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

# Solution Notebook¶

## Constraints¶

• Can we assume this is a stack of ints?
• Yes
• Can we assume the input values for push are valid?
• Yes
• If we call this function on an empty stack, can we return sys.maxsize?
• Yes
• Can we assume we already have a stack class that can be used for this problem?
• Yes
• Can we assume this fits memory?
• Yes

## Test Cases¶

• Push/pop on empty stack
• Push/pop on non-empty stack
• Min on empty stack
• Min on non-empty stack

## Algorithm¶

We'll use a second stack to keep track of the minimum values.

### Min¶

• If the second stack is empty, return an error code (max int value)
• Else, return the top of the stack, without popping it

Complexity:

• Time: O(1)
• Space: O(1)

### Push¶

• Push the data
• If the data is less than min
• Push data to second stack

Complexity:

• Time: O(1)
• Space: O(1)

### Pop¶

• Pop the data
• If the data is equal to min
• Pop the top of the second stack
• Return the data

Complexity:

• Time: O(1)
• Space: O(1)

## Code¶

In [1]:
%run ../stack/stack.py

In [2]:
import sys

class StackMin(Stack):

def __init__(self, top=None):
super(StackMin, self).__init__(top)
self.stack_of_mins = Stack()

def minimum(self):
if self.stack_of_mins.top is None:
return sys.maxsize
else:
return self.stack_of_mins.peek()

def push(self, data):
super(StackMin, self).push(data)
if data < self.minimum():
self.stack_of_mins.push(data)

def pop(self):
data = super(StackMin, self).pop()
if data == self.minimum():
self.stack_of_mins.pop()
return data


## Unit Test¶

In [3]:
%%writefile test_stack_min.py
import unittest

class TestStackMin(unittest.TestCase):

def test_stack_min(self):
print('Test: Push on empty stack, non-empty stack')
stack = StackMin()
stack.push(5)
self.assertEqual(stack.peek(), 5)
self.assertEqual(stack.minimum(), 5)
stack.push(1)
self.assertEqual(stack.peek(), 1)
self.assertEqual(stack.minimum(), 1)
stack.push(3)
self.assertEqual(stack.peek(), 3)
self.assertEqual(stack.minimum(), 1)
stack.push(0)
self.assertEqual(stack.peek(), 0)
self.assertEqual(stack.minimum(), 0)

print('Test: Pop on non-empty stack')
self.assertEqual(stack.pop(), 0)
self.assertEqual(stack.minimum(), 1)
self.assertEqual(stack.pop(), 3)
self.assertEqual(stack.minimum(), 1)
self.assertEqual(stack.pop(), 1)
self.assertEqual(stack.minimum(), 5)
self.assertEqual(stack.pop(), 5)
self.assertEqual(stack.minimum(), sys.maxsize)

print('Test: Pop empty stack')
self.assertEqual(stack.pop(), None)

print('Success: test_stack_min')

def main():
test = TestStackMin()
test.test_stack_min()

if __name__ == '__main__':
main()

Overwriting test_stack_min.py

In [4]:
run -i test_stack_min.py

Test: Push on empty stack, non-empty stack
Test: Pop on non-empty stack
Test: Pop empty stack
Success: test_stack_min