This notebook was prepared by Donne Martin. Source and license info is on GitHub.

Solution Notebook

Problem: Create a class with an insert method to insert an int to a list. It should also support calculating the max, min, mean, and mode in O(1).

Constraints

  • Can we assume the inputs are valid?
    • No
  • Is there a range of inputs?
    • 0 <= item <= 100
  • Should mean return a float?
    • Yes
  • Should the other results return an int?
    • Yes
  • If there are multiple modes, what do we return?
    • Any of the modes
  • Can we assume this fits memory?
    • Yes

Test Cases

  • None -> TypeError
  • [] -> ValueError
  • [5, 2, 7, 9, 9, 2, 9, 4, 3, 3, 2]
    • max: 9
    • min: 2
    • mean: 55
    • mode: 9 or 2

Algorithm

  • We'll init our max and min to None. Alternatively, we can init them to -sys.maxsize and sys.maxsize, respectively.
  • For mean, we'll keep track of the number of items we have inserted so far, as well as the running sum.
  • For mode, we'll keep track of the current mode and an array with the size of the given upper limit
    • Each element in the array will be init to 0
    • Each time we insert, we'll increment the element corresponding to the inserted item's value
  • On each insert:
    • Update the max and min
    • Update the mean by calculating running_sum / num_items
    • Update the mode by comparing the mode array's value with the current mode

Complexity:

  • Time: O(1)
  • Space: O(1), we are treating the 101 element array as a constant O(1), we could also see this as O(k)

Code

In [1]:
from __future__ import division


class Solution(object):

    def __init__(self, upper_limit=100):
        self.max = None
        self.min = None
        # Mean
        self.num_items = 0
        self.running_sum = 0
        self.mean = None
        # Mode
        self.array = [0] * (upper_limit + 1)
        self.mode_occurrences = 0
        self.mode = None

    def insert(self, val):
        if val is None:
            raise TypeError('val cannot be None')
        if self.max is None or val > self.max:
            self.max = val
        if self.min is None or val < self.min:
            self.min = val
        # Calculate the mean
        self.num_items += 1
        self.running_sum += val
        self.mean = self.running_sum / self.num_items
        # Calculate the mode
        self.array[val] += 1
        if self.array[val] > self.mode_occurrences:
            self.mode_occurrences = self.array[val]
            self.mode = val

Unit Test

In [2]:
%%writefile test_math_ops.py
import unittest


class TestMathOps(unittest.TestCase):

    def test_math_ops(self):
        solution = Solution()
        self.assertRaises(TypeError, solution.insert, None)
        solution.insert(5)
        solution.insert(2)
        solution.insert(7)
        solution.insert(9)
        solution.insert(9)
        solution.insert(2)
        solution.insert(9)
        solution.insert(4)
        solution.insert(3)
        solution.insert(3)
        solution.insert(2)
        self.assertEqual(solution.max, 9)
        self.assertEqual(solution.min, 2)
        self.assertEqual(solution.mean, 5)
        self.assertTrue(solution.mode in (2, 9))
        print('Success: test_math_ops')


def main():
    test = TestMathOps()
    test.test_math_ops()


if __name__ == '__main__':
    main()
Overwriting test_math_ops.py
In [3]:
%run -i test_math_ops.py
Success: test_math_ops