Delete Node at Specific Position in DSA Rust - Time & Space Complexity

Time Complexity: Delete Node at Specific Position

O(n)

Understanding Time Complexity

We want to understand how long it takes to remove a node from a linked list at a certain position.

How does the time needed change when the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

fn delete_node_at_position(head: &mut Option>, pos: usize) {
    if pos == 0 {
        if let Some(node) = head.take() {
            *head = node.next;
        }
        return;
    }
    let mut current = head.as_mut();
    for _ in 0..pos - 1 {
        if let Some(node) = current {
            current = node.next.as_mut();
        } else {
            return;
        }
    }
    if let Some(node) = current {
        if let Some(next_node) = node.next.take() {
            node.next = next_node.next;
        }
    }
}
    

This code removes a node at a given position from a singly linked list by moving through the list to find the node before the target.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Loop that moves through the list nodes to reach the position before the one to delete.
• How many times: Up to pos - 1 times, depending on the position.

How Execution Grows With Input

As the position to delete moves further in the list, the code must check more nodes one by one.

Input Size (n)	Approx. Operations
10	Up to 9 steps to reach position
100	Up to 99 steps to reach position
1000	Up to 999 steps to reach position

Pattern observation: The number of steps grows roughly in direct proportion to the position number.

Final Time Complexity

Time Complexity: O(n)

This means the time to delete a node grows linearly with the position in the list.

Common Mistake

[X] Wrong: "Deleting a node at any position takes the same fixed time."

[OK] Correct: Because you must first move through the list to find the node before the one to delete, which takes longer for nodes farther down.

Interview Connect

Understanding how linked list operations scale helps you explain your code clearly and shows you know how data structures work under the hood.

Self-Check

"What if the list was doubly linked? How would the time complexity of deleting a node at a specific position change?"

Practice

1. What does deleting a node at a specific position in a linked list mean?

easy

A. Removing the node located at that position and linking its neighbors

B. Adding a new node at that position

C. Swapping two nodes in the list

D. Counting the number of nodes up to that position

Solution

1. Step 1: Understand node deletion

   Deleting a node means removing it from the list and connecting the previous node to the next node.

2. Step 2: Apply to specific position

   At a specific position, the node at that index is removed and neighbors are linked to maintain the list.

3. Final Answer:

   Removing the node located at that position and linking its neighbors -> Option A

4. Quick Check:

   Delete node = Remove and link neighbors [OK]

Hint: Delete means remove node and link neighbors [OK]

Common Mistakes:

• Confusing deletion with insertion
• Thinking deletion swaps nodes
• Ignoring neighbor linking after deletion

2. Which Rust syntax correctly declares a mutable linked list node struct?

easy

A. struct Node { data: i32, mut next: Option }

B. struct Node { data: i32, next: Option }

C. struct Node { data: i32, next: Box<Node> }

D. struct Node { data: i32, next: &Node }

Solution

1. Step 1: Check struct fields

   Rust linked list nodes use Option for next to allow null and ownership.

2. Step 2: Validate mutability

   Mutability is controlled outside struct fields; 'mut' keyword inside struct is invalid.

3. Final Answer:

   struct Node { data: i32, next: Option } -> Option B

4. Quick Check:

   Option for next pointer [OK]

Hint: Use Option for next pointer [OK]

Common Mistakes:

• Adding 'mut' inside struct fields
• Using Box<Node> without Option causing no null
• Using references (&Node) causing lifetime issues

3. What is the output linked list after deleting the node at position 2 (0-based) from this list: 10 -> 20 -> 30 -> 40 -> null?

fn main() {
    let mut head = Some(Box::new(Node { data: 10, next: Some(Box::new(Node { data: 20, next: Some(Box::new(Node { data: 30, next: Some(Box::new(Node { data: 40, next: None })) })) })) }));
    delete_at_position(&mut head, 2);
    print_list(&head);
}

fn delete_at_position(head: &mut Option, pos: usize) {
    if pos == 0 {
        *head = head.as_mut().and_then(|node| node.next.take());
        return;
    }
    let mut current = head.as_mut();
    for _ in 0..pos-1 {
        if let Some(node) = current {
            current = node.next.as_mut();
        }
    }
    if let Some(node) = current {
        node.next = node.next.as_mut().and_then(|next_node| next_node.next.take());
    }
}

fn print_list(head: &Option) {
    let mut current = head;
    while let Some(node) = current {
        print!("{} -> ", node.data);
        current = &node.next;
    }
    println!("null");
}

struct Node {
    data: i32,
    next: Option,
}

medium

A. 10 -> 20 -> 30 -> null

B. 10 -> 30 -> 40 -> null

C. 10 -> 20 -> 40 -> null

D. 20 -> 30 -> 40 -> null

Solution

1. Step 1: Identify node to delete at position 2

   Position 2 node has data 30 in list 10 -> 20 -> 30 -> 40 -> null.

2. Step 2: Remove node 30 and link 20 to 40

   After deletion, list becomes 10 -> 20 -> 40 -> null.

3. Final Answer:

   10 -> 20 -> 40 -> null -> Option C

4. Quick Check:

   Deleted node 30 at pos 2 [OK]

Hint: Delete node at pos links previous to next [OK]

Common Mistakes:

• Deleting wrong node index
• Not linking neighbors correctly
• Confusing 0-based and 1-based positions

4. Identify the bug in this Rust function that deletes a node at a given position in a linked list:

fn delete_at_position(head: &mut Option, pos: usize) {
    let mut current = head.as_mut();
    for _ in 0..pos {
        if let Some(node) = current {
            current = node.next.as_mut();
        }
    }
    if let Some(node) = current {
        node.next = node.next.as_mut().and_then(|next_node| next_node.next.take());
    }
}

medium

A. All of the above

B. Loop runs one time too many, skipping the previous node

C. Does not update head pointer when deleting first node

D. Function does not handle deleting head node (pos 0)

Solution

1. Step 1: Analyze loop range for traversal

   The loop runs from 0 to pos, moving current to node at pos, not previous node needed for deletion.

2. Step 2: Check head deletion handling

   Function does not handle pos 0 case, so head pointer is never updated if first node is deleted.

3. Step 3: Summarize all issues

   Loop skips previous node, no head update on pos 0, so all listed bugs exist.

4. Final Answer:

   All of the above -> Option A

5. Quick Check:

   Loop and head update bugs = All above [OK]

Hint: Check loop range and head update for deletion [OK]

Common Mistakes:

• Looping to node instead of previous node
• Ignoring deletion of head node
• Not updating head pointer on deletion

5. Given a singly linked list with nodes: 5 -> 15 -> 25 -> 35 -> 45 -> null, write a Rust function to delete the node at position 3 (0-based). What will be the final list after deletion? Choose the correct final list output.

medium

A. 5 -> 15 -> 35 -> 45 -> null

B. 5 -> 15 -> 25 -> 35 -> null

C. 15 -> 25 -> 35 -> 45 -> null

D. 5 -> 15 -> 25 -> 45 -> null

Solution

1. Step 1: Identify node at position 3

   Position 3 node has value 35 in list 5 -> 15 -> 25 -> 35 -> 45 -> null.

2. Step 2: Delete node 35 and link 25 to 45

   After deletion, list becomes 5 -> 15 -> 25 -> 45 -> null.

3. Final Answer:

   5 -> 15 -> 25 -> 45 -> null -> Option D

4. Quick Check:

   Deleted node 35 at pos 3 [OK]

Hint: Delete node at pos and link neighbors [OK]

Common Mistakes:

• Deleting wrong position node
• Not linking previous node to next
• Confusing 0-based indexing