This notebook was prepared by [Donne Martin](http://donnemartin.com). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges).

Solution Notebook

Problem: Implement n stacks using a single array.

Constraints
Test Cases
Algorithm
Code
Unit Test

Constraints

Are the stacks and array a fixed size?
- 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

Algorithm

Absolute Index

return stack size * stack index + stack pointer

Complexity:

Time: O(1)
Space: O(1)

Push

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

Complexity:

Time: O(1)
Space: O(1)

Pop

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

Complexity:

Time: O(1)
Space: O(1)

Code



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] * num_stacks
        self.stack_array = [None] * num_stacks * 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')
        else:
            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')
        else:
            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]:

    
%%writefile test_n_stacks.py
from nose.tools import assert_equal
from nose.tools import raises


class TestStacks(object):

    @raises(Exception)
    def test_pop_on_empty(self, num_stacks, stack_size):
        print('Test: Pop on empty stack')
        stacks = Stacks(num_stacks, stack_size)
        stacks.pop(0)

    @raises(Exception)
    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')
        assert_equal(stacks.pop(0), 2)
        assert_equal(stacks.pop(0), 1)
        assert_equal(stacks.pop(1), 3)
        assert_equal(stacks.pop(2), 4)

        print('Success: test_stacks\n')


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


if __name__ == '__main__':
    main()









    



Overwriting test_n_stacks.py



In [3]:

    
run -i test_n_stacks.py









    



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