160. Intersection of Two Linked Lists - Explanation
Description
You are given the heads of two singly linked-lists headA and headB, return the node at which the two lists intersect. If the two linked lists have no intersection at all, return null.
Note that the linked lists must retain their original structure after the function returns.
Custom Judge:
The inputs to the judge are given as follows (your program is not given these inputs):
intersectVal- The value of the node where the intersection occurs. This is0if there is no intersected node.listA- The first linked list.listB- The second linked list.skipA- The number of nodes to skip ahead inlistA(starting from the head) to get to the intersected node.skipB- The number of nodes to skip ahead inlistB(starting from the head) to get to the intersected node.
The judge will then create the linked structure based on these inputs and pass the two heads, headA and headB to your program. If you correctly return the intersected node, then your solution will be accepted.
Example 1:
Input: intersectVal = 8, listA = [4,1,8,4,5], listB = [5,6,1,8,4,5], skipA = 2, skipB = 3
Output: 8Example 2:
Input: intersectVal = 0, listA = [2,6,4], listB = [1,5], skipA = 3, skipB = 2
Output: nullConstraints:
- The number of nodes of
listAis in them. - The number of nodes of
listBis in then. 1 <= m, n <= 30,0001 <= Node.val <= 100,0000 <= skipA <= m0 <= skipB <= n- intersectVal is
0iflistAandlistBdo not intersect. intersectVal == listA[skipA] == listB[skipB]iflistAandlistBintersect.
Follow up: Could you write a solution that runs in O(m + n) time and use only O(1) memory?
Topics
Prerequisites
Before attempting this problem, you should be comfortable with:
- Linked Lists - Traversing singly linked lists and understanding node references vs values
- Hash Set - Using sets to store and lookup node references in O(1) time
- Two Pointers - Manipulating two pointers simultaneously to traverse linked structures
- List Length Calculation - Computing the length of a linked list by traversal
1. Brute Force
Intuition
The most straightforward approach is to check every node in the first list against every node in the second list. If two nodes are the same object (not just equal values), we found the intersection point. This works because intersection means the lists share actual node references, not just duplicate values.
Algorithm
- Start with
headAand traverse the first list. - For each node in the first list, traverse the entire second list.
- If any node in the second list matches the current node from the first list (by reference), return it.
- If no intersection is found after checking all nodes, return
null.
# Definition for singly-linked list.
# class ListNode:
# def __init__(self, x):
# self.val = x
# self.next = None
class Solution:
def getIntersectionNode(self, headA: ListNode, headB: ListNode) -> Optional[ListNode]:
while headA:
cur = headB
while cur:
if headA == cur:
return headA
cur = cur.next
headA = headA.next
return NoneTime & Space Complexity
- Time complexity:
- Space complexity: extra space.
Where is the length of the first list and is the length of the second list.
2. Hash Set
Intuition
We can use a hash set to store all nodes from the first list. Then, as we traverse the second list, we check if each node exists in the set. The first node found in the set is the intersection point since it is the earliest shared node.
Algorithm
- Traverse the first list and add every node to a hash set.
- Traverse the second list.
- For each node in the second list, check if it exists in the set.
- Return the first matching node, or
nullif no intersection exists.
# Definition for singly-linked list.
# class ListNode:
# def __init__(self, x):
# self.val = x
# self.next = None
class Solution:
def getIntersectionNode(self, headA: ListNode, headB: ListNode) -> Optional[ListNode]:
nodeSet = set()
cur = headA
while cur:
nodeSet.add(cur)
cur = cur.next
cur = headB
while cur:
if cur in nodeSet:
return cur
cur = cur.next
return NoneTime & Space Complexity
- Time complexity:
- Space complexity:
Where is the length of the first list and is the length of the second list.
3. Two Pointers - I
Intuition
If the two lists have different lengths, the intersection point is at the same distance from the end of both lists. By computing the lengths and advancing the pointer on the longer list by the difference, we align the two pointers. Then we move both forward together until they meet at the intersection or reach the end.
Algorithm
- Compute the lengths
mandnof both lists. - Identify the longer list and advance its pointer by
|m - n|nodes. - Move both pointers forward one step at a time.
- When they point to the same node, return it. If they both reach
null, returnnull.
# Definition for singly-linked list.
# class ListNode:
# def __init__(self, x):
# self.val = x
# self.next = None
class Solution:
def getIntersectionNode(self, headA: ListNode, headB: ListNode) -> Optional[ListNode]:
def getLength(head):
length, cur = 0, head
while cur:
length += 1
cur = cur.next
return length
m = getLength(headA)
n = getLength(headB)
l1, l2 = headA, headB
if m < n:
m, n = n, m
l1, l2 = headB, headA
while m - n:
m -= 1
l1 = l1.next
while l1 != l2:
l1 = l1.next
l2 = l2.next
return l1Time & Space Complexity
- Time complexity:
- Space complexity: extra space.
Where is the length of the first list and is the length of the second list.
4. Two Pointers - II
Intuition
A clever approach avoids computing lengths explicitly. Two pointers start at the heads of each list. When a pointer reaches the end, it jumps to the head of the other list. After at most m + n steps, both pointers will have traversed the same total distance. If an intersection exists, they will meet there; otherwise, they both reach null simultaneously.
Algorithm
- Initialize
l1 = headAandl2 = headB. - While
l1 != l2:- If
l1isnull, setl1 = headB; otherwise advancel1. - If
l2isnull, setl2 = headA; otherwise advancel2.
- If
- Return
l1(which equalsl2), the intersection node ornull.
# Definition for singly-linked list.
# class ListNode:
# def __init__(self, x):
# self.val = x
# self.next = None
class Solution:
def getIntersectionNode(self, headA: ListNode, headB: ListNode) -> Optional[ListNode]:
l1, l2 = headA, headB
while l1 != l2:
l1 = l1.next if l1 else headB
l2 = l2.next if l2 else headA
return l1Time & Space Complexity
- Time complexity:
- Space complexity: extra space.
Where is the length of the first list and is the length of the second list.
Common Pitfalls
Comparing Node Values Instead of References
Intersection means the lists share the same node object, not just nodes with equal values. Using nodeA.val == nodeB.val will give false positives. You must compare node references directly (nodeA == nodeB or nodeA === nodeB in JavaScript) to correctly identify shared nodes.
Not Handling Non-Intersecting Lists
When two lists do not intersect, the two-pointer approach naturally terminates when both pointers become null simultaneously. However, some implementations create infinite loops by not properly handling the case where pointers should redirect to the other list's head. Ensure your loop condition checks for pointer equality including the null == null case.
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