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

Solution Notebook

Problem: Implement SetOfStacks that wraps a list of stacks, where each stack is bound by a capacity.


  • Can we assume we already have a stack class that can be used for this problem?
    • Yes
  • Are all stack bound by the same capacity?
    • Yes
  • If a stack becomes full, should automatically create one?
    • Yes
  • If a stack becomes empty, should we delete it?
    • Yes
  • If we pop on an empty stack, should we return None?
    • Yes
  • Can we assume this fits memory?
    • Yes

Test Cases

  • Push and pop on an empty stack
  • Push and pop on a non-empty stack
  • Push on a capacity stack to create a new one
  • Pop on a stack to destroy it



  • If there are no stacks or the last stack is full
    • Create a new stack
  • Push to the new stack


  • Time: O(1)
  • Space: O(m), where m is the size of the new stack if the last stack is full


  • If there are no stacks, return None
  • Else if the last stack has one element
    • Pop the last element's data
    • Delete the now empty stack
    • Update the last stack pointer
  • Else Pop the last element's data
  • Return the last element's data


  • Time: O(1)
  • Space: O(1)


In [1]:
%run ../stack/
In [2]:
class StackWithCapacity(Stack):

    def __init__(self, top=None, capacity=10):
        super(StackWithCapacity, self).__init__(top)
        self.capacity = capacity
        self.num_items = 0

    def push(self, data):
        if self.is_full():
            raise Exception('Stack full')
        super(StackWithCapacity, self).push(data)
        self.num_items += 1

    def pop(self):
        self.num_items -= 1
        return super(StackWithCapacity, self).pop()

    def is_full(self):
        return self.num_items == self.capacity

    def is_empty(self):
        return self.num_items == 0

class SetOfStacks(object):

    def __init__(self, indiv_stack_capacity):
        self.indiv_stack_capacity = indiv_stack_capacity
        self.stacks = []
        self.last_stack = None

    def push(self, data):
        if self.last_stack is None or self.last_stack.is_full():
            self.last_stack = StackWithCapacity(None, self.indiv_stack_capacity)

    def pop(self):
        if self.last_stack is None:
            return None
        data = self.last_stack.pop()
        if self.last_stack.is_empty():
            self.last_stack = self.stacks[-1] if self.stacks else None
        return data

Unit Test

In [3]:
import unittest

class TestSetOfStacks(unittest.TestCase):

    def test_set_of_stacks(self):
        print('Test: Push on an empty stack')
        stacks = SetOfStacks(indiv_stack_capacity=2)

        print('Test: Push on a non-empty stack')

        print('Test: Push on a capacity stack to create a new one')

        print('Test: Pop on a stack to destroy it')
        self.assertEqual(stacks.pop(), 'a')

        print('Test: Pop general case')
        self.assertEqual(stacks.pop(), 5)
        self.assertEqual(stacks.pop(), 3)

        print('Test: Pop on no elements')
        self.assertEqual(stacks.pop(), None)

        print('Success: test_set_of_stacks')

def main():
    test = TestSetOfStacks()

if __name__ == '__main__':
In [4]:
%run -i
Test: Push on an empty stack
Test: Push on a non-empty stack
Test: Push on a capacity stack to create a new one
Test: Pop on a stack to destroy it
Test: Pop general case
Test: Pop on no elements
Success: test_set_of_stacks