actual = probability
expected = 0.272
self.assertAlmostEqual(actual, expected, delta = 0.01, msg = 'Expected experiment method to return a different probability.')
hat = probability_calculator.Hat(yellow=5,red=1,green=3,blue=9,test=1)
probability = probability_calculator.experiment(hat=hat, expected_balls={"yellow":2,"blue":3,"test":1}, num_balls_drawn=20, num_experiments=100)
actual = probability
expected = 1.0
self.assertAlmostEqual(actual, expected, delta = 0.01, msg = 'Expected experiment method to return a different probability.')
`
);
const testCode = `
from unittest import main
import test_module
from importlib import reload
reload(test_module)
t = main(module='test_module', exit=False)
t.result.wasSuccessful()
`;
const out = runPython(testCode);
assert(out);
},
});
--seed--
--seed-contents--
import copy
import random
class Hat:
pass
def experiment(hat, expected_balls, num_balls_drawn, num_experiments):
pass
--solutions--
import copy
import random
class Hat:
def __init__(self, **hat):
self.hat = hat
contents = []
for i in hat:
for j in range(hat[i]):
contents.append(i)
self.contents = contents
def draw(self, number):
drawn = []
if number >= len(self.contents):
drawn.extend(self.contents)
self.contents = []
else:
for i in range(number):
drawn.append(
self.contents.pop(random.randrange(len(self.contents)))
)
return drawn
def experiment(hat, expected_balls, num_balls_drawn, num_experiments):
expected_balls_list = []
drawn_list = []
success = 0
for i in expected_balls:
for j in range(expected_balls[i]):
expected_balls_list.append(i)
for j in range(num_experiments):
hat_copy = copy.deepcopy(hat)
drawn_list.append(hat_copy.draw(num_balls_drawn))
exp_ball_list_copy = expected_balls_list[:]
for k in range(len(drawn_list[j])):
try:
ind = exp_ball_list_copy.index(drawn_list[j][k])
exp_ball_list_copy.pop(ind)
except:
continue
if len(exp_ball_list_copy) == 0:
success += 1
probability = success/num_experiments
return probability