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

# Solution Notebook¶

## Constraints¶

• 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

## Algorithm¶

### Push¶

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

Complexity:

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

### Pop¶

• 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

Complexity:

• Time: O(1)
• Space: O(1)

## Code¶

In [1]:
%run ../stack/stack.py

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)
self.stacks.append(self.last_stack)
self.last_stack.push(data)

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


## Unit Test¶

In [3]:
%%writefile test_set_of_stacks.py
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)
stacks.push(3)

print('Test: Push on a non-empty stack')
stacks.push(5)

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

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()
test.test_set_of_stacks()

if __name__ == '__main__':
main()

Overwriting test_set_of_stacks.py

In [4]:
%run -i test_set_of_stacks.py

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