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Singly Linked List

A linear data structure where each element (node) contains a value and a reference to the next node in the sequence.

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Overview

Singly linked lists provide efficient insertion and deletion at the head (O(1)) but require O(n) time for access to arbitrary positions. Perfect for scenarios with frequent insertions and deletions.

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Implementation

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Node Structure

class Node<T = number> {
  value: T;
  next: Node<T> | null = null;

  constructor(value: T) {
    this.value = value;
  }
}
Reference: node.ts:1-9

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Class Definition

class SinglyLinkedList<T = number> {
  head: Node<T> | null = null;
  size = 0;
  
  // ... methods
}
Reference: singly-linked-list.ts:3-6

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API Reference

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push(value: T): void

Adds an element to the end of the linked list. 
const list = new SinglyLinkedList<number>();
list.push(1);
list.push(2);
list.push(3);
// List: (1) -> (2) -> (3) ->
Complexity: O(n) Reference: singly-linked-list.ts:10-12

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insert(value: T, index: number): void

Inserts a new element at the specified position. 
const list = new SinglyLinkedList<number>();
list.push(1);
list.push(3);
list.insert(2, 1);
// List: (1) -> (2) -> (3) ->
Parameters:
  • value: The value to insert
  • index: Position to insert at (0-based)
Complexity:
  • Insert at head: O(1)
  • Insert at tail: O(n)
  • Insert at arbitrary position: O(n)
Reference: singly-linked-list.ts:17-56

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pop(): Node<T> | null

Removes and returns the last element from the linked list. 
const list = new SinglyLinkedList<number>();
list.push(1);
list.push(2);
const last = list.pop(); // returns node with value 2
// List: (1) ->
Complexity: O(n) Reference: singly-linked-list.ts:61-85

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at(index: number): Node<T> | null

Returns the element at the given index without removing it. 
const list = new SinglyLinkedList<number>();
list.push(1);
list.push(2);
list.push(3);
const node = list.at(1); // returns node with value 2
Complexity: O(n) Reference: singly-linked-list.ts:90-103

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remove(value: T): void

Removes the first occurrence of an element from the list. 
const list = new SinglyLinkedList<number>();
list.push(1);
list.push(2);
list.push(3);
list.remove(2);
// List: (1) -> (3) ->
Complexity: O(n) Reference: singly-linked-list.ts:108-128

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removeAt(index: number): void

Removes an element from the specified position in the list. 
const list = new SinglyLinkedList<number>();
list.push(1);
list.push(2);
list.push(3);
list.removeAt(1);
// List: (1) -> (3) ->
Complexity: O(n) Reference: singly-linked-list.ts:133-157

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isEmpty(): boolean

Returns true if the list is empty, false otherwise. 
const list = new SinglyLinkedList<number>();
console.log(list.isEmpty()); // true
list.push(1);
console.log(list.isEmpty()); // false
Complexity: O(1) Reference: singly-linked-list.ts:162-164

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toString(): string

Returns a string representation of the list. 
const list = new SinglyLinkedList<number>();
list.push(1);
list.push(2);
list.push(3);
console.log(list.toString()); // "(1) -> (2) -> (3) -> "
Complexity: O(n) Reference: singly-linked-list.ts:169-183

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Problems & Solutions

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Problem 1: Partition List

Partition a linked list around a value x, such that all nodes less than x come before nodes greater than or equal to x. 
/**
 * Time complexity: O(n)
 * Space complexity: O(1)
 */
function partitionList(list: SinglyLinkedList<number>, x: number) {
  let current = list.head;
  
  for (let i = 0; current?.next; i++) {
    const next = current.next;

    if (current.next.value < x) {
      current.next = next.next;

      // Move it to the left (head)
      const temp = list.head;
      list.head = next;
      next.next = temp;
    } else {
      current = next;
    }
  }
}

// Example: [3,5,8,5,10,2,1], x = 5
// Result: [1,2,3,5,8,5,10]
Reference: singly-linked-list.problems.test.ts:5-42

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Problem 2: Add Two Numbers

Add two numbers represented by linked lists, where each node contains a single digit stored in reverse order. 
/**
 * Time complexity: O(n * m)
 * Space complexity: O(n)
 */
function addTwoNumbers(
  n1: SinglyLinkedList<number>,
  n2: SinglyLinkedList<number>
): SinglyLinkedList<number> {
  const output = new SinglyLinkedList<number>();
  let current1 = n1.head;
  let current2 = n2.head;
  let carry = 0;

  while (current1) {
    if (current2) {
      const sum = current1.value + current2.value + carry;

      if (sum >= 10) {
        output.push(sum % 10);
        carry = Math.floor(sum / 10);
      } else {
        output.push(sum);
        carry = 0;
      }

      current1 = current1.next;
      current2 = current2.next;
    } else {
      output.push(current1.value + carry);
      carry = 0;
      current1 = current1.next;
    }
  }

  return output;
}

// Example: 617 + 295 = 912
// Input: (7) -> (1) -> (6) + (5) -> (9) -> (2)
// Output: (2) -> (1) -> (9)
Reference: singly-linked-list.problems.test.ts:45-94

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Complexity Summary

OperationTime ComplexitySpace Complexity
pushO(n)O(1)
insert (head)O(1)O(1)
insert (tail)O(n)O(1)
insert (arbitrary)O(n)O(1)
popO(n)O(1)
atO(n)O(1)
removeO(n)O(1)
removeAtO(n)O(1)
isEmptyO(1)O(1)
toStringO(n)O(1)

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Key Characteristics

Advantages:
  • Dynamic size
  • Efficient insertion/deletion at head (O(1))
  • No memory waste
  • Easy to implement
Disadvantages:
  • No random access (O(n) to reach arbitrary position)
  • Extra memory for pointers
  • Not cache-friendly
  • No backward traversal

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Use Cases

  • Stack implementation: Fast push/pop at head
  • Queue implementation: When combined with tail pointer
  • Dynamic memory allocation: When size is unknown
  • Undo functionality: Storing state history
For frequent access to tail, consider maintaining a tail pointer or use a Doubly Linked List instead.

Doubly Linked List

Bidirectional traversal support

Stack

Built using singly linked list

Queue

Built using singly linked list

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