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List

A list is an abstract data structure concept that represents an ordered collection of elements, supporting operations such as element access, modification, insertion, deletion, and traversal, without requiring users to consider capacity limitations. Lists can be implemented based on linked lists or arrays.

  • A linked list can naturally be viewed as a list: it supports insertion, deletion, search, and update, and can grow flexibly as needed.
  • An array also supports insertion, deletion, search, and update, but because its length is fixed, it can only be regarded as a list with a capacity limit.

When a list is implemented with an array, its fixed length makes it less practical. This is because we usually cannot determine in advance how much data we need to store, making it difficult to choose an appropriate capacity. If the capacity is too small, it may fail to meet our needs; if it is too large, memory space will be wasted.

To solve this problem, we can use a dynamic array to implement a list. It inherits all the advantages of arrays while supporting dynamic resizing during program execution.

In fact, the list types provided by the standard libraries of many programming languages are implemented with dynamic arrays, such as list in Python, ArrayList in Java, vector in C++, and List in C#. In the following discussion, we will treat "list" and "dynamic array" as equivalent concepts.

Common List Operations

Initialize a List

We typically initialize a list in one of two ways: empty or with predefined values:

list.py
# Initialize a list
# Without initial values
nums1: list[int] = []
# With initial values
nums: list[int] = [1, 3, 2, 5, 4]
list.cpp
/* Initialize a list */
// Note that vector in C++ is equivalent to nums as described in this article
// Without initial values
vector<int> nums1;
// With initial values
vector<int> nums = { 1, 3, 2, 5, 4 };
list.java
/* Initialize a list */
// Without initial values
List<Integer> nums1 = new ArrayList<>();
// With initial values (note that array elements should use the wrapper class Integer[] instead of int[])
Integer[] numbers = new Integer[] { 1, 3, 2, 5, 4 };
List<Integer> nums = new ArrayList<>(Arrays.asList(numbers));
list.cs
/* Initialize a list */
// Without initial values
List<int> nums1 = [];
// With initial values
int[] numbers = [1, 3, 2, 5, 4];
List<int> nums = [.. numbers];
list_test.go
/* Initialize a list */
// Without initial values
nums1 := []int{}
// With initial values
nums := []int{1, 3, 2, 5, 4}
list.swift
/* Initialize a list */
// Without initial values
let nums1: [Int] = []
// With initial values
var nums = [1, 3, 2, 5, 4]
list.js
/* Initialize a list */
// Without initial values
const nums1 = [];
// With initial values
const nums = [1, 3, 2, 5, 4];
list.ts
/* Initialize a list */
// Without initial values
const nums1: number[] = [];
// With initial values
const nums: number[] = [1, 3, 2, 5, 4];
list.dart
/* Initialize a list */
// Without initial values
List<int> nums1 = [];
// With initial values
List<int> nums = [1, 3, 2, 5, 4];
list.rs
/* Initialize a list */
// Without initial values
let nums1: Vec<i32> = Vec::new();
// With initial values
let nums: Vec<i32> = vec![1, 3, 2, 5, 4];
list.c
// C does not provide built-in dynamic arrays
list.kt
/* Initialize a list */
// Without initial values
var nums1 = listOf<Int>()
// With initial values
var numbers = arrayOf(1, 3, 2, 5, 4)
var nums = numbers.toMutableList()
list.rb
# Initialize a list
# Without initial values
nums1 = []
# With initial values
nums = [1, 3, 2, 5, 4]
Code Visualization

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Access Elements

Since a list is essentially an array, we can access and update elements in \(O(1)\) time complexity, which is very efficient.

list.py
# Access an element
num: int = nums[1]  # Access element at index 1

# Update an element
nums[1] = 0    # Update element at index 1 to 0
list.cpp
/* Access an element */
int num = nums[1];  // Access element at index 1

/* Update an element */
nums[1] = 0;  // Update element at index 1 to 0
list.java
/* Access an element */
int num = nums.get(1);  // Access element at index 1

/* Update an element */
nums.set(1, 0);  // Update element at index 1 to 0
list.cs
/* Access an element */
int num = nums[1];  // Access element at index 1

/* Update an element */
nums[1] = 0;  // Update element at index 1 to 0
list_test.go
/* Access an element */
num := nums[1]  // Access element at index 1

/* Update an element */
nums[1] = 0     // Update element at index 1 to 0
list.swift
/* Access an element */
let num = nums[1] // Access element at index 1

/* Update an element */
nums[1] = 0 // Update element at index 1 to 0
list.js
/* Access an element */
const num = nums[1];  // Access element at index 1

/* Update an element */
nums[1] = 0;  // Update element at index 1 to 0
list.ts
/* Access an element */
const num: number = nums[1];  // Access element at index 1

/* Update an element */
nums[1] = 0;  // Update element at index 1 to 0
list.dart
/* Access an element */
int num = nums[1];  // Access element at index 1

/* Update an element */
nums[1] = 0;  // Update element at index 1 to 0
list.rs
/* Access an element */
let num: i32 = nums[1];  // Access element at index 1
/* Update an element */
nums[1] = 0;             // Update element at index 1 to 0
list.c
// C does not provide built-in dynamic arrays
list.kt
/* Access an element */
val num = nums[1]       // Access element at index 1
/* Update an element */
nums[1] = 0             // Update element at index 1 to 0
list.rb
# Access an element
num = nums[1] # Access element at index 1
# Update an element
nums[1] = 0 # Update element at index 1 to 0
Code Visualization

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Insert and Delete Elements

Compared to arrays, lists can freely add and delete elements. Adding an element at the end of a list has a time complexity of \(O(1)\), but inserting and deleting elements still have the same efficiency as arrays, with a time complexity of \(O(n)\).

list.py
# Clear the list
nums.clear()

# Add elements at the end
nums.append(1)
nums.append(3)
nums.append(2)
nums.append(5)
nums.append(4)

# Insert an element in the middle
nums.insert(3, 6)  # Insert number 6 at index 3

# Delete an element
nums.pop(3)        # Delete element at index 3
list.cpp
/* Clear the list */
nums.clear();

/* Add elements at the end */
nums.push_back(1);
nums.push_back(3);
nums.push_back(2);
nums.push_back(5);
nums.push_back(4);

/* Insert an element in the middle */
nums.insert(nums.begin() + 3, 6);  // Insert number 6 at index 3

/* Delete an element */
nums.erase(nums.begin() + 3);      // Delete element at index 3
list.java
/* Clear the list */
nums.clear();

/* Add elements at the end */
nums.add(1);
nums.add(3);
nums.add(2);
nums.add(5);
nums.add(4);

/* Insert an element in the middle */
nums.add(3, 6);  // Insert number 6 at index 3

/* Delete an element */
nums.remove(3);  // Delete element at index 3
list.cs
/* Clear the list */
nums.Clear();

/* Add elements at the end */
nums.Add(1);
nums.Add(3);
nums.Add(2);
nums.Add(5);
nums.Add(4);

/* Insert an element in the middle */
nums.Insert(3, 6);  // Insert number 6 at index 3

/* Delete an element */
nums.RemoveAt(3);  // Delete element at index 3
list_test.go
/* Clear the list */
nums = nil

/* Add elements at the end */
nums = append(nums, 1)
nums = append(nums, 3)
nums = append(nums, 2)
nums = append(nums, 5)
nums = append(nums, 4)

/* Insert an element in the middle */
nums = append(nums[:3], append([]int{6}, nums[3:]...)...) // Insert number 6 at index 3

/* Delete an element */
nums = append(nums[:3], nums[4:]...) // Delete element at index 3
list.swift
/* Clear the list */
nums.removeAll()

/* Add elements at the end */
nums.append(1)
nums.append(3)
nums.append(2)
nums.append(5)
nums.append(4)

/* Insert an element in the middle */
nums.insert(6, at: 3) // Insert number 6 at index 3

/* Delete an element */
nums.remove(at: 3) // Delete element at index 3
list.js
/* Clear the list */
nums.length = 0;

/* Add elements at the end */
nums.push(1);
nums.push(3);
nums.push(2);
nums.push(5);
nums.push(4);

/* Insert an element in the middle */
nums.splice(3, 0, 6); // Insert number 6 at index 3

/* Delete an element */
nums.splice(3, 1);  // Delete element at index 3
list.ts
/* Clear the list */
nums.length = 0;

/* Add elements at the end */
nums.push(1);
nums.push(3);
nums.push(2);
nums.push(5);
nums.push(4);

/* Insert an element in the middle */
nums.splice(3, 0, 6); // Insert number 6 at index 3

/* Delete an element */
nums.splice(3, 1);  // Delete element at index 3
list.dart
/* Clear the list */
nums.clear();

/* Add elements at the end */
nums.add(1);
nums.add(3);
nums.add(2);
nums.add(5);
nums.add(4);

/* Insert an element in the middle */
nums.insert(3, 6); // Insert number 6 at index 3

/* Delete an element */
nums.removeAt(3); // Delete element at index 3
list.rs
/* Clear the list */
nums.clear();

/* Add elements at the end */
nums.push(1);
nums.push(3);
nums.push(2);
nums.push(5);
nums.push(4);

/* Insert an element in the middle */
nums.insert(3, 6);  // Insert number 6 at index 3

/* Delete an element */
nums.remove(3);    // Delete element at index 3
list.c
// C does not provide built-in dynamic arrays
list.kt
/* Clear the list */
nums.clear();

/* Add elements at the end */
nums.add(1);
nums.add(3);
nums.add(2);
nums.add(5);
nums.add(4);

/* Insert an element in the middle */
nums.add(3, 6);  // Insert number 6 at index 3

/* Delete an element */
nums.remove(3);  // Delete element at index 3
list.rb
# Clear the list
nums.clear

# Add elements at the end
nums << 1
nums << 3
nums << 2
nums << 5
nums << 4

# Insert an element in the middle
nums.insert(3, 6) # Insert number 6 at index 3

# Delete an element
nums.delete_at(3) # Delete element at index 3
Code Visualization

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Traverse a List

Like arrays, lists can be traversed by index or by directly iterating through elements.

list.py
# Traverse the list by index
count = 0
for i in range(len(nums)):
    count += nums[i]

# Traverse list elements directly
for num in nums:
    count += num
list.cpp
/* Traverse the list by index */
int count = 0;
for (int i = 0; i < nums.size(); i++) {
    count += nums[i];
}

/* Traverse list elements directly */
count = 0;
for (int num : nums) {
    count += num;
}
list.java
/* Traverse the list by index */
int count = 0;
for (int i = 0; i < nums.size(); i++) {
    count += nums.get(i);
}

/* Traverse list elements directly */
for (int num : nums) {
    count += num;
}
list.cs
/* Traverse the list by index */
int count = 0;
for (int i = 0; i < nums.Count; i++) {
    count += nums[i];
}

/* Traverse list elements directly */
count = 0;
foreach (int num in nums) {
    count += num;
}
list_test.go
/* Traverse the list by index */
count := 0
for i := 0; i < len(nums); i++ {
    count += nums[i]
}

/* Traverse list elements directly */
count = 0
for _, num := range nums {
    count += num
}
list.swift
/* Traverse the list by index */
var count = 0
for i in nums.indices {
    count += nums[i]
}

/* Traverse list elements directly */
count = 0
for num in nums {
    count += num
}
list.js
/* Traverse the list by index */
let count = 0;
for (let i = 0; i < nums.length; i++) {
    count += nums[i];
}

/* Traverse list elements directly */
count = 0;
for (const num of nums) {
    count += num;
}
list.ts
/* Traverse the list by index */
let count = 0;
for (let i = 0; i < nums.length; i++) {
    count += nums[i];
}

/* Traverse list elements directly */
count = 0;
for (const num of nums) {
    count += num;
}
list.dart
/* Traverse the list by index */
int count = 0;
for (var i = 0; i < nums.length; i++) {
    count += nums[i];
}

/* Traverse list elements directly */
count = 0;
for (var num in nums) {
    count += num;
}
list.rs
// Traverse the list by index
let mut _count = 0;
for i in 0..nums.len() {
    _count += nums[i];
}

// Traverse list elements directly
_count = 0;
for num in &nums {
    _count += num;
}
list.c
// C does not provide built-in dynamic arrays
list.kt
/* Traverse the list by index */
var count = 0
for (i in nums.indices) {
    count += nums[i]
}

/* Traverse list elements directly */
for (num in nums) {
    count += num
}
list.rb
# Traverse the list by index
count = 0
for i in 0...nums.length
    count += nums[i]
end

# Traverse list elements directly
count = 0
for num in nums
    count += num
end
Code Visualization

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Concatenate Lists

Given a new list nums1, we can concatenate it to the end of the original list.

list.py
# Concatenate two lists
nums1: list[int] = [6, 8, 7, 10, 9]
nums += nums1  # Concatenate list nums1 to the end of nums
list.cpp
/* Concatenate two lists */
vector<int> nums1 = { 6, 8, 7, 10, 9 };
// Concatenate list nums1 to the end of nums
nums.insert(nums.end(), nums1.begin(), nums1.end());
list.java
/* Concatenate two lists */
List<Integer> nums1 = new ArrayList<>(Arrays.asList(new Integer[] { 6, 8, 7, 10, 9 }));
nums.addAll(nums1);  // Concatenate list nums1 to the end of nums
list.cs
/* Concatenate two lists */
List<int> nums1 = [6, 8, 7, 10, 9];
nums.AddRange(nums1);  // Concatenate list nums1 to the end of nums
list_test.go
/* Concatenate two lists */
nums1 := []int{6, 8, 7, 10, 9}
nums = append(nums, nums1...)  // Concatenate list nums1 to the end of nums
list.swift
/* Concatenate two lists */
let nums1 = [6, 8, 7, 10, 9]
nums.append(contentsOf: nums1) // Concatenate list nums1 to the end of nums
list.js
/* Concatenate two lists */
const nums1 = [6, 8, 7, 10, 9];
nums.push(...nums1);  // Concatenate list nums1 to the end of nums
list.ts
/* Concatenate two lists */
const nums1: number[] = [6, 8, 7, 10, 9];
nums.push(...nums1);  // Concatenate list nums1 to the end of nums
list.dart
/* Concatenate two lists */
List<int> nums1 = [6, 8, 7, 10, 9];
nums.addAll(nums1);  // Concatenate list nums1 to the end of nums
list.rs
/* Concatenate two lists */
let nums1: Vec<i32> = vec![6, 8, 7, 10, 9];
nums.extend(nums1);
list.c
// C does not provide built-in dynamic arrays
list.kt
/* Concatenate two lists */
val nums1 = intArrayOf(6, 8, 7, 10, 9).toMutableList()
nums.addAll(nums1)  // Concatenate list nums1 to the end of nums
list.rb
# Concatenate two lists
nums1 = [6, 8, 7, 10, 9]
nums += nums1
Code Visualization

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Sort a List

After sorting a list, we can use "binary search" and "two-pointer" algorithms, which are frequently tested in array algorithm problems.

list.py
# Sort a list
nums.sort()  # After sorting, list elements are arranged from smallest to largest
list.cpp
/* Sort a list */
sort(nums.begin(), nums.end());  // After sorting, list elements are arranged from smallest to largest
list.java
/* Sort a list */
Collections.sort(nums);  // After sorting, list elements are arranged from smallest to largest
list.cs
/* Sort a list */
nums.Sort(); // After sorting, list elements are arranged from smallest to largest
list_test.go
/* Sort a list */
sort.Ints(nums)  // After sorting, list elements are arranged from smallest to largest
list.swift
/* Sort a list */
nums.sort() // After sorting, list elements are arranged from smallest to largest
list.js
/* Sort a list */
nums.sort((a, b) => a - b);  // After sorting, list elements are arranged from smallest to largest
list.ts
/* Sort a list */
nums.sort((a, b) => a - b);  // After sorting, list elements are arranged from smallest to largest
list.dart
/* Sort a list */
nums.sort(); // After sorting, list elements are arranged from smallest to largest
list.rs
/* Sort a list */
nums.sort(); // After sorting, list elements are arranged from smallest to largest
list.c
// C does not provide built-in dynamic arrays
list.kt
/* Sort a list */
nums.sort() // After sorting, list elements are arranged from smallest to largest
list.rb
# Sort a list
nums = nums.sort { |a, b| a <=> b } # After sorting, list elements are arranged from smallest to largest
Code Visualization

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List Implementation

Many programming languages have built-in lists, such as Java, C++, and Python. Their implementations are quite complex, and the parameters are carefully considered, such as initial capacity, expansion multiples, and so on. Interested readers can consult the source code to learn more.

To deepen our understanding of how lists work, we attempt to implement a simple list with three key design considerations:

  • Initial capacity: Select a reasonable initial capacity for the underlying array. In this example, we choose 10 as the initial capacity.
  • Size tracking: Declare a variable size to record the current number of elements in the list and update it in real-time as elements are inserted and deleted. Based on this variable, we can locate the end of the list and determine whether expansion is needed.
  • Expansion mechanism: When the list capacity is full upon inserting an element, we need to expand. We create a larger array based on the expansion multiple and then move all elements from the current array to the new array in order. In this example, we specify that the array should be expanded to 2 times its previous size each time.
[file]{my_list}-[class]{my_list}-[func]{}