Calculate the number of grains of wheat on a chessboard given that the number on each square doubles.
There once was a wise servant who saved the life of a prince. The king promised to pay whatever the servant could dream up. Knowing that the king loved chess, the servant told the king he would like to have grains of wheat. One grain on the first square of a chess board, with the number of grains doubling on each successive square.
There are 64 squares on a chessboard (where square 1 has one grain, square 2 has two grains, and so on).
Write code that shows:
Did you get the tests passing and the code clean? If you want to, these are some additional things you could try:
Then please share your thoughts in a comment on the submission. Did this experiment make the code better? Worse? Did you learn anything from it?
Sometimes it is necessary to raise an exception. When you do this, you should include a meaningful error message to indicate what the source of the error is. This makes your code more readable and helps significantly with debugging. Not every exercise will require you to raise an exception, but for those that do, the tests will only pass if you include a message.
To raise a message with an exception, just write it as an argument to the exception type. For example, instead of
raise Exception, you should write:
raise Exception("Meaningful message indicating the source of the error")
To run the tests, run
Alternatively, you can tell Python to run the pytest module:
python -m pytest grains_test.py
-v: enable verbose output
-x: stop running tests on first failure
--ff: run failures from previous test before running other test cases
For other options, see
python -m pytest -h
Note that, when trying to submit an exercise, make sure the solution is in the
You can find your Exercism workspace by running
exercism debug and looking for the line that starts with
For more detailed information about running tests, code style and linting, please see Running the Tests.
JavaRanch Cattle Drive, exercise 6 http://www.javaranch.com/grains.jsp
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
import unittest from grains import square, total # Tests adapted from `problem-specifications//canonical-data.json` class GrainsTest(unittest.TestCase): def test_1(self): self.assertEqual(square(1), 1) def test_2(self): self.assertEqual(square(2), 2) def test_3(self): self.assertEqual(square(3), 4) def test_4(self): self.assertEqual(square(4), 8) def test_16(self): self.assertEqual(square(16), 32768) def test_32(self): self.assertEqual(square(32), 2147483648) def test_64(self): self.assertEqual(square(64), 9223372036854775808) def test_square_0_raises_an_exception(self): with self.assertRaisesWithMessage(ValueError): square(0) def test_negative_square_raises_an_exception(self): with self.assertRaisesWithMessage(ValueError): square(-1) def test_square_greater_than_64_raises_an_exception(self): with self.assertRaisesWithMessage(ValueError): square(65) def test_returns_the_total_number_of_grains_on_the_board(self): self.assertEqual(total(), 18446744073709551615) # Utility functions def assertRaisesWithMessage(self, exception): return self.assertRaisesRegex(exception, r".+") if __name__ == "__main__": unittest.main()
from functools import lru_cache # memoize or cache the results of each square # since this function is so cheap, little gain @lru_cache def orig_square(number): if number <= 0 or number > 64: raise ValueError("only numbers between 1 and 64 are supported") # insignificant performance diff with shifting # return 1 << number-1 return pow(2, number-1) # alternative: # pre build this LUT to have some performance gains # start with 0 so no subtraction to get index lut = [0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592, 17179869184, 34359738368, 68719476736, 137438953472, 274877906944, 549755813888, 1099511627776, 2199023255552, 4398046511104, 8796093022208, 17592186044416, 35184372088832, 70368744177664, 140737488355328, 281474976710656, 562949953421312, 1125899906842624, 2251799813685248, 4503599627370496, 9007199254740992, 18014398509481984, 36028797018963968, 72057594037927936, 144115188075855872, 288230376151711744, 576460752303423488, 1152921504606846976, 2305843009213693952, 4611686018427387904, 9223372036854775808] def square(number): if number <= 0 or number > 64: raise ValueError("only numbers between 1 and 64 are supported") return lut[number] def total(): return sum(square(x) for x in range(1, 65))
A huge amount can be learned from reading other people’s code. This is why we wanted to give exercism users the option of making their solutions public.
Here are some questions to help you reflect on this solution and learn the most from it.