Can binary search be used on linked lists, and if so, how?

Question

Ryan McCombe · Accepted Answer

Binary search cannot be efficiently applied to linked lists because it requires random access to the elements.

Linked lists only support sequential access, which means you can't directly jump to the middle element like you can with arrays or vectors.

However, you can still perform a search on a linked list, but it won't be as efficient as binary search.

Why Binary Search Doesn't Work on Linked Lists

Binary search works by dividing the search space in half repeatedly, which requires $O(1)$ time access to the middle element.

Linked lists, however, have $O(n)$ time access to elements, as you must traverse from the head node to reach any specific element.

Alternative: Linear Search

For linked lists, a linear search is more suitable. Here's an example of performing a linear search on a singly linked list:

1#include <iostream>
2
3// Define a node in the linked list
4struct Node {
5  int data;
6  Node* next;
7};
8
9// Function to search for a value in the linked list
10bool linearSearch(Node* head, int target) {
11  Node* current = head;
12  while (current != nullptr) {
13    if (current->data == target) {
14      return true;
15    }
16    current = current->next;
17  }
18  return false;
19}
20
21int main() {
22  // Create a linked list: 1 -> 2 -> 3 -> 4 -> 5
23  Node n1{1, nullptr},
24    n2{2, nullptr},
25    n3{3, nullptr},
26    n4{4, nullptr},
27    n5{5, nullptr};
28
29  n1.next = &n2;
30  n2.next = &n3;
31  n3.next = &n4;
32  n4.next = &n5;
33
34  int target = 3;
35  bool found = linearSearch(&n1, target);
36
37  std::cout << "The number " << target
38    << (found ? " was" : " was not") << " found";
39}

1The number 3 was found

Optimizing Search in Linked Lists

If you need faster search capabilities, consider these alternatives:

Convert to Array: Copy the linked list elements to an array, sort the array, and then perform binary search.
Skip List: A skip list is a layered linked list that allows faster search by skipping over nodes, achieving $O(log n)$ time complexity for search operations.
Binary Search Tree (BST): Convert your linked list to a BST for efficient searching.

Example of Converting Linked List to Array

Here's a simple example to convert a linked list to an array and then perform a binary search:

1#include <algorithm>
2#include <iostream>
3#include <vector>
4
5struct Node {
6  int data;
7  Node* next;
8};
9
10std::vector<int> linkedListToArray(Node* head) {
11  std::vector<int> arr;
12  Node* current = head;
13  while (current != nullptr) {
14    arr.push_back(current->data);
15    current = current->next;
16  }
17  return arr;
18}
19
20int main() {
21  Node n1{1, nullptr},
22    n2{2, nullptr},
23    n3{3, nullptr},
24    n4{4, nullptr},
25    n5{5, nullptr};
26
27  n1.next = &n2;
28  n2.next = &n3;
29  n3.next = &n4;
30  n4.next = &n5;
31
32  std::vector<int> array = linkedListToArray(&n1);
33  std::sort(array.begin(), array.end());
34
35  bool found = std::binary_search(
36    array.begin(), array.end(), 3);
37
38  std::cout << "The number 3 "
39    << (found ? "was" : "was not") << " found";
40}

1The number 3 was found

While binary search is not suitable for linked lists due to their sequential access nature, you can use linear search or consider alternative data structures to achieve efficient searching.

Binary Search in C++

Using Binary Search on Linked Lists

Why Binary Search Doesn't Work on Linked Lists

Alternative: Linear Search

Optimizing Search in Linked Lists

Example of Converting Linked List to Array

Binary Search in C++

Professional C++

Questions & Answers