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

# Solution Notebook¶

## Constraints¶

• Is this a singly linked list?
• Yes
• Can we assume we are always passed a circular linked list?
• No
• When we find a loop, do we return the node or the node's data?
• The node
• Can we assume we already have a linked list class that can be used for this problem?
• Yes

## Test Cases¶

• Empty list -> None
• Not a circular linked list -> None
• One element
• Two or more elements
• Circular linked list general case

## Algorithm¶

• Use two references slow, fast, initialized to the head
• Increment slow and fast until they meet
• fast is incremented twice as fast as slow
• If fast.next is None, we do not have a circular list
• When slow and fast meet, move slow to the head
• Increment slow and fast one node at a time until they meet
• Where they meet is the start of the loop

Complexity:

• Time: O(n)
• Space: O(1)

## Code¶

In [1]:
%run ../linked_list/linked_list.py

In [2]:
class MyLinkedList(LinkedList):

def find_loop_start(self):
return None
while fast.next is not None:
slow = slow.next
fast = fast.next.next
if fast is None:
return None
if slow == fast:
break
while slow != fast:
slow = slow.next
fast = fast.next
if fast is None:
return None
return slow


## Unit Test¶

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

class TestFindLoopStart(unittest.TestCase):

def test_find_loop_start(self):
print('Test: Empty list')

print('Test: Not a circular linked list: One element')

print('Test: Not a circular linked list: Two elements')

print('Test: Not a circular linked list: Three or more elements')

print('Test: General case: Circular linked list')
node10 = Node(10)
node9 = Node(9, node10)
node8 = Node(8, node9)
node7 = Node(7, node8)
node6 = Node(6, node7)
node5 = Node(5, node6)
node4 = Node(4, node5)
node3 = Node(3, node4)
node2 = Node(2, node3)
node1 = Node(1, node2)
node0 = Node(0, node1)
node10.next = node3

print('Success: test_find_loop_start')

def main():
test = TestFindLoopStart()
test.test_find_loop_start()

if __name__ == '__main__':
main()

Overwriting test_find_loop_start.py

In [4]:
%run -i test_find_loop_start.py

Test: Empty list
Test: Not a circular linked list: One element
Test: Not a circular linked list: Two elements
Test: Not a circular linked list: Three or more elements
Test: General case: Circular linked list
Success: test_find_loop_start