Binary Search on Singly Linked List

Given a singly linked list and a key, find key using binary search approach. 
To perform a Binary search based on Divide and Conquer Algorithm, determination of the middle element is important. Binary Search is usually fast and efficient for arrays because accessing the middle index between two given indices is easy and fast(Time Complexity O(1)). But memory allocation for the singly linked list is dynamic and non-contiguous, which makes finding the middle element difficult. One approach could be of using skip list, one could be traversing the linked list using one pointer.

Prerequisite: Finding middle of a linked list.

Note: The approach and implementation provided below are to show how Binary Search can be implemented on a linked list. The implementation takes O(n) time.

Approach :

• Here, start node(set to Head of list), and the last node(set to NULL initially) are given.
• Middle is calculated using two pointers approach.
• If middle’s data matches the required value of search, return it.
• Else if middle’s data < value, move to upper half(setting start to middle’s next).
• Else go to lower half(setting last to middle).
• The condition to come out is, either element found or entire list is traversed. When entire list is traversed, last points to start i.e. last -> next == start.

In main function, function InsertAtHead inserts value at the beginning of linked list. Inserting such values(for sake of simplicity) so that the list created is sorted. 

Examples : 

Input : Enter value to search : 7
Output : Found

Input : Enter value to search : 12
Output : Not Found

Implementation:

C++

// CPP code to implement binary search
// on Singly Linked List
#include<stdio.h>
#include<stdlib.h>

struct Node
{
    int data;
    struct Node* next;
};

Node *newNode(int x)
{
    struct Node* temp = new Node;
    temp->data = x;
    temp->next = NULL;
    return temp;
}

// function to find out middle element
struct Node* middle(Node* start, Node* last)
{
    if (start == NULL)
        return NULL;

    struct Node* slow = start;
    struct Node* fast = start -> next;

    while (fast != last)
    {
        fast = fast -> next;
        if (fast != last)
        {
            slow = slow -> next;
            fast = fast -> next;
        }
    }

    return slow;
}

// Function for implementing the Binary
// Search on linked list
struct Node* binarySearch(Node *head, int value)
{
    struct Node* start = head;
    struct Node* last = NULL;

    do
    {
        // Find middle
        Node* mid = middle(start, last);

        // If middle is empty
        if (mid == NULL)
            return NULL;

        // If value is present at middle
        if (mid -> data == value)
            return mid;

        // If value is more than mid
        else if (mid -> data < value)
            start = mid -> next;

        // If the value is less than mid.
        else
            last = mid;

    } while (last == NULL ||
             last != start);

    // value not present
    return NULL;
}

// Driver Code
int main()
{
    Node *head = newNode(1);
    head->next = newNode(4);
    head->next->next = newNode(7);
    head->next->next->next = newNode(8);
    head->next->next->next->next = newNode(9);
    head->next->next->next->next->next = newNode(10);
    int value = 7;
    if (binarySearch(head, value) == NULL)
        printf("Value not present\n");
    else
        printf("Present");
    return 0;
}

Java

// Java code to implement binary search
// on Singly Linked List

// Node Class
class Node
{
    int data;
    Node next;

    // Constructor to create a new node
    Node(int d)
    {
        data = d;
        next = null;
    }
}

class BinarySearch
{
    // function to insert a node at the beginning
    // of the Singly Linked List
    static Node push(Node head, int data)
    {
        Node newNode = new Node(data);
        newNode.next = head;
        head = newNode;
        return head;
    }

    // Function to find middle element
    // using Fast and Slow pointers
    static Node middleNode(Node start, Node last)
    {
        if (start == null)
            return null;

        Node slow = start;
        Node fast = start.next;

        while (fast != last)
        {
            fast = fast.next;
            if (fast != last)
            {
                slow = slow.next;
                fast = fast.next;
            }
        }
        return slow;
    }

    // function to insert a node at the beginning
    // of the Singly Linked List
    static Node binarySearch(Node head, int value)
    {
        Node start = head;
        Node last = null;

        do
        {
            // Find Middle
            Node mid = middleNode(start, last);

            // If middle is empty
            if (mid == null)
                return null;

            // If value is present at middle
            if (mid.data == value)
                return mid;

            // If value is less than mid
            else if (mid.data > value)
            {
              last = mid;
            }

            // If the value is more than mid.
            else
                 start = mid.next;
        } while (last == null || last != start);

        // value not present
        return null;
    }

    // Driver Code
    public static void main(String[] args)
    {
        Node head = null;

        // Using push() function to
        // convert singly linked list
        // 10 -> 9 -> 8 -> 7 -> 4 -> 1
        head = push(head, 1);
        head = push(head, 4);
        head = push(head, 7);
        head = push(head, 8);
        head = push(head, 9);
        head = push(head, 10);
        int value = 7;

        if (binarySearch(head, value) == null)
        {
            System.out.println("Value not present");
        }
        else
        {
            System.out.println("Present");
        }
    }
}

// This code is contributed by Vivekkumar Singh

Python

# Python code to implement binary search
# on Singly Linked List

# Link list node
class Node:

    def __init__(self, data):
        self.data = data
        self.next = None
        self.prev = None

def newNode(x):

    temp = Node(0)
    temp.data = x
    temp.next = None
    return temp

# function to find out middle element
def middle(start, last):

    if (start == None):
        return None

    slow = start
    fast = start . next

    while (fast != last):

        fast = fast . next
        if (fast != last):

            slow = slow . next
            fast = fast . next

    return slow

# Function for implementing the Binary
# Search on linked list
def binarySearch(head,value):

    start = head
    last = None

    while True :

        # Find middle
        mid = middle(start, last)

        # If middle is empty
        if (mid == None):
            return None

        # If value is present at middle
        if (mid . data == value):
            return mid

        # If value is more than mid
        elif (mid . data < value):
            start = mid . next

        # If the value is less than mid.
        else:
            last = mid

        if not (last == None or last != start):
            break

    # value not present
    return None

# Driver Code

head = newNode(1)
head.next = newNode(4)
head.next.next = newNode(7)
head.next.next.next = newNode(8)
head.next.next.next.next = newNode(9)
head.next.next.next.next.next = newNode(10)
value = 7
if (binarySearch(head, value) == None):
    print("Value not present\n")
else:
    print("Present")

# This code is contributed by Arnab Kundu

C#

// C# code to implement binary search
// on Singly Linked List

using System;

// Node Class
public class Node
{
    public int data;
    public Node next;

    // Constructor to create a new node
    public Node(int d)
    {
        data = d;
        next = null;
    }
}

class BinarySearch
{
    // function to insert a node at the beginning
    // of the Singly Linked List
    static Node push(Node head, int data)
    {
        Node newNode = new Node(data);
        newNode.next = head;
        head = newNode;
        return head;
    }

    // Function to find middle element
    // using Fast and Slow pointers
    static Node middleNode(Node start, Node last)
    {
        if (start == null)
            return null;

        Node slow = start;
        Node fast = start.next;

        while (fast != last)
        {
            fast = fast.next;
            if (fast != last)
            {
                slow = slow.next;
                fast = fast.next;
            }
        }
        return slow;
    }

    // function to insert a node at the beginning
    // of the Singly Linked List
    static Node binarySearch(Node head, int value)
    {
        Node start = head;
        Node last = null;

        do
        {
            // Find Middle
            Node mid = middleNode(start, last);

            // If middle is empty
            if (mid == null)
                return null;

            // If value is present at middle
            if (mid.data == value)
                return mid;

            // If value is less than mid
            else if (mid.data > value)
            {
                start = mid.next;
            }

            // If the value is more than mid.
            else
                last = mid;
        } while (last == null || last != start);

        // value not present
        return null;
    }

    // Driver Code
    public static void Main(String []args)
    {
        Node head = null;

        // Using push() function to
        // convert singly linked list
        // 10 -> 9 -> 8 -> 7 -> 4 -> 1
        head = push(head, 1);
        head = push(head, 4);
        head = push(head, 7);
        head = push(head, 8);
        head = push(head, 9);
        head = push(head, 10);
        int value = 7;

        if (binarySearch(head, value) == null)
        {
            Console.WriteLine("Value not present");
        }
        else
        {
            Console.WriteLine("Present");
        }
    }
}

// This code is contributed by Arnab Kundu

Javascript

<script>

// JavaScript code to implement binary search
// on Singly Linked List

// Node Class
class Node
{
    constructor(data)
    {
        this.data = data;
        this.next = null;
    }
}

// function to insert a node at the beginning
// of the Singly Linked List
function push(head, data)
{
    var newNode = new Node(data);
    newNode.next = head;
    head = newNode;
    return head;
}

// Function to find middle element
// using Fast and Slow pointers
function middleNode(start, last)
{
    if (start == null)
        return null;
    var slow = start;
    var fast = start.next;
    while (fast != last)
    {
        fast = fast.next;
        if (fast != last)
        {
            slow = slow.next;
            fast = fast.next;
        }
    }
    return slow;
}
// function to insert a node at the beginning
// of the Singly Linked List
function binarySearch(head, value)
{
    var start = head;
    var last = null;
    do
    {
        // Find Middle
        var mid = middleNode(start, last);
        // If middle is empty
        if (mid == null)
            return null;
        // If value is present at middle
        if (mid.data == value)
            return mid;
        // If value is less than mid
        else if (mid.data > value)
        {
            start = mid.next;
        }
        // If the value is more than mid.
        else
            last = mid;
    } while (last == null || last != start);
    // value not present
    return null;
}

// Driver Code
var head = null;
// Using push() function to
// convert singly linked list
// 10 -> 9 -> 8 -> 7 -> 4 -> 1
head = push(head, 1);
head = push(head, 4);
head = push(head, 7);
head = push(head, 8);
head = push(head, 9);
head = push(head, 10);
var value = 7;
if (binarySearch(head, value) == null)
{
    document.write("Value not present");
}
else
{
    document.write("Present");
}


</script>

Output

Present

Complexity Analysis:

• Time Complexity: O(N) 
• Auxiliary Space: O(1)