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

Solution Notebook

Problem: Partition a linked list around a value x, such that all nodes less than x come before all nodes greater than or equal to x.

Constraints

  • Can we assume this is a non-circular, singly linked list?
    • Yes
  • Do we expect the function to return a new list?
    • Yes
  • Can we assume the input x is valid?
    • Yes
  • Can we assume we already have a linked list class that can be used for this problem?
    • Yes
  • Can we create additional data structures?
    • Yes
  • Can we assume this fits in memory?
    • Yes

Test Cases

  • Empty list -> []
  • One element list -> [element]
  • Left linked list is empty
  • Right linked list is empty
  • General case
    • Partition = 10
    • Input: 4, 3, 13, 8, 10, 1, 10, 12
    • Output: 4, 3, 8, 1, 10, 10, 13, 12

Algorithm

  • Create left and right linked lists
  • For each element in the list
    • If elem < x, append to the left list
    • else, append to the right list
  • Merge left and right lists

Complexity:

  • Time: O(n)
  • Space: O(n)

Code

In [1]:
%run ../linked_list/linked_list.py
In [2]:
class MyLinkedList(LinkedList):

    def partition(self, data):
        if self.head is None:
            return
        left = MyLinkedList(None)
        right = MyLinkedList(None)
        curr = self.head

        # Build the left and right lists
        while curr is not None:
            if curr.data < data:
                left.append(curr.data)
            elif curr.data == data:
                right.insert_to_front(curr.data)
            else:
                right.append(curr.data)
            curr = curr.next
        curr_left = left.head
        if curr_left is None:
            return right
        else:
            # Merge the two lists
            while curr_left.next is not None:
                curr_left = curr_left.next
            curr_left.next = right.head
            return left

Unit Test

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


class TestPartition(unittest.TestCase):

    def test_partition(self):
        print('Test: Empty list')
        linked_list = MyLinkedList(None)
        linked_list.partition(10)
        self.assertEqual(linked_list.get_all_data(), [])

        print('Test: One element list, left list empty')
        linked_list = MyLinkedList(Node(5))
        linked_list.partition(0)
        self.assertEqual(linked_list.get_all_data(), [5])

        print('Test: Right list is empty')
        linked_list = MyLinkedList(Node(5))
        linked_list.partition(10)
        self.assertEqual(linked_list.get_all_data(), [5])

        print('Test: General case')
        # Partition = 10
        # Input: 4, 3, 13, 8, 10, 1, 14, 10, 12
        # Output: 4, 3, 8, 1, 10, 10, 13, 14, 12
        linked_list = MyLinkedList(Node(12))
        linked_list.insert_to_front(10)
        linked_list.insert_to_front(14)
        linked_list.insert_to_front(1)
        linked_list.insert_to_front(10)
        linked_list.insert_to_front(8)
        linked_list.insert_to_front(13)
        linked_list.insert_to_front(3)
        linked_list.insert_to_front(4)
        partitioned_list = linked_list.partition(10)
        self.assertEqual(partitioned_list.get_all_data(),
                     [4, 3, 8, 1, 10, 10, 13, 14, 12])

        print('Success: test_partition')


def main():
    test = TestPartition()
    test.test_partition()


if __name__ == '__main__':
    main()
Overwriting test_partition.py
In [4]:
run -i test_partition.py
Test: Empty list
Test: One element list, left list empty
Test: Right list is empty
Test: General case
Success: test_partition