There are two singly linked lists in a system. By some programming error, the end node of one of the linked lists got linked to the second list, forming an inverted Y-shaped list. Write a program to get the point where two linked lists merge.
Intersection Point of Two Linked Lists
The above diagram shows an example with two linked lists having 15 as intersection points.
Method 1(Simply use two loops): Use 2 nested for loops. The outer loop will be for each node of the 1st list and the inner loop will be for the 2nd list. In the inner loop, check if any of the nodes of the 2nd list is the same as the current node of the first linked list. The time complexity of this method will be O(M * N) where m and n are the numbers of nodes in two lists.
Below is the code for the above approach:
C++
// C++ program to get intersection point of two linked list
#include <bits/stdc++.h>
usingnamespacestd;
/* Link list node */
classNode {
public:
intdata;
Node* next;
};
/* function to get the intersection point of two linked
Time Complexity: O(m*n), where m and n are number of nodes in two linked list. Auxiliary Space: O(1), Constant Space is used.
Method 2 (Mark Visited Nodes): This solution requires modifications to the basic linked list data structure. Have a visited flag with each node. Traverse the first linked list and keep marking visited nodes. Now traverse the second linked list, If you see a visited node again then there is an intersection point, return the intersecting node. This solution works in O(m+n) but requires additional information with each node. A variation of this solution that doesn’t require modification to the basic data structure can be implemented using a hash. Traverse the first linked list and store the addresses of visited nodes in a hash. Now traverse the second linked list and if you see an address that already exists in the hash then return the intersecting node.
Console.WriteLine("The node of intersection is : "
+ getIntersectNode(head1, head2));
}
}
Javascript
// JavaScript program for the above approach
class Node{
constructor(data){
this.data = data;
this.next = null;
this.visited = false;
}
}
functiongetIntersectNode(head1, head2){
let temp1 = head1;
while(temp1 != null){
temp1.visited = true;
temp1 = temp1.next;
}
temp1 = head2;
while(temp1 != null){
if(temp1.visited)
returntemp1.data;
else
temp1.visited = true;
temp1 = temp1.next;
}
}
// driver program to test above function
let head1 = newNode(1);
head1.next = newNode(2);
head1.next.next = newNode(3);
head1.next.next.next = newNode(4);
head1.next.next.next.next = newNode(5);
head1.next.next.next.next.next = newNode(6);
head1.next.next.next.next.next.next = newNode(7);
// list 2
let head2 = newNode(10);
head2.next = newNode(9);
head2.next.next = newNode(8);
head2.next.next.next = head1.next.next.next;
console.log("The node of intersection is : "+ getIntersectNode(head1, head2));
Output
The node of intersection is : 4
Time Complexity: The time complexity of the getIntersectNode function is O(m+n) where m and n are the lengths of the input linked lists. This is because in the worst case scenario, we need to traverse both lists once to mark visited nodes, and then traverse the second list to find the first node that has already been visited.
Auxiliary space: The auxiliary space required by the program is O(max(m,n)), which is the maximum length of the input linked lists. This is because we are marking visited nodes in the linked lists using a boolean flag, and we need to do this for the entire length of the longer list.
Method 3(Using the difference in node counts)
Get the count of the nodes in the first list, let the count be c1.
Get the count of the nodes in the second list, let the count be c2.
Get the difference of counts d = abs(c1 – c2)
Now traverse the bigger list from the first node to d nodes so that from here onwards both the lists have an equal no of nodes
Then we can traverse both lists in parallel till we come across a common node. (Note that getting a common node is done by comparing the address of the nodes)
Below image is a dry run of the above approach:
Step 1: Traverse the bigger list from the first node to d nodes so that from here onwards both the lists have an equal no of nodes
Step 1
Step 2: Traverse both lists in parallel till we come across a common node
Step 2
Below is the implementation of the above approach :
C++
// C++ program to get intersection point of two linked list
#include <bits/stdc++.h>
usingnamespacestd;
/* Link list node */
classNode {
public:
intdata;
Node* next;
};
/* Function to get the counts of node in a linked list */
intgetCount(Node* head);
/* function to get the intersection point of two linked
lists head1 and head2 where head1 has d more nodes than
Console.WriteLine("The node of intersection is "+ list.getNode());
}
}
// This code is contributed by Arnab Kundu
Javascript
<script>
class Node
{
constructor(item)
{
this.data=item;
this.next=null;
}
}
let head1,head2;
functiongetNode()
{
let c1 = getCount(head1);
let c2 = getCount(head2);
let d;
if(c1 > c2) {
d = c1 - c2;
return_getIntesectionNode(d, head1, head2);
}
else{
d = c2 - c1;
return_getIntesectionNode(d, head2, head1);
}
}
function_getIntesectionNode(d,node1,node2)
{
let i;
let current1 = node1;
let current2 = node2;
for(i = 0; i < d; i++) {
if(current1 == null) {
return-1;
}
current1 = current1.next;
}
while(current1 != null&& current2 != null) {
if(current1.data == current2.data) {
returncurrent1.data;
}
current1 = current1.next;
current2 = current2.next;
}
return-1;
}
functiongetCount(node)
{
let current = node;
let count = 0;
while(current != null) {
count++;
current = current.next;
}
returncount;
}
head1 = newNode(3);
head1.next = newNode(6);
head1.next.next = newNode(9);
head1.next.next.next = newNode(15);
head1.next.next.next.next = newNode(30);
// creating second linked list
head2 = newNode(10);
head2.next = newNode(15);
head2.next.next = newNode(30);
document.write("The node of intersection is "+ getNode());
// This code is contributed by avanitrachhadiya2155
</script>
Output
The node of intersection is 15
Time Complexity: O(m+n) Auxiliary Space: O(1)
Method 4(Make a circle in the first list) Thanks to Saravanan Man for providing the below solution. 1. Traverse the first linked list(count the elements) and make a circular linked list. (Remember the last node so that we can break the circle later on). 2. Now view the problem as finding the loop in the second linked list. So the problem is solved. 3. Since we already know the length of the loop(size of the first linked list) we can traverse those many numbers of nodes in the second list, and then start another pointer from the beginning of the second list. we have to traverse until they are equal, and that is the required intersection point. 4. remove the circle from the linked list.
Time Complexity: O(m+n) Auxiliary Space: O(1)
Method 5 (Reverse the first list and make equations) Thanks to Saravanan Mani for providing this method.
1) Let X be the length of the first linked list until intersection point.
Let Y be the length of the second linked list until the intersection point.
Let Z be the length of the linked list from the intersection point to End of
the linked list including the intersection node.
We Have
X + Z = C1;
Y + Z = C2;
2) Reverse first linked list.
3) Traverse Second linked list. Let C3 be the length of second list - 1.
Now we have
X + Y = C3
We have 3 linear equations. By solving them, we get
X = (C1 + C3 – C2)/2;
Y = (C2 + C3 – C1)/2;
Z = (C1 + C2 – C3)/2;
WE GOT THE INTERSECTION POINT.
4) Reverse first linked list.
Advantage: No Comparison of pointers. Disadvantage: Modifying linked list(Reversing list). Time complexity: O(m+n) Auxiliary Space: O(1)
Method 6 (Traverse both lists and compare addresses of last nodes) This method is only to detect if there is an intersection point or not. (Thanks to NeoTheSaviour for suggesting this)
1) Traverse the list 1, store the last node address
2) Traverse the list 2, store the last node address.
3) If nodes stored in 1 and 2 are same then they are intersecting.
Time Complexity: O(m+n) Auxiliary Space: O(1)
Method 7 (Use Hashing) Basically, we need to find a common node of two linked lists. So we hash all nodes of the first list and then check the second list. 1) Create an empty hash set. 2) Traverse the first linked list and insert all nodes’ addresses in the hash set. 3) Traverse the second list. For every node check if it is present in the hash set. If we find a node in the hash set, return the node.
C++
// C++ program to get intersection point of two linked list
#include <iostream>
#include <unordered_set>
usingnamespacestd;
classNode
{
public:
intdata;
Node* next;
Node(intd)
{
data = d;
next = NULL;
}
};
// function to find the intersection point of two lists
// Java program to get intersection point of two linked list
importjava.util.*;
classNode {
intdata;
Node next;
Node(intd)
{
data = d;
next = null;
}
}
classLinkedListIntersect {
publicstaticvoidmain(String[] args)
{
// list 1
Node n1 = newNode(1);
n1.next = newNode(2);
n1.next.next = newNode(3);
n1.next.next.next = newNode(4);
n1.next.next.next.next = newNode(5);
n1.next.next.next.next.next = newNode(6);
n1.next.next.next.next.next.next = newNode(7);
// list 2
Node n2 = newNode(10);
n2.next = newNode(9);
n2.next.next = newNode(8);
n2.next.next.next = n1.next.next.next;
Print(n1);
Print(n2);
System.out.println(MegeNode(n1, n2).data);
}
// function to print the list
publicstaticvoidPrint(Node n)
{
Node cur = n;
while(cur != null) {
System.out.print(cur.data + " ");
cur = cur.next;
}
System.out.println();
}
// function to find the intersection of two node
publicstaticNode MegeNode(Node n1, Node n2)
{
// define hashset
HashSet<Node> hs = newHashSet<Node>();
while(n1 != null) {
hs.add(n1);
n1 = n1.next;
}
while(n2 != null) {
if(hs.contains(n2)) {
returnn2;
}
n2 = n2.next;
}
returnnull;
}
}
Python3
# Python program to get intersection
# point of two linked list
classNode :
def__init__(self, d):
self.data =d;
self.next=None;
# Function to print the list
defPrint(n):
cur =n;
while(cur !=None) :
print(cur.data, end=" ");
cur =cur.next;
print("");
# Function to find the intersection of two node
defMegeNode(n1, n2):
# Define hashset
hs =set();
while(n1 !=None):
hs.add(n1);
n1 =n1.next;
while(n2 !=None):
if(n2 inhs):
returnn2;
n2 =n2.next;
returnNone;
# Driver code
# list 1
n1 =Node(1);
n1.next=Node(2);
n1.next.next=Node(3);
n1.next.next.next=Node(4);
n1.next.next.next.next=Node(5);
n1.next.next.next.next.next=Node(6);
n1.next.next.next.next.next.next=Node(7);
# list 2
n2 =Node(10);
n2.next=Node(9);
n2.next.next=Node(8);
n2.next.next.next=n1.next.next.next;
Print(n1);
Print(n2);
print(MegeNode(n1, n2).data);
# This code is contributed by _saurabh_jaiswal
C#
// C# program to get intersection point of two linked list
usingSystem;
usingSystem.Collections.Generic;
publicclassNode
{
publicintdata;
publicNode next;
publicNode(intd)
{
data = d;
next = null;
}
}
publicclassLinkedListIntersect
{
publicstaticvoidMain(String[] args)
{
// list 1
Node n1 = newNode(1);
n1.next = newNode(2);
n1.next.next = newNode(3);
n1.next.next.next = newNode(4);
n1.next.next.next.next = newNode(5);
n1.next.next.next.next.next = newNode(6);
n1.next.next.next.next.next.next = newNode(7);
// list 2
Node n2 = newNode(10);
n2.next = newNode(9);
n2.next.next = newNode(8);
n2.next.next.next = n1.next.next.next;
Print(n1);
Print(n2);
Console.WriteLine(MegeNode(n1, n2).data);
}
// function to print the list
publicstaticvoidPrint(Node n)
{
Node cur = n;
while(cur != null)
{
Console.Write(cur.data + " ");
cur = cur.next;
}
Console.WriteLine();
}
// function to find the intersection of two node
publicstaticNode MegeNode(Node n1, Node n2)
{
// define hashset
HashSet<Node> hs = newHashSet<Node>();
while(n1 != null)
{
hs.Add(n1);
n1 = n1.next;
}
while(n2 != null)
{
if(hs.Contains(n2))
{
returnn2;
}
n2 = n2.next;
}
returnnull;
}
}
// This code is contributed by 29AjayKumar
Javascript
<script>
// Javascript program to get intersection
// point of two linked list
class Node
{
constructor(d)
{
this.data = d;
this.next = null;
}
}
// Function to print the list
functionPrint(n)
{
let cur = n;
while(cur != null)
{
document.write(cur.data + " ");
cur = cur.next;
}
document.write("<br>");
}
// Function to find the intersection of two node
functionMegeNode(n1, n2)
{
// Define hashset
let hs = newSet();
while(n1 != null)
{
hs.add(n1);
n1 = n1.next;
}
while(n2 != null)
{
if(hs.has(n2))
{
returnn2;
}
n2 = n2.next;
}
returnnull;
}
// Driver code
// list 1
let n1 = newNode(1);
n1.next = newNode(2);
n1.next.next = newNode(3);
n1.next.next.next = newNode(4);
n1.next.next.next.next = newNode(5);
n1.next.next.next.next.next = newNode(6);
n1.next.next.next.next.next.next = newNode(7);
// list 2
let n2 = newNode(10);
n2.next = newNode(9);
n2.next.next = newNode(8);
n2.next.next.next = n1.next.next.next;
Print(n1);
Print(n2);
document.write(MegeNode(n1, n2).data);
// This code is contributed by rag2127
</script>
Output
1 2 3 4 5 6 7
10 9 8 4 5 6 7
4
The time complexity of this solution is O(n) where n is the length of the longer list. This is because we need to traverse both of the linked lists in order to find the intersection point. And space complexity is O(n) , because we are using unordered set.
Method 8( 2-pointer technique ):
Using Two pointers :
Initialize two pointers ptr1 and ptr2 at head1 and head2.
Traverse through the lists, one node at a time.
When ptr1 reaches the end of a list, then redirect it to head2.
similarly, when ptr2 reaches the end of a list, redirect it to the head1.
Once both of them go through reassigning, they will be equidistant from the collision point
If at any node ptr1 meets ptr2, then it is the intersection node.
After the second iteration if there is no intersection node it returns NULL.
C++
// CPP program to print intersection of lists
#include <bits/stdc++.h>
usingnamespacestd;
/* Link list node */
classNode {
public:
intdata;
Node* next;
};
// A utility function to return intersection node
Node* intersectPoint(Node* head1, Node* head2)
{
// Maintaining two pointers ptr1 and ptr2
// at the head of A and B,
Node* ptr1 = head1;
Node* ptr2 = head2;
// If any one of head is NULL i.e
// no Intersection Point
if(ptr1 == NULL || ptr2 == NULL)
returnNULL;
// Traverse through the lists until they
// reach Intersection node
while(ptr1 != ptr2) {
ptr1 = ptr1->next;
ptr2 = ptr2->next;
// If at any node ptr1 meets ptr2, then it is
// intersection node.Return intersection node.
if(ptr1 == ptr2)
returnptr1;
/* Once both of them go through reassigning,
they will be equidistant from the collision point.*/
// When ptr1 reaches the end of a list, then
// reassign it to the head2.
if(ptr1 == NULL)
ptr1 = head2;
// When ptr2 reaches the end of a list, then
// redirect it to the head1.
if(ptr2 == NULL)
ptr2 = head1;
}
returnptr1;
}
// Function to print intersection nodes
// in a given linked list
voidprint(Node* node)
{
if(node == NULL)
cout << "NULL";
while(node->next != NULL) {
cout << node->data << "->";
node = node->next;
}
cout << node->data;
}
// Driver code
intmain()
{
/*
Create two linked lists
1st Linked list is 3->6->9->15->30
2nd Linked list is 10->15->30
15 30 are elements in the intersection list
*/
Node* newNode;
Node* head1 = newNode();
head1->data = 10;
Node* head2 = newNode();
head2->data = 3;
newNode = newNode();
newNode->data = 6;
head2->next = newNode;
newNode = newNode();
newNode->data = 9;
head2->next->next = newNode;
newNode = newNode();
newNode->data = 15;
head1->next = newNode;
head2->next->next->next = newNode;
newNode = newNode();
newNode->data = 30;
head1->next->next = newNode;
head1->next->next->next = NULL;
Node* intersect_node = NULL;
// Find the intersection node of two linked lists
intersect_node = intersectPoint(head1, head2);
cout << "INTERSEPOINT LIST :";
print(intersect_node);
return0;
}
// This code is contributed by Aditya Kumar (adityakumar129)
C
// c program to print intersection of lists
#include <stdio.h>
#include <stdlib.h>
/* Link list node */
typedefstructNode {
intdata;
structNode* next;
}Node;
// A utility function to return intersection node
Node* intersectPoint(Node* head1, Node* head2)
{
// Maintaining two pointers ptr1 and ptr2
// at the head of A and B,
Node* ptr1 = head1;
Node* ptr2 = head2;
// If any one of head is NULL i.e
// no Intersection Point
if(ptr1 == NULL || ptr2 == NULL)
returnNULL;
// Traverse through the lists until they
// reach Intersection node
while(ptr1 != ptr2) {
ptr1 = ptr1->next;
ptr2 = ptr2->next;
// If at any node ptr1 meets ptr2, then it is
// intersection node.Return intersection node.
if(ptr1 == ptr2)
returnptr1;
/* Once both of them go through reassigning,
they will be equidistant from the collision point.*/
// When ptr1 reaches the end of a list, then
// reassign it to the head2.
if(ptr1 == NULL)
ptr1 = head2;
// When ptr2 reaches the end of a list, then
// redirect it to the head1.
if(ptr2 == NULL)
ptr2 = head1;
}
returnptr1;
}
// Function to print intersection nodes
// in a given linked list
voidprint(Node* node)
{
if(node == NULL)
printf("NULL");
while(node->next != NULL) {
printf("%d->", node->data);
node = node->next;
}
printf("%d", node->data);
}
// Driver code
intmain()
{
/*
Create two linked lists
1st Linked list is 3->6->9->15->30
2nd Linked list is 10->15->30
15 30 are elements in the intersection list
*/
Node* newNode;
Node* head1 = (Node*)malloc(sizeof(Node));
head1->data = 10;
Node* head2 = (Node*)malloc(sizeof(Node));
head2->data = 3;
newNode = (Node*)malloc(sizeof(Node));
newNode->data = 6;
head2->next = newNode;
newNode = (Node*)malloc(sizeof(Node));
newNode->data = 9;
head2->next->next = newNode;
newNode = (Node*)malloc(sizeof(Node));
newNode->data = 15;
head1->next = newNode;
head2->next->next->next = newNode;
newNode = (Node*)malloc(sizeof(Node));
newNode->data = 30;
head1->next->next = newNode;
head1->next->next->next = NULL;
Node* intersect_node = NULL;
// Find the intersection node of two linked lists
intersect_node = intersectPoint(head1, head2);
printf("INTERSEPOINT LIST :");
print(intersect_node);
return0;
}
// This code is contributed by Aditya Kumar (adityakumar129)
Java
// JAVA program to print intersection of lists
importjava.util.*;
classGFG{
/* Link list node */
staticclassNode {
intdata;
Node next;
};
// A utility function to return intersection node
staticNode intersectPoint(Node head1, Node head2)
{
// Maintaining two pointers ptr1 and ptr2
// at the head of A and B,
Node ptr1 = head1;
Node ptr2 = head2;
// If any one of head is null i.e
// no Intersection Point
if(ptr1 == null|| ptr2 == null) {
returnnull;
}
// Traverse through the lists until they
// reach Intersection node
while(ptr1 != ptr2) {
ptr1 = ptr1.next;
ptr2 = ptr2.next;
// If at any node ptr1 meets ptr2, then it is
// intersection node.Return intersection node.
if(ptr1 == ptr2) {
returnptr1;
}
/* Once both of them go through reassigning,
they will be equidistant from the collision point.*/
// When ptr1 reaches the end of a list, then
// reassign it to the head2.
if(ptr1 == null) {
ptr1 = head2;
}
// When ptr2 reaches the end of a list, then
// redirect it to the head1.
if(ptr2 == null) {
ptr2 = head1;
}
}
returnptr1;
}
// Function to print intersection nodes
// in a given linked list
staticvoidprint(Node node)
{
if(node == null)
System.out.print("null");
while(node.next != null) {
System.out.print(node.data+ ".");
node = node.next;
}
System.out.print(node.data);
}
// Driver code
publicstaticvoidmain(String[] args)
{
/*
Create two linked lists
1st Linked list is 3.6.9.15.30
2nd Linked list is 10.15.30
15 30 are elements in the intersection list
*/
Node newNode;
Node head1 = newNode();
head1.data = 10;
Node head2 = newNode();
head2.data = 3;
newNode = newNode();
newNode.data = 6;
head2.next = newNode;
newNode = newNode();
newNode.data = 9;
head2.next.next = newNode;
newNode = newNode();
newNode.data = 15;
head1.next = newNode;
head2.next.next.next = newNode;
newNode = newNode();
newNode.data = 30;
head1.next.next = newNode;
head1.next.next.next = null;
Node intersect_node = null;
// Find the intersection node of two linked lists
intersect_node = intersectPoint(head1, head2);
System.out.print("INTERSEPOINT LIST :");
print(intersect_node);
}
}
// This code is contributed by umadevi9616.
Python3
# Python3 program to print intersection of lists
# Link list node
classNode:
def__init__(self, data =0, next=None):
self.data =data
self.next=next
# A utility function to return intersection node
defintersectPoint(head1, head2):
# Maintaining two pointers ptr1 and ptr2
# at the head of A and B,
ptr1 =head1
ptr2 =head2
# If any one of head is None i.e
# no Intersection Point
if(ptr1 ==Noneorptr2 ==None):
returnNone
# Traverse through the lists until they
# reach Intersection node
while(ptr1 !=ptr2):
ptr1 =ptr1.next
ptr2 =ptr2.next
# If at any node ptr1 meets ptr2, then it is
# intersection node.Return intersection node.
if(ptr1 ==ptr2):
returnptr1
# Once both of them go through reassigning,
# they will be equidistant from the collision point.
// This code is contributed by Tapesh(tapeshdua420)
Output
INTERSECTION POINT :15
Time Complexity: O(M + N), where N and M are the length of the two lists. Auxiliary Space: O(M + N)
Please write comments if you find any bug in the above algorithm or a better way to solve the same problem.
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