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

Solution Notebook

Problem: Implement n stacks using a single array.


  • Are the stacks and array a fixed size?
    • Yes
  • Are the stacks equally sized?
    • Yes
  • Does pushing to a full stack result in an exception?
    • Yes
  • Does popping from an empty stack result in an exception?
    • Yes
  • Can we assume the user passed in stack index is valid?
    • Yes
  • Can we assume this fits memory?
    • Yes

Test Cases

  • Test the following on the three stacks:
    • Push to full stack -> Exception
    • Push to non-full stack
    • Pop on empty stack -> Exception
    • Pop on non-empty stack


Absolute Index

  • return stack size * stack index + stack pointer


  • Time: O(1)
  • Space: O(1)


  • If stack is full, throw exception
  • Else
    • Increment stack pointer
    • Get the absolute array index
    • Insert the value to this index


  • Time: O(1)
  • Space: O(1)


  • If stack is empty, throw exception
  • Else
    • Store the value contained in the absolute array index
    • Set the value in the absolute array index to None
    • Decrement stack pointer
    • return value


  • Time: O(1)
  • Space: O(1)


In [1]:
class Stacks(object):

    def __init__(self, num_stacks, stack_size):
        self.num_stacks = num_stacks
        self.stack_size = stack_size
        self.stack_pointers = [-1] * self.num_stacks
        self.stack_array = [None] * self.num_stacks * self.stack_size

    def abs_index(self, stack_index):
        return stack_index * self.stack_size + self.stack_pointers[stack_index]

    def push(self, stack_index, data):
        if self.stack_pointers[stack_index] == self.stack_size - 1:
            raise Exception('Stack is full')
        self.stack_pointers[stack_index] += 1
        array_index = self.abs_index(stack_index)
        self.stack_array[array_index] = data

    def pop(self, stack_index):
        if self.stack_pointers[stack_index] == -1:
            raise Exception('Stack is empty')
        array_index = self.abs_index(stack_index)
        data = self.stack_array[array_index]
        self.stack_array[array_index] = None
        self.stack_pointers[stack_index] -= 1
        return data

Unit Test

In [2]:
import unittest

class TestStacks(unittest.TestCase):

    def test_pop_on_empty(self, num_stacks, stack_size):
        print('Test: Pop on empty stack')
        stacks = Stacks(num_stacks, stack_size)

    def test_push_on_full(self, num_stacks, stack_size):
        print('Test: Push to full stack')
        stacks = Stacks(num_stacks, stack_size)
        for i in range(0, stack_size):
            stacks.push(2, i)
        stacks.push(2, stack_size)

    def test_stacks(self, num_stacks, stack_size):
        print('Test: Push to non-full stack')
        stacks = Stacks(num_stacks, stack_size)
        stacks.push(0, 1)
        stacks.push(0, 2)
        stacks.push(1, 3)
        stacks.push(2, 4)

        print('Test: Pop on non-empty stack')
        self.assertEqual(stacks.pop(0), 2)
        self.assertEqual(stacks.pop(0), 1)
        self.assertEqual(stacks.pop(1), 3)
        self.assertEqual(stacks.pop(2), 4)

        print('Success: test_stacks\n')

def main():
    num_stacks = 3
    stack_size = 100
    test = TestStacks()
    test.assertRaises(Exception, test.test_pop_on_empty, num_stacks,
    test.assertRaises(Exception, test.test_push_on_full, num_stacks,
    test.test_stacks(num_stacks, stack_size)

if __name__ == '__main__':
In [3]:
run -i
Test: Pop on empty stack
Test: Push to full stack
Test: Push to non-full stack
Test: Pop on non-empty stack
Success: test_stacks

In [ ]: