Hash Map vs Array vs Linked List for Lookup in DSA Rust - Complexity Comparison

Time Complexity: Hash Map vs Array vs Linked List for Lookup

O(n) for array and linked list, O(1) average for hash map

Understanding Time Complexity

We want to understand how fast we can find an item in different data structures.

How does the time to look up a value change as the data grows?

Scenario Under Consideration

Analyze the time complexity of the following lookup operations.

// Lookup in an array
fn lookup_array(arr: &[i32], target: i32) -> Option {
    for (i, &val) in arr.iter().enumerate() {
        if val == target {
            return Some(i);
        }
    }
    None
}

// Lookup in a linked list
struct Node {
    val: i32,
    next: Option>,
}

fn lookup_linked_list(head: &Option>, target: i32) -> bool {
    let mut current = head;
    while let Some(node) = current {
        if node.val == target {
            return true;
        }
        current = &node.next;
    }
    false
}

// Lookup in a hash map
use std::collections::HashMap;

fn lookup_hash_map(map: &HashMap, key: i32) -> Option<&String> {
    map.get(&key)
}
    

This code shows how to find a value in an array, a linked list, and a hash map.

Identify Repeating Operations

Look at what repeats when searching for the target.

• Array and Linked List: Loop through each element one by one.
• Hash Map: Use a direct calculation to find the value without looping.
• Dominant operation: The loop in array and linked list; constant time lookup in hash map.

How Execution Grows With Input

As the number of items grows, how many steps do we take?

Input Size (n)	Approx. Operations
10	Array/Linked List: up to 10 checks; Hash Map: about 1 check
100	Array/Linked List: up to 100 checks; Hash Map: about 1 check
1000	Array/Linked List: up to 1000 checks; Hash Map: about 1 check

Pattern observation: Array and linked list grow linearly with input size; hash map stays almost constant.

Final Time Complexity

Time Complexity: O(n) for array and linked list, O(1) average for hash map

This means array and linked list take longer as data grows, but hash map stays fast most of the time.

Common Mistake

[X] Wrong: "Hash map lookup always takes the same time no matter what."

[OK] Correct: Sometimes hash maps have collisions that slow lookup, but on average they are very fast.

Interview Connect

Knowing these differences helps you choose the right data structure and explain your choices clearly.

Self-Check

"What if the array was sorted? How would the time complexity of lookup change?"

Practice

1. Which data structure provides the fastest average lookup time for a key-value pair in Rust?

easy

A. Array

B. Vector

C. Linked List

D. Hash Map

Solution

1. Step 1: Understand lookup times for data structures

   Hash Map uses hashing to find keys quickly, usually in constant time O(1).

2. Step 2: Compare with Array and Linked List

   Array and Linked List require searching elements linearly, which is slower (O(n)).

3. Final Answer:

   Hash Map -> Option D

4. Quick Check:

   Fastest lookup = Hash Map [OK]

Hint: Hash Map uses hashing for O(1) lookup, arrays and lists are slower [OK]

Common Mistakes:

• Thinking arrays have O(1) lookup for keys (only for indices)
• Confusing linked list traversal with direct access
• Assuming vector is same as hash map for lookup

2. Which Rust syntax correctly declares a mutable HashMap named map with String keys and i32 values?

easy

A. let map: HashMap = HashMap::new();

B. let mut map: HashMap = HashMap::new();

C. let mut map = HashMap::new();

D. let map = HashMap::new();

Solution

1. Step 1: Check correct syntax for mutable HashMap declaration

   In Rust, let mut declares a mutable variable. The type is HashMap<String, i32>. The constructor is HashMap::new().

2. Step 2: Identify errors in other options

   let map = HashMap::new(); misses mut. let mut map = HashMap::new(); has wrong generic syntax. let map: HashMap = HashMap::new(); swaps key and value types.

3. Final Answer:

   let mut map: HashMap = HashMap::new(); -> Option B

4. Quick Check:

   Mutable HashMap syntax = let mut map: HashMap = HashMap::new(); [OK]

Hint: Use let mut with HashMap::new() and correct generics [OK]

Common Mistakes:

• Forgetting mut keyword for mutable map
• Wrong generic syntax with new()
• Swapping key and value types

3. What is the output of this Rust code snippet?

use std::collections::HashMap;

fn main() {
    let mut map = HashMap::new();
    map.insert("apple", 3);
    map.insert("banana", 2);
    map.insert("orange", 5);

    let lookup = map.get("banana");
    println!("{:?}", lookup);
}

medium

A. None

B. 2

C. Some(2)

D. banana

Solution

1. Step 1: Understand HashMap get method return type

   The get method returns an Option type: Some(&value) if key exists, else None.

2. Step 2: Check if key "banana" exists and its value

   Key "banana" exists with value 2, so get("banana") returns Some(&2). Printing with {:?} shows Some(2).

3. Final Answer:

   Some(2) -> Option C

4. Quick Check:

   HashMap get returns Option = Some(2) [OK]

Hint: HashMap get returns Option; Some(value) if found, else None [OK]

Common Mistakes:

• Expecting direct value instead of Option
• Confusing None with Some
• Printing key instead of value

4. Identify the error in this Rust code that tries to find a value in a linked list:

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

fn find(head: &Option, target: i32) -> bool {
    let mut current = head;
    while current.is_some() {
        if current.as_ref().unwrap().value == target {
            return true;
        }
        current = current.unwrap().next;
    }
    false
}

medium

A. Using unwrap() twice causes ownership error

B. Missing mutable keyword for current

C. Incorrect comparison operator in if statement

D. next field should be a reference, not Box

Solution

1. Step 1: Analyze ownership in while loop

   Calling unwrap() on current moves ownership, so current cannot be used again.

2. Step 2: Identify why unwrap() causes error

   Using unwrap() twice consumes current, causing ownership error. Instead, use references or pattern matching.

3. Final Answer:

   Using unwrap() twice causes ownership error -> Option A

4. Quick Check:

   Ownership error due to unwrap() usage [OK]

Hint: unwrap() moves ownership; use references to avoid errors [OK]

Common Mistakes:

• Ignoring ownership rules with unwrap()
• Thinking mutable needed for current here
• Confusing Box with reference types

5. You need to store a large collection of user IDs (integers) and quickly check if a user ID exists. Which data structure is best and why? Choose the best option considering lookup speed and memory efficiency.

hard

A. Hash Map, because it offers average constant time lookup for keys

B. Array, because it provides constant time lookup for any integer key

C. Linked List, because it uses less memory and is easy to implement

D. Vector, because it automatically resizes and supports fast lookup

Solution

1. Step 1: Consider lookup speed for large collections

   Linked List has O(n) lookup, which is slow. Array lookup by index is O(1), but only if keys are indices, not arbitrary integers.

2. Step 2: Evaluate Hash Map and Vector

   Hash Map provides average O(1) lookup for arbitrary keys like user IDs. Vector lookup by index is O(1), but user IDs may not be continuous indices.

3. Final Answer:

   Hash Map, because it offers average constant time lookup for keys -> Option A

4. Quick Check:

   Best lookup for arbitrary keys = Hash Map [OK]

Hint: Use Hash Map for fast lookup of arbitrary keys like user IDs [OK]

Common Mistakes:

• Assuming array lookup works for arbitrary keys
• Choosing linked list for speed
• Confusing vector with hash map for key lookup