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Mean of distinct odd fibonacci nodes in a Linked List
  • Last Updated : 07 Dec, 2020

Given a singly linked list containing N nodes, the task is to find the mean of all the distinct nodes from the list whose data value is an odd Fibonacci number.

Examples:

Input: LL = 5 -> 21 -> 8 ->12-> 3 -> 13 ->144 -> 6
Output 10.5
Explanation:
Fibonacci Nodes present in the Linked List are {5, 21, 8, 3, 13, 144}
Odd Fibonacci Nodes present in the List are {5, 21, 3, 13}
Count of Odd Fibonacci Nodes is 4
Therefore , Mean of Odd Fibonacci Node Values = (5 + 21 + 3 + 13) / 4 = 10.5

Input: LL = 55 -> 3 -> 91 -> 89  -> 76 -> 233 -> 34 -> 87 -> 5 -> 100
Output:77
Explanation:
Fibonacci Nodes present in the Linked List are {55, 3, 89, 233, 34, 5}
Odd Fibonacci Nodes present in the Linked List are {55, 3, 89, 233, 5}
Count of Odd Fibonacci Nodes is 5
Therefore , Mean of Odd Fibonacci Node Values = (55 + 5 + 3 + 89 + 233) / 5 = 77

Approach:The idea is to use hashing to pre-compute and store all Fibonacci numbers up to the largest element in the linked list.
Follow the steps given below to solve the problem:



  1. Initialize two variables, say cnt, sum to store the count of odd Fibonacci nodes and the sum of all odd Fibonacci nodes respectively.
  2. Traverse the singly linked list and store the largest element of the linked list, say Max.
  3. Create a set, say hashmap to store all the Fibonacci numbers up to Max.
  4. Traverse the linked list and check if the current node is an odd and Fibonacci number or not. If found to be true, then increment the value of cnt and add the data value of the current node to sum and remove the node from Hashmap.
  5. Finally, print the value of (sum / cnt) as the required answer.

Below is the implementation of the above approach:

C++

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// C++ program to implement
// the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Structure of a
// singly Linked List
struct Node {
     
    // Stores data value
    // of a Node
    int data;
     
    // Stores pointer
    // to next Node
    Node* next;
};
 
// Function to insert a node at the
// beginning of the singly Linked List
void push(Node** head_ref, int new_data)
{
 
    // Create a new Node
    Node* new_node = new Node;
 
    // Insert the data into
    // the Node
    new_node->data = new_data;
     
    // Insert pointer to
    // the next Node
    new_node->next = (*head_ref);
 
    // Update head_ref
    (*head_ref) = new_node;
}
 
// Function to find the largest
// element from the linked list
int largestElement(struct Node* head_ref)
{
    // Stores the largest element
    // in the linked list
    int Max = INT_MIN;
 
    Node* head = head_ref;
 
    // Iterate over the linked list
    while (head != NULL) {
     
        // If max is less than
        // head->data
        if (Max < head->data) {
         
            // Update  max
            Max = head->data;
        }
         
        // Update head
        head = head->next;
    }
    return Max;
}
 
// Function to store all Fibonacci numbers
// up to the largest element of the list
set<int> createHashMap(int Max)
{
     
    // Store all Fibonacci numbers
    // up to Max
    set<int> hashmap;
     
     
    // Stores first element of
    // Fibonacci number
    int prev = 0;
     
    // Stores second element of
    // Fibonacci number
    int curr = 1;
     
    // Insert prev into hashmap
    hashmap.insert(prev);
     
    // Insert curr into hashmap
    hashmap.insert(curr);
 
    // Insert all elements of
    // Fibonacci numbers up to Max
    while (curr <= Max) {
         
        // Stores current fibonacci number
        int temp = curr + prev;
         
        // Insert temp into hashmap
        hashmap.insert(temp);
         
        // Update prev
        prev = curr;
         
        // Update curr
        curr = temp;
    }
    return hashmap;
}
 
// Function to find the mean
// of odd Fibonacci nodes
double meanofnodes(struct Node* head)
{
    // Stores the largest element
    // in the linked list
    int Max = largestElement(head);
 
    // Stores all fibonacci numbers
    // up to Max
    set<int> hashmap
           = createHashMap(Max);
     
    // Stores current node
    // of linked list
    Node* curr = head;
     
    // Stores count of
    // odd Fibonacci nodes
    int cnt = 0;
     
    // Stores sum of all
    // odd fibonacci nodes
    double sum = 0.0;
     
    // Traverse the linked list
    while (curr != NULL) {
     
        // if the data value of
        // current node is an odd number
        if ((curr->data) & 1){
             
            // if data value of the node
            // is present in hashmap
            if (hashmap.count(curr->data)) {
                 
                // Update cnt
                cnt++;
                 
                // Update sum
                sum += curr->data;
                 
                // Remove current fibonacci number
                // from hashmap so that duplicate
                // elements can't be counted
                hashmap.erase(curr->data);
            }
             
        }
         
        // Update curr
        curr = curr->next;
    }
 
    // Return the required mean
    return (sum / cnt);
}
 
// Driver Code
int main()
{  
    // Stores head node of
    // the linked list
    Node* head = NULL;
     
    // Insert all data values
    // in the linked list
    push(&head, 5);
    push(&head, 21);
    push(&head, 8);
    push(&head, 12);
    push(&head, 3);
    push(&head, 13);
    push(&head, 144);
    push(&head, 6);
     
     
    cout<<meanofnodes(head);
 
    return 0;
}

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Java

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// Java program to implement
// the above approach
import java.util.*;
class GFG{
 
// Structure of a
// singly Linked List
static class Node
{
  // Stores data value
  // of a Node
  int data;
 
  // Stores pointer
  // to next Node
  Node next;
};
   
static Node head;
 
// Function to insert a
// node at the beginning
// of the singly Linked List
static Node push(Node head_ref,
                 int new_data)
{
  // Create a new Node
  Node new_node = new Node();
 
  // Insert the data into
  // the Node
  new_node.data = new_data;
 
  // Insert pointer to
  // the next Node
  new_node.next = head_ref;
 
  // Update head_ref
  head_ref = new_node;
  return head_ref;
}
 
// Function to find the largest
// element from the linked list
static int largestElement(Node head_ref)
{
  // Stores the largest element
  // in the linked list
  int Max = Integer.MIN_VALUE;
 
  Node head = head_ref;
 
  // Iterate over the
  // linked list
  while (head != null)
  {
    // If max is less than
    // head.data
    if (Max < head.data)
    {
      // Update  max
      Max = head.data;
    }
 
    // Update head
    head = head.next;
  }
  return Max;
}
 
// Function to store all
// Fibonacci numbers up
// to the largest element
// of the list
static HashSet<Integer>
       createHashMap(int Max)
{   
  // Store all Fibonacci
  // numbers up to Max
  HashSet<Integer> hashmap =
          new HashSet<>();
 
  // Stores first element of
  // Fibonacci number
  int prev = 0;
 
  // Stores second element of
  // Fibonacci number
  int curr = 1;
 
  // Insert prev into hashmap
  hashmap.add(prev);
 
  // Insert curr into hashmap
  hashmap.add(curr);
 
  // Insert all elements of
  // Fibonacci numbers up
  // to Max
  while (curr <= Max)
  {
    // Stores current fibonacci
    // number
    int temp = curr + prev;
 
    // Insert temp into hashmap
    hashmap.add(temp);
 
    // Update prev
    prev = curr;
 
    // Update curr
    curr = temp;
  }
  return hashmap;
}
 
// Function to find the mean
// of odd Fibonacci nodes
static double meanofnodes()
{
  // Stores the largest element
  // in the linked list
  int Max = largestElement(head);
 
  // Stores all fibonacci numbers
  // up to Max
  HashSet<Integer> hashmap =
          createHashMap(Max);
 
  // Stores current node
  // of linked list
  Node curr = head;
 
  // Stores count of
  // odd Fibonacci nodes
  int cnt = 0;
 
  // Stores sum of all
  // odd fibonacci nodes
  double sum = 0.0;
 
  // Traverse the linked list
  while (curr != null)
  {
    // if the data value of
    // current node is an
    // odd number
    if ((curr.data) %2== 1)
    {
      // if data value of the node
      // is present in hashmap
      if (hashmap.contains(curr.data))
      {
        // Update cnt
        cnt++;
 
        // Update sum
        sum += curr.data;
 
        // Remove current fibonacci
        // number from hashmap so that
        // duplicate elements can't be
        // counted
        hashmap.remove(curr.data);
      }
 
    }
 
    // Update curr
    curr = curr.next;
  }
 
  // Return the required mean
  return (sum / cnt);
}
 
// Driver Code
public static void main(String[] args)
{  
  // Stores head node of
  // the linked list
  head = null;
 
  // Insert all data values
  // in the linked list
  head = push(head, 5);
  head = push(head, 21);
  head = push(head, 8);
  head = push(head, 12);
  head = push(head, 3);
  head = push(head, 13);
  head = push(head, 144);
  head = push(head, 6);
 
  System.out.print(meanofnodes());
}
}
 
// This code is contributed by 29AjayKumar

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Python3

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# Python3 program to implement
# the above approach
  
# Structure of a
# singly Linked List
class Node:
     
    def __init__(self):
      
        # Stores data value
        # of a Node
        self.data = 0
      
        # Stores pointer
        # to next Node
        self.next = None
  
# Function to add a node at the
# beginning of the singly Linked List
def push( head_ref, new_data):
  
    # Create a new Node
    new_node = Node()
  
    # Insert the data into
    # the Node
    new_node.data = new_data;
      
    # Insert pointer to
    # the next Node
    new_node.next = head_ref
  
    # Update head_ref
    head_ref = new_node;
     
    return head_ref
  
# Function to find the largest
# element from the linked list
def largestElement(head_ref):
 
    # Stores the largest element
    # in the linked list
    Max = -10000000
  
    head = head_ref;
  
    # Iterate over the linked list
    while (head != None):
      
        # If max is less than
        # head.data
        if (Max < head.data):
          
            # Update  max
            Max = head.data;
          
        # Update head
        head = head.next;
     
    return Max;
  
# Function to store all Fibonacci numbers
# up to the largest element of the list
def createHashMap(Max):
      
    # Store all Fibonacci numbers
    # up to Max
    hashmap = set()
      
    # Stores first element of
    # Fibonacci number
    prev = 0;
      
    # Stores second element of
    # Fibonacci number
    curr = 1;
      
    # Insert prev into hashmap
    hashmap.add(prev);
      
    # Insert curr into hashmap
    hashmap.add(curr);
  
    # Insert all elements of
    # Fibonacci numbers up to Max
    while (curr <= Max):
          
        # Stores current fibonacci number
        temp = curr + prev;
          
        # Insert temp into hashmap
        hashmap.add(temp);
          
        # Update prev
        prev = curr;
          
        # Update curr
        curr = temp;
     
    return hashmap;
  
# Function to find the mean
# of odd Fibonacci nodes
def meanofnodes(head):
 
    # Stores the largest element
    # in the linked list
    Max = largestElement(head);
  
    # Stores all fibonacci numbers
    # up to Max
    hashmap = createHashMap(Max);
      
    # Stores current node
    # of linked list
    curr = head;
      
    # Stores count of
    # odd Fibonacci nodes
    cnt = 0;
      
    # Stores sum of all
    # odd fibonacci nodes
    sum = 0.0;
      
    # Traverse the linked list
    while (curr != None):
      
        # if the data value of
        # current node is an odd number
        if ((curr.data) % 2 == 1):
              
            # if data value of the node
            # is present in hashmap
            if (curr.data in hashmap):
                  
                # Update cnt
                cnt += 1
                  
                # Update sum
                sum += curr.data;
                  
                # Remove current fibonacci number
                # from hashmap so that duplicate
                # elements can't be counted
                hashmap.remove(curr.data);
          
        # Update curr
        curr = curr.next;
  
    # Return the required mean
    return (sum / cnt);
  
# Driver Code
if __name__=='__main__':
     
    # Stores head node of
    # the linked list
    head = None;
      
    # Insert all data values
    # in the linked list
    head = push(head, 5);
    head = push(head, 21);
    head = push(head, 8);
    head = push(head, 12);
    head = push(head, 3);
    head = push(head, 13);
    head = push(head, 144);
    head = push(head, 6);
           
    print(meanofnodes(head))
  
# This code is contributed by rutvik_56

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C#

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// C# program to implement
// the above approach
using System;
using System.Collections.Generic;
 
class GFG{
 
// Structure of a
// singly Linked List
public class Node
{
   
  // Stores data value
  // of a Node
  public int data;
   
  // Stores pointer
  // to next Node
  public Node next;
};
   
static Node head;
 
// Function to insert a
// node at the beginning
// of the singly Linked List
static Node push(Node head_ref,
                 int new_data)
{
   
  // Create a new Node
  Node new_node = new Node();
 
  // Insert the data into
  // the Node
  new_node.data = new_data;
 
  // Insert pointer to
  // the next Node
  new_node.next = head_ref;
 
  // Update head_ref
  head_ref = new_node;
  return head_ref;
}
 
// Function to find the largest
// element from the linked list
static int largestElement(Node head_ref)
{
   
  // Stores the largest element
  // in the linked list
  int Max = int.MinValue;
 
  Node head = head_ref;
 
  // Iterate over the
  // linked list
  while (head != null)
  {
     
    // If max is less than
    // head.data
    if (Max < head.data)
    {
       
      // Update  max
      Max = head.data;
    }
 
    // Update head
    head = head.next;
  }
  return Max;
}
 
// Function to store all
// Fibonacci numbers up
// to the largest element
// of the list
static HashSet<int> createDictionary(int Max)
{  
   
  // Store all Fibonacci
  // numbers up to Max
  HashSet<int> hashmap = new HashSet<int>();
   
  // Stores first element of
  // Fibonacci number
  int prev = 0;
 
  // Stores second element of
  // Fibonacci number
  int curr = 1;
 
  // Insert prev into hashmap
  hashmap.Add(prev);
 
  // Insert curr into hashmap
  hashmap.Add(curr);
 
  // Insert all elements of
  // Fibonacci numbers up
  // to Max
  while (curr <= Max)
  {
     
    // Stores current fibonacci
    // number
    int temp = curr + prev;
 
    // Insert temp into hashmap
    hashmap.Add(temp);
 
    // Update prev
    prev = curr;
 
    // Update curr
    curr = temp;
  }
  return hashmap;
}
 
// Function to find the mean
// of odd Fibonacci nodes
static double meanofnodes()
{
   
  // Stores the largest element
  // in the linked list
  int Max = largestElement(head);
 
  // Stores all fibonacci numbers
  // up to Max
  HashSet<int> hashmap = createDictionary(Max);
   
  // Stores current node
  // of linked list
  Node curr = head;
 
  // Stores count of
  // odd Fibonacci nodes
  int cnt = 0;
 
  // Stores sum of all
  // odd fibonacci nodes
  double sum = 0.0;
 
  // Traverse the linked list
  while (curr != null)
  {
     
    // if the data value of
    // current node is an
    // odd number
    if ((curr.data) % 2 == 1)
    {
       
      // if data value of the node
      // is present in hashmap
      if (hashmap.Contains(curr.data))
      {
         
        // Update cnt
        cnt++;
 
        // Update sum
        sum += curr.data;
 
        // Remove current fibonacci
        // number from hashmap so that
        // duplicate elements can't be
        // counted
        hashmap.Remove(curr.data);
      }
 
    }
 
    // Update curr
    curr = curr.next;
  }
 
  // Return the required mean
  return (sum / cnt);
}
 
// Driver Code
public static void Main(String[] args)
{  
   
  // Stores head node of
  // the linked list
  head = null;
 
  // Insert all data values
  // in the linked list
  head = push(head, 5);
  head = push(head, 21);
  head = push(head, 8);
  head = push(head, 12);
  head = push(head, 3);
  head = push(head, 13);
  head = push(head, 144);
  head = push(head, 6);
 
  Console.Write(meanofnodes());
}
}
 
// This code is contributed by Amit Katiyar

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Output: 

10.5

 

Time Complexity: O(N)
Auxiliary Space: O(N)

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