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:
/* 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));
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.
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 \(O(n)\).
/* 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
/* 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
/* 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
/* 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
/* 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
Code Visualization
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Traverse a List¶
Like arrays, lists can be traversed by index or by directly iterating through elements.
Code Visualization
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Concatenate Lists¶
Given a new list nums1, we can concatenate it to the end of the original list.
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.
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
sizeto 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.