Replace every node in a linked list with its closest bell number

19 June 2025

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Given a singly linked list, the task is to replace every node with its closest bell number.

Bell numbers are a sequence of numbers that represent the number of partitions of a set. In other words, given a set of n elements, the Bell number for n represents the total number of distinct ways that the set can be partitioned into subsets.

The first few Bell numbers are 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, …

Examples:

Input: 14 -> 7 -> 190 -> 2 -> 5 -> NULL
Output: 15 -> 5 -> 203 -> 2 -> 5 -> NULL
Explanation: The closest Bell numbers for each node are:

Node 1 (value = 14): Closest Bell number = 15.

Node 2 (value = 7): Closest Bell number = 5.

Node 3 (value = 190): Closest Bell number = 203.

Node 4 (value = 2): Closest Bell number = 2.

Node 5 (value = 5): Closest Bell number = 5.

Input: 50 -> 1 -> 4 -> NULL
Output: 52 -> 1 -> 5 -> NULL
Explanation: The closest Bell numbers for each node are:

Node 1 (value = 50): Closest Bell number = 52.

Node 1 (value = 1): Closest Bell number = 1.

Node 1 (value = 4): Closest Bell number = 5.

Approach: This can be solved with the following idea:

The algorithm first calculates the Bell number at a given index by filling a 2D array using a dynamic programming approach. Then, it finds the closest Bell number to a given node value by iterating through the Bell numbers until it finds a Bell number greater than or equal to the node value. It then compares the difference between the previous and current Bell numbers to determine which one is closer to the node value. Finally, it replaces each node in the linked list with its closest Bell number using a while loop that iterates through each node in the linked list.

Steps of the above approach:

Define a bellNumber function that takes an integer n as an argument and returns the nth Bell number. The function uses dynamic programming to calculate the Bell number.
Define a closestBell function that takes an integer n as an argument and returns the closest Bell number to n.
This function iteratively calls the bellNumber function until it finds the smallest Bell number greater than or equal to n.
If n is less than the first Bell number (which is 1), then the function returns the first Bell number. Otherwise, the function compares the difference between n and the previous Bell number to the difference between the next Bell number and n and returns the closer Bell number.
Define a replaceWithBell function that takes the head of a linked list as an argument and replaces the data value of each node in the list with the closest Bell number to its original data value.
The function iterates through each node in the list, calls the closestBell function to find the closest Bell number to the node’s original data value, and assigns that value to the node’s data field.

Below is the implementation of the above approach:

C++

// C++ code for the above approach:
#include <cmath>
#include <iostream>
using namespace std;
 
// Node structure of singly linked list
struct Node {
    int data;
    Node* next;
};
 
// Function to add a new node at the
// beginning of the linked list
void push(Node** head_ref, int new_data)
{
    Node* new_node = new Node;
    new_node->data = new_data;
    new_node->next = (*head_ref);
    (*head_ref) = new_node;
}
 
// Function to print the linked list
void printList(Node* node)
{
    while (node != NULL) {
        cout << node->data;
        if (node->next != NULL) {
            cout << " -> ";
        }
        node = node->next;
    }
}
 
// Function to find the Bell number at
// the given index
int bellNumber(int n)
{
    int bell[n + 1][n + 1];
    bell[0][0] = 1;
 
    for (int i = 1; i <= n; i++) {
        bell[i][0] = bell[i - 1][i - 1];
 
        for (int j = 1; j <= i; j++) {
            bell[i][j]
                = bell[i - 1][j - 1] + bell[i][j - 1];
        }
    }
 
    return bell[n][0];
}
 
// Function to find the closest Bell number
// to a given node value
int closestBell(int n)
{
    int bellNum = 0;
    while (bellNumber(bellNum) < n) {
        bellNum++;
    }
 
    if (bellNum == 0) {
        return bellNumber(bellNum);
    }
    else {
        int prev = bellNumber(bellNum - 1);
        int curr = bellNumber(bellNum);
        return (n - prev < curr - n) ? prev : curr;
    }
}
 
// Function to replace every node with
// its closest Bell number
void replaceWithBell(Node* node)
{
    while (node != NULL) {
        node->data = closestBell(node->data);
        node = node->next;
    }
}
 
// Driver code
int main()
{
    Node* head = NULL;
 
    // Creating the linked list
    push(&head, 5);
    push(&head, 2);
    push(&head, 190);
    push(&head, 7);
    push(&head, 14);
 
    // Function call
    replaceWithBell(head);
 
    printList(head);
 
    return 0;
}

Java

// Java code for the above approach
class GFG {
 
    // Node structure of singly linked list
    static class Node {
        int data;
        Node next;
 
        Node(int data) {
            this.data = data;
            this.next = null;
        }
    }
 
    // Function to add a new node at the
    // beginning of the linked list
    static void push(Node[] head_ref, int newData) {
        Node newNode = new Node(newData);
        newNode.next = head_ref[0];
        head_ref[0] = newNode;
    }
 
    // Function to print the linked list
    static void printList(Node node) {
        while (node != null) {
            System.out.print(node.data);
            if (node.next != null) {
                System.out.print(" -> ");
            }
            node = node.next;
        }
    }
 
    // Function to find the Bell number at
    // the given index
    static int bellNumber(int n) {
        int[][] bell = new int[n + 1][n + 1];
        bell[0][0] = 1;
 
        for (int i = 1; i <= n; i++) {
            bell[i][0] = bell[i - 1][i - 1];
 
            for (int j = 1; j <= i; j++) {
                bell[i][j] = bell[i - 1][j - 1] + bell[i][j - 1];
            }
        }
 
        return bell[n][0];
    }
 
    // Function to find the closest Bell number
    // to a given node value
    static int closestBell(int n) {
        int bellNum = 0;
        while (bellNumber(bellNum) < n) {
            bellNum++;
        }
 
        if (bellNum == 0) {
            return bellNumber(bellNum);
        } else {
            int prev = bellNumber(bellNum - 1);
            int curr = bellNumber(bellNum);
            return (n - prev < curr - n) ? prev : curr;
        }
    }
 
    // Function to replace every node with
    // its closest Bell number
    static void replaceWithBell(Node node) {
        while (node != null) {
            node.data = closestBell(node.data);
            node = node.next;
        }
    }
 
    // Driver code
    public static void main(String[] args) {
        Node[] head = new Node[1];
 
        // Creating the linked list
        push(head, 5);
        push(head, 2);
        push(head, 190);
        push(head, 7);
        push(head, 14);
 
        // Function call
        replaceWithBell(head[0]);
 
        printList(head[0]);
    }
}
 
 
// This code is contributed by shivamgupta310570

Python3

import math
 
# Node class for singly linked list
class Node:
    def __init__(self, data):
        self.data = data
        self.next = None
 
# Function to add a new node at the beginning of the linked list
def push(head_ref, new_data):
    new_node = Node(new_data)
    new_node.next = head_ref
    head_ref = new_node
    return head_ref
 
# Function to print the linked list
def printList(node):
    while node is not None:
        print(node.data, end="")
        if node.next is not None:
            print(" -> ", end="")
        node = node.next
    print()
 
# Function to find the Bell number at the given index
def bellNumber(n):
    bell = [[0 for _ in range(n+1)] for _ in range(n+1)]
    bell[0][0] = 1
 
    for i in range(1, n+1):
        bell[i][0] = bell[i-1][i-1]
 
        for j in range(1, i+1):
            bell[i][j] = bell[i-1][j-1] + bell[i][j-1]
 
    return bell[n][0]
 
# Function to find the closest Bell number to a given node value
def closestBell(n):
    bellNum = 0
    while bellNumber(bellNum) < n:
        bellNum += 1
 
    if bellNum == 0:
        return bellNumber(bellNum)
    else:
        prev = bellNumber(bellNum - 1)
        curr = bellNumber(bellNum)
        return prev if n - prev < curr - n else curr
 
# Function to replace every node with its closest Bell number
def replaceWithBell(node):
    while node is not None:
        node.data = closestBell(node.data)
        node = node.next
 
# Driver code
if __name__ == "__main__":
    head = None
 
    # Creating the linked list
    head = push(head, 5)
    head = push(head, 2)
    head = push(head, 190)
    head = push(head, 7)
    head = push(head, 14)
 
    # Function call
    replaceWithBell(head)
 
    printList(head)

C#

using System;
 
// Node class for singly linked list
class Node
{
    public int data;
    public Node next;
 
    public Node(int data)
    {
        this.data = data;
        this.next = null;
    }
}
 
class GFG
{
    // Function to add a new node at the beginning of the linked list
    static Node Push(Node head_ref, int new_data)
    {
        Node new_node = new Node(new_data);
        new_node.next = head_ref;
        head_ref = new_node;
        return head_ref;
    }
 
    // Function to print the linked list
    static void PrintList(Node node)
    {
        while (node != null)
        {
            Console.Write(node.data);
            if (node.next != null)
            {
                Console.Write(" -> ");
            }
            node = node.next;
        }
        Console.WriteLine();
    }
 
    // Function to find the Bell number at the given index
    static int BellNumber(int n)
    {
        int[][] bell = new int[n + 1][];
        for (int i = 0; i <= n; i++)
        {
            bell[i] = new int[n + 1];
        }
        bell[0][0] = 1;
 
        for (int i = 1; i <= n; i++)
        {
            bell[i][0] = bell[i - 1][i - 1];
 
            for (int j = 1; j <= i; j++)
            {
                bell[i][j] = bell[i - 1][j - 1] + bell[i][j - 1];
            }
        }
 
        return bell[n][0];
    }
 
    // Function to find the closest Bell number to a given node value
    static int ClosestBell(int n)
    {
        int bellNum = 0;
        while (BellNumber(bellNum) < n)
        {
            bellNum++;
        }
 
        if (bellNum == 0)
        {
            return BellNumber(bellNum);
        }
        else
        {
            int prev = BellNumber(bellNum - 1);
            int curr = BellNumber(bellNum);
            return (n - prev < curr - n) ? prev : curr;
        }
    }
 
    // Function to replace every node with its closest Bell number
    static void ReplaceWithBell(Node node)
    {
        while (node != null)
        {
            node.data = ClosestBell(node.data);
            node = node.next;
        }
    }
 
    // Driver code
    static void Main()
    {
        Node head = null;
 
        // Creating the linked list
        head = Push(head, 5);
        head = Push(head, 2);
        head = Push(head, 190);
        head = Push(head, 7);
        head = Push(head, 14);
 
        // Function call
        ReplaceWithBell(head);
 
        PrintList(head);
    }
}

Javascript

// Javascript Implementation
 
// Node class for singly linked list
function Node(data) {
    this.data = data;
    this.next = null;
}
 
// Function to add a new node at the beginning of the linked list
function push(head_ref, new_data) {
    var new_node = new Node(new_data);
    new_node.next = head_ref;
    head_ref = new_node;
    return head_ref;
}
 
// Function to print the linked list
function printList(node) {
    while (node != null) {
        console.log(node.data + " ");
        if (node.next != null) {
           console.log("-> ");
        }
        node = node.next;
    }
}
 
// Function to find the Bell number at the given index
function bellNumber(n) {
    var bell = [];
    for (var i = 0; i <= n; i++) {
        bell[i] = [];
        for (var j = 0; j <= n; j++) {
            bell[i][j] = 0;
        }
    }
    bell[0][0] = 1;
 
    for (var i = 1; i <= n; i++) {
        bell[i][0] = bell[i - 1][i - 1];
 
        for (var j = 1; j <= i; j++) {
            bell[i][j] = bell[i - 1][j - 1] + bell[i][j - 1];
        }
    }
 
    return bell[n][0];
}
 
// Function to find the closest Bell number to a given node value
function closestBell(n) {
    var bellNum = 0;
    while (bellNumber(bellNum) < n) {
        bellNum += 1;
    }
 
    if (bellNum == 0) {
        return bellNumber(bellNum);
    } else {
        var prev = bellNumber(bellNum - 1);
        var curr = bellNumber(bellNum);
        return n - prev < curr - n ? prev : curr;
    }
}
 
// Function to replace every node with its closest Bell number
function replaceWithBell(node) {
    while (node != null) {
        node.data = closestBell(node.data);
        node = node.next;
    }
}
 
// Driver code
 
 
var head = null;
 
// creating the linked list
head = push(head, 5);
head = push(head, 2);
head = push(head, 190);
head = push(head, 7);
head = push(head, 14);
 
// Function call
replaceWithBell(head);
 
printList(head);
 
// This code is contributed by Tapesh(tapeshdua420)

Output

15 -> 5 -> 203 -> 2 -> 5

Time Complexity: O(n³)
Auxiliary Space: O(n²)

Efficient approach: Space Optimized solution O(N)

In previous approach we are using 2D array to store the computations of subproblems but the current value is only dependent on the current and previous row of matrix so in this approach we are using 2 vector to store the current and previous rows of matrix.

Implementation steps:

Initialize 2 vectors curr and prev of size N to store the current and previous rows of matrix.
Now initialize the base case for n=0.
Now iterate over subproblems to get the current value from previous computations.
After every iteration assign values of prev to curr vector.

C++

// C++ code for the above approach:
#include <bits/stdc++.h>
using namespace std;
 
// Node structure of singly linked list
struct Node {
    int data;
    Node* next;
};
 
// Function to add a new node at the
// beginning of the linked list
void push(Node** head_ref, int new_data)
{
    Node* new_node = new Node;
    new_node->data = new_data;
    new_node->next = (*head_ref);
    (*head_ref) = new_node;
}
 
// Function to print the linked list
void printList(Node* node)
{
    while (node != NULL) {
        cout << node->data;
        if (node->next != NULL) {
            cout << " -> ";
        }
        node = node->next;
    }
}
 
 
// Function to find the Bell number at
// the given index in O(N) space complexity
int bellNumber(int n)
{   
    // initialize vectors
    vector<int>curr(n + 1 , 0);
    vector<int>prev(n + 1 , 0);
     
    //Base case
    curr[0] = 1;
    prev[0] = 1;
 
    for (int i = 1; i <= n; i++) {
        curr[0] = prev[i - 1];
 
        for (int j = 1; j <= i; j++) {
            curr[j]
                = prev[j - 1] + curr[j - 1];
        }
        // assigning values to iterate further
        prev= curr;
    }
 
    return curr[0];
}
 
 
 
// Function to find the closest Bell number
// to a given node value
int closestBell(int n)
{
    int bellNum = 0;
    while (bellNumber(bellNum) < n) {
        bellNum++;
    }
 
    if (bellNum == 0) {
        return bellNumber(bellNum);
    }
    else {
        int prev = bellNumber(bellNum - 1);
        int curr = bellNumber(bellNum);
        return (n - prev < curr - n) ? prev : curr;
    }
}
 
// Function to replace every node with
// its closest Bell number
void replaceWithBell(Node* node)
{
    while (node != NULL) {
        node->data = closestBell(node->data);
        node = node->next;
    }
}
 
// Driver code
int main()
{
    Node* head = NULL;
 
    // Creating the linked list
    push(&head, 5);
    push(&head, 2);
    push(&head, 190);
    push(&head, 7);
    push(&head, 14);
 
    // Function call
    replaceWithBell(head);
 
    printList(head);
 
    return 0;
}

Time Complexity: O(n^2)

Auxiliary Space: O(n)

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