Tracing List Implementations
Step-by-Step Approach
- Identify the operation: Determine whether the algorithm is inserting, removing, or accessing elements.
- Follow the steps: Break down the operation into individual steps, such as shifting elements or traversing nodes.
- Track changes: Monitor how the list structure changes after each step.
- Analyse Complexity: Consider the time and space complexity of each operation.
Hint
Tracing can help identify potential performance bottlenecks.
Tracing Algorithms
Inserting an element: ArrayList and LinkedList have an add(index, item) method (index can be omitted, then it will be added ) for adding elements.
Example
// get initial list
ArrayList<Integer> list = new ArrayList<>();
list.add(10);
list.add(20);
list.add(30);
list.add(2, 25); // perform action- Initial List: [10, 20, 30, 40]
- Operation: insert(list, 2, 25)
- The add method shifts elements at index 2 and beyond one position to the right.
- The value 25 is inserted at index 2.
- Final List: [10, 20, 25, 30, 40]
Removing an element: ArrayList and LinkedList have the method remove(index) for deleting an element at a specific position (or remove(object) to remove by value).
Example
// get initial list
ArrayList<Integer> list = new ArrayList<>();
list.add(10);
list.add(20);
list.add(25);
list.add(30);
list.add(40);
list.remove(2); // perform action
- Initial List: [10, 20, 25, 30, 40]
- Operation: remove(list, 2)
- The remove method deletes the element at index 2.
- All elements after index 2 are shifted one position to the left.
- The list size decreases by one.
- Final List: [10, 20, 30, 40]
Note
- Both add with index and remove operations in an ArrayList have O(n) time complexity due to shifts when adding or removing elements.
- The add with index operation in a LinkedList has a time complexity of O(n) for traversal, but O(1) for insertion once the position is found.
Self review
- How does the time complexity of insertion differ between ArrayLists and LinkedLists?
- Why is tracing important for debugging algorithms?
- Can you trace an algorithm that combines both insertion and removal operations?
