Determine If Two Linked Lists Intersect
Question
Given 2 linked list head pointers, determine whether they intersect at some point.
Solution
First of all, linked list can have loop or not, and this gives 3 possible situations.

For the 2 loops head pointer 1 and head pointer 2, move pointer 1 at normal speed, and pointer 2 at double speed. If they intersect, node will be the same at some point. Otherwise infinity loop occurs. (need to be fixed)

For 2 straight linked list, they would have the same tails if they intersect.

For a loop and a straight list, use the first algorithm and let the loop to move at double speed. If they don’t intersect, tail of the straight list will end the checking.
So one of the key idea is to check if a linked list is loop. Since loop may start not at the head, we can not use head pointer as the checking reference. We could instead use the algorithm 1 against itself, if it has loop the 2 moving pointer will meet at some point.
Sample Code
# node structure
class Node:
def __init__(self, value, next_node=None):
self.value = value
self.next = next_node
# check if the list has loop and return the length of the list
def is_loop(head):
if not head: return 0
slow = fast = head
while fast and fast.next:
slow = slow.next
fast = fast.next.next
if slow == fast:
count = 1
slow = slow.next
while(slow != fast):
slow = slow.next
count += 1
return count
return 0
# check meet up if list is loop
def check_intersect_with_loop(head_1, head_2, length_1, length_2): # todo: infinite loop if not meeting up
counter = length_1 * length_2
while head_1 != head_2 and head_1 and head_2 and counter > 0:
head_1 = head_1.next
head_2 = head_2.next
if head_2.next: head_2 = head_2.next
counter = 1
return head_1 == head_2 and head_1 is not None and head_2 is not None
# check meet up if list is not loop
def check_intersect_without_loop(head_1, head_2):
tail_1 = head_1
tail_2 = head_2
while tail_1.next: tail_1 = tail_1.next
while tail_2.next: tail_2 = tail_2.next
return tail_1 == tail_2
# combine both
def check_intersect(head_1, head_2):
loop_length_list_1 = is_loop(head_1)
loop_length_list_2 = is_loop(head_2)
if loop_length_list_1 > 0 and loop_length_list_2 > 0:
print '> check_intersect_with_loop'
return check_intersect_with_loop(head_1, head_2, loop_length_list_1, loop_length_list_2)
elif loop_length_list_1 == 0 and loop_length_list_2 == 0:
print '> check_intersect_without_loop'
return check_intersect_without_loop(head_1, head_2)
return False
# list 1
node_9 = Node(9)
node_8 = Node(8, node_9) # meet of list 1 and 2
node_7 = Node(7, node_8)
node_6 = Node(6, node_7)
node_5 = Node(5, node_6)
head_1 = node_5
assert is_loop(head_1) == False
# list 2, will meet with list 1
node_4 = Node(4, node_8)
node_3 = Node(3, node_4)
node_2 = Node(2, node_3)
head_2 = node_2
assert is_loop(head_2) == False
# list 3, separate list
node_1 = Node(1)
node_0 = Node(0, node_1)
head_3 = node_0
assert is_loop(head_3) == False
# list 4 with loop
node_15 = Node(15)
node_14 = Node(14, node_15)
node_13 = Node(13, node_14)
node_12 = Node(12, node_13)
node_11 = Node(11, node_12)
node_15.next = node_11
head_4 = node_11
assert is_loop(head_4) # true
# list 5 same loop with 4
node_25 = Node(25, node_14)
node_24 = Node(24, node_25)
head_5 = node_24
assert is_loop(head_5) # true
# list 6, separate loop
node_35 = Node(35)
node_34 = Node(34, node_35)
node_35.next = node_34
head_6 = node_34
assert is_loop(head_6) # true
# checking print
print "checking list 1 and 2"
assert check_intersect(head_1, head_2) == True
print "checking list 1 and 3"
assert check_intersect(head_1, head_3) == False
print "checking list 4 and 5"
assert check_intersect(head_4, head_5) == True
print "checking list 4 and 6"
assert check_intersect(head_4, head_6) == False
print "all good"