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C++ Program For Selecting A Random Node From A Singly Linked List

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  • Last Updated : 28 Dec, 2021
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Given a singly linked list, select a random node from the linked list (the probability of picking a node should be 1/N if there are N nodes in the list). You are given a random number generator.
Below is a Simple Solution:

  1. Count the number of nodes by traversing the list.
  2. Traverse the list again and select every node with probability 1/N. The selection can be done by generating a random number from 0 to N-i for i’th node, and selecting the i’th node only if the generated number is equal to 0 (or any other fixed number from 0 to N-i).

We get uniform probabilities with the above schemes.  

i = 1, probability of selecting first node = 1/N
i = 2, probability of selecting second node =
                   [probability that first node is not selected] * 
                   [probability that second node is selected]
                  = ((N-1)/N)* 1/(N-1)
                  = 1/N  

Similarly, probabilities of other selecting other nodes is 1/N
The above solution requires two traversals of linked list. 

How to select a random node with only one traversal allowed? 
The idea is to use Reservoir Sampling. Following are the steps. This is a simpler version of Reservoir Sampling as we need to select only one key instead of k keys.

(1) Initialize result as first node
    result = head->key 
(2) Initialize n = 2
(3) Now one by one consider all nodes from 2nd node onward.
    (a) Generate a random number from 0 to n-1. 
        Let the generated random number is j.
    (b) If j is equal to 0 (we could choose other fixed numbers 
        between 0 to n-1), then replace result with the current node.
    (c) n = n+1
    (d) current = current->next

Below is the implementation of above algorithm.


/* C++ program to randomly select 
   a node from a singly linked list */
#include <time.h>
using namespace std;
// Link list node 
class Node
    int key;
    Node* next;
    void printRandom(Node*);
    void push(Node**, int);
// A reservoir sampling-based function to 
// print a random node from a linked list
void Node::printRandom(Node *head)
    // If list is empty
    if (head == NULL)
    // Use a different seed value so that 
    // we don't get same result each time 
    // we run this program
    // Initialize result as first node
    int result = head->key;
    // Iterate from the (k+1)th element 
    // to nth element
    Node *current = head;
    int n;
    for (n = 2; current != NULL; n++)
        // Change result with 
        // probability 1/n
        if (rand() % n == 0)
        result = current->key;
        // Move to next node
        current = current->next;
    cout << "Randomly selected key is " << 
/* A utility function to create 
   a new node */
Node* newNode(int new_key)
    // Allocate node 
    Node* new_node = 
          (Node*) malloc(sizeof( Node));
    /// Put in the key 
    new_node->key = new_key;
    new_node->next = NULL;
    return new_node;
/* A utility function to insert a 
   node at the beginning of linked list */
void Node:: push(Node** head_ref, 
                 int new_key)
    // Allocate node 
    Node* new_node = new Node;
    // Put in the key 
    new_node->key = new_key;
    // Link the old list off the 
    // new node 
    new_node->next = (*head_ref);
    // Move the head to point to 
    // the new node 
    (*head_ref) = new_node;
// Driver code
int main()
    Node n1;
    Node *head = NULL;
    n1.push(&head, 5);
    n1.push(&head, 20);
    n1.push(&head, 4);
    n1.push(&head, 3);
    n1.push(&head, 30);
    return 0;
// This code is contributed by SoumikMondal

Note that the above program is based on the outcome of a random function and may produce different output.

How does this work? 
Let there be total N nodes in list. It is easier to understand from the last node.
The probability that the last node is result simply 1/N [For last or N’th node, we generate a random number between 0 to N-1 and make the last node as a result if the generated number is 0 (or any other fixed number]
The probability that second last node is result should also be 1/N. 

The probability that the second last node is result 
          = [Probability that the second last node replaces result] X 
            [Probability that the last node doesn't replace the result] 
          = [1 / (N-1)] * [(N-1)/N]
          = 1/N

Similarly, we can show probability for 3rd last node and other nodes.
Please refer complete article on Select a Random Node from a Singly Linked List for more details!

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