Longest Increasing Subsequence in given Linked List

Given a sequence of numbers in the form of a linked list lis. Find the length of the Longest Increasing Subsequence(LIS) of the given Linked List.

Examples:

Input:  list = 3->10->2->1->20
Output: 3
Explanation: The longest increasing subsequence is 3->10-> 20

Input:  list = 3-> 2
Output: 1
Explanation: The longest increasing subsequence are 3 and 2

Input: list = 50->3->10->7->40->80
Output: Length of LIS = 4
Explanation: The longest increasing subsequence is {3->7->40->80} or {3->10->40->80}

Approach: The basic intuition of the solution is to start iterating from the first node to the end of linked list .In the process of moving calculate length of LIS ending at every node and store it in a count variable. Finally, calculate maximum count value among all nodes. Follow the steps mentioned below to solve the problem: 

• Traverse the linked list from the starting node.
  • LIS length of  a  linked list with one node is 1 .So we initialize  every node count variable to 1.
  • For every ith node traverse the first (i-1) nodes and do the following:
    • if value of current node is greater than the value of previous node, extend  sequence length.
    • As maximum length ending with current  node is required. select node from first (i-1) nodes which satisfy the previous condition and have maximum count value .
• Once all the nodes are traversed following the above procedure .find maximum count value among all nodes.
• The maximum count value is the required length of the LIS.

Below is the implementation of the above approach:

C++

// C++ program to find LIS on LinkedList
#include <bits/stdc++.h>
using namespace std;

// Structure of a node
class Node {
public:
    int data;
    struct Node* next;

    // "count" variable is to keep track
    // of LIS_LENGTH ending with
    // that particular element
    int count;
};

// Function to find the length of the LIS
int LIS(struct Node* head)
{
    // If linked list is empty length is 0
    if (head == NULL)
        return 0;

    // If linked list has only one node
    // LIS length is 1
    if (head->next == NULL)
        return 1;
    Node* curr_p = head->next;

    // This loop calculates what is
    // LIS_LENGTH ending with each and
    // every node and stores in
    // curr->count variable
    while (curr_p != NULL) {
        int maxi = 0;
        Node* prev_p = head;

        // This while loop traverse all nodes
        // before curr_p and finds which node
        // to extend so that maximum LIS
        // length ending with curr_P can be
        while (prev_p != curr_p) {

            // Only extend if present data
            // greater than previous value
            if (curr_p->data
                > prev_p->data) {
                if (prev_p->count > maxi) {
                    maxi = prev_p->count;
                }
            }
            prev_p = prev_p->next;
        }
        curr_p->count = 1 + maxi;
        curr_p = curr_p->next;
    }
    int LIS_length = 0;
    curr_p = head;

    // Finding Maximum LIS_LENGTH
    while (curr_p != NULL) {
        if (LIS_length < curr_p->count) {
            LIS_length = curr_p->count;
        }
        curr_p = curr_p->next;
    }
    return LIS_length;
}

// Function to push a node in linked list
void push(struct Node** head_ref,
          int new_data)
{
    // Allocate node
    Node* new_node = new Node();

    // Put in the data
    new_node->data = new_data;

    // Link the old list with the new node
    new_node->next = (*head_ref);

    // Assign count value to 1
    new_node->count = 1;

    // Move the head to point the new node
    (*head_ref) = new_node;
}

// Driver code
int main()
{
    // Start with the empty list
    struct Node* head = NULL;

    // Create a linked list
    // Created linked list will be
    // 3->10->2->1->20
    push(&head, 20);
    push(&head, 1);
    push(&head, 2);
    push(&head, 10);
    push(&head, 3);

    // Call LIS function which calculates
    // LIS of Linked List
    int ans = LIS(head);
    cout << ans;
    return 0;
}

Java

// Java program to find LIS on LinkedList

import java.util.*;

class GFG{

// Structure of a node
static class Node {
    int data;
    Node next;

    // "count" variable is to keep track
    // of LIS_LENGTH ending with
    // that particular element
    int count;
};

// Function to find the length of the LIS
static int LIS(Node head)
{
    // If linked list is empty length is 0
    if (head == null)
        return 0;

    // If linked list has only one node
    // LIS length is 1
    if (head.next == null)
        return 1;
    Node curr_p = head.next;

    // This loop calculates what is
    // LIS_LENGTH ending with each and
    // every node and stores in
    // curr.count variable
    while (curr_p != null) {
        int maxi = 0;
        Node prev_p = head;

        // This while loop traverse all nodes
        // before curr_p and finds which node
        // to extend so that maximum LIS
        // length ending with curr_P can be
        while (prev_p != curr_p) {

            // Only extend if present data
            // greater than previous value
            if (curr_p.data
                > prev_p.data) {
                if (prev_p.count > maxi) {
                    maxi = prev_p.count;
                }
            }
            prev_p = prev_p.next;
        }
        curr_p.count = 1 + maxi;
        curr_p = curr_p.next;
    }
    int LIS_length = 0;
    curr_p = head;

    // Finding Maximum LIS_LENGTH
    while (curr_p != null) {
        if (LIS_length < curr_p.count) {
            LIS_length = curr_p.count;
        }
        curr_p = curr_p.next;
    }
    return LIS_length;
}

// Function to push a node in linked list
static Node push(Node head_ref,
          int new_data)
{
    // Allocate node
    Node new_node = new Node();

    // Put in the data
    new_node.data = new_data;

    // Link the old list with the new node
    new_node.next = head_ref;

    // Assign count value to 1
    new_node.count = 1;

    // Move the head to point the new node
    head_ref = new_node;
    return head_ref;
}

// Driver code
public static void main(String[] args)
{
    // Start with the empty list
    Node head = null;

    // Create a linked list
    // Created linked list will be
    // 3.10.2.1.20
    head = push(head, 20);
    head = push(head, 1);
    head = push(head, 2);
    head = push(head, 10);
    head = push(head, 3);

    // Call LIS function which calculates
    // LIS of Linked List
    int ans = LIS(head);
    System.out.print(ans);
}
}

// This code is contributed by 29AjayKumar

Python3

# Python code for the above approach

# Structure of a node
class Node:

    def __init__(self, d):
        self.data = d
        self.next = None
        self.count = 1

    # "count" variable is to keep track
    # of LIS_LENGTH ending with
    # that particular element

# Function to find the length of the LIS
def LIS(head):

    # If linked list is empty length is 0
    if (head == None):
        return 0

    # If linked list has only one node
    # LIS length is 1
    if (head.next == None):
        return 1
    curr_p = head.next

    # This loop calculates what is
    # LIS_LENGTH ending with each and
    # every node and stores in
    # curr.count variable
    while (curr_p != None):
        maxi = 0
        prev_p = head

        # This while loop traverse all nodes
        # before curr_p and finds which node
        # to extend so that maximum LIS
        # length ending with curr_P can be
        while (prev_p != curr_p):

            # Only extend if present data
            # greater than previous value
            if (curr_p.data > prev_p.data):
                if (prev_p.count > maxi):
                    maxi = prev_p.count
            prev_p = prev_p.next

        curr_p.count = 1 + maxi
        curr_p = curr_p.next

    LIS_length = 0
    curr_p = head

    # Finding Maximum LIS_LENGTH
    while (curr_p != None):
        if (LIS_length < curr_p.count):
            LIS_length = curr_p.count
        curr_p = curr_p.next

    return LIS_length

# Driver code

# Start with the empty list
# Create a linked list
# Created linked list will be
# 3->10->2->1->20
head = Node(3)
head.next = Node(10)
head.next.next = Node(2)
head.next.next.next = Node(1)
head.next.next.next.next = Node(20)

# Call LIS function which calculates
# LIS of Linked List
ans = LIS(head)
print(ans)

# This code is contributed by Saurabh Jaiswal

C#

// C# program to find LIS on List
using System;
using System.Collections.Generic;

public class GFG {

  // Structure of a node
  public class Node {
    public int data;
    public Node next;

    // "count" variable is to keep track
    // of LIS_LENGTH ending with
    // that particular element
    public int count;
  };

  // Function to find the length of the LIS
  static int LIS(Node head)
  {

    // If linked list is empty length is 0
    if (head == null)
      return 0;

    // If linked list has only one node
    // LIS length is 1
    if (head.next == null)
      return 1;
    Node curr_p = head.next;

    // This loop calculates what is
    // LIS_LENGTH ending with each and
    // every node and stores in
    // curr.count variable
    while (curr_p != null) {
      int maxi = 0;
      Node prev_p = head;

      // This while loop traverse all nodes
      // before curr_p and finds which node
      // to extend so that maximum LIS
      // length ending with curr_P can be
      while (prev_p != curr_p) {

        // Only extend if present data
        // greater than previous value
        if (curr_p.data > prev_p.data) {
          if (prev_p.count > maxi) {
            maxi = prev_p.count;
          }
        }
        prev_p = prev_p.next;
      }
      curr_p.count = 1 + maxi;
      curr_p = curr_p.next;
    }
    int LIS_length = 0;
    curr_p = head;

    // Finding Maximum LIS_LENGTH
    while (curr_p != null) {
      if (LIS_length < curr_p.count) {
        LIS_length = curr_p.count;
      }
      curr_p = curr_p.next;
    }
    return LIS_length;
  }

  // Function to push a node in linked list
  static Node push(Node head_ref, int new_data)
  {

    // Allocate node
    Node new_node = new Node();

    // Put in the data
    new_node.data = new_data;

    // Link the old list with the new node
    new_node.next = head_ref;

    // Assign count value to 1
    new_node.count = 1;

    // Move the head to point the new node
    head_ref = new_node;
    return head_ref;
  }

  // Driver code
  public static void Main(String[] args)
  {

    // Start with the empty list
    Node head = null;

    // Create a linked list
    // Created linked list will be
    // 3.10.2.1.20
    head = push(head, 20);
    head = push(head, 1);
    head = push(head, 2);
    head = push(head, 10);
    head = push(head, 3);

    // Call LIS function which calculates
    // LIS of Linked List
    int ans = LIS(head);
    Console.Write(ans);
  }
}

// This code is contributed by Rajput-Ji

Javascript

<script>
      // JavaScript code for the above approach

      // Structure of a node
      class Node {

          constructor(d) {
              this.data = d;
              this.next = null;
              this.count = 1;
          }

          // "count" variable is to keep track
          // of LIS_LENGTH ending with
          // that particular element

      };

      // Function to find the length of the LIS
      function LIS(head)
      {

          // If linked list is empty length is 0
          if (head == null)
              return 0;

          // If linked list has only one node
          // LIS length is 1
          if (head.next == null)
              return 1;
          let curr_p = head.next;

          // This loop calculates what is
          // LIS_LENGTH ending with each and
          // every node and stores in
          // curr.count variable
          while (curr_p != null) {
              let maxi = 0;
              let prev_p = head;

              // This while loop traverse all nodes
              // before curr_p and finds which node
              // to extend so that maximum LIS
              // length ending with curr_P can be
              while (prev_p != curr_p) {

                  // Only extend if present data
                  // greater than previous value
                  if (curr_p.data
                      > prev_p.data) {
                      if (prev_p.count > maxi) {
                          maxi = prev_p.count;
                      }
                  }
                  prev_p = prev_p.next;
              }
              curr_p.count = 1 + maxi;
              curr_p = curr_p.next;
          }
          let LIS_length = 0;
          curr_p = head;

          // Finding Maximum LIS_LENGTH
          while (curr_p != null) {
              if (LIS_length < curr_p.count) {
                  LIS_length = curr_p.count;
              }
              curr_p = curr_p.next;
          }
          return LIS_length;
      }


      // Driver code

      // Start with the empty list

      // Create a linked list
      // Created linked list will be
      // 3->10->2->1->20
      let head = new Node(3);
      head.next = new Node(10);
      head.next.next = new Node(2);
      head.next.next.next = new Node(1);
      head.next.next.next.next = new Node(20);

      // Call LIS function which calculates
      // LIS of Linked List
      let ans = LIS(head);
      document.write(ans);

     // This code is contributed by Potta Lokesh
  </script>

Output

3

Time Complexity: O(N * N) where N is the length of the linked list
Auxiliary Space: O(N)