Two Sum Problem Classic Hash Solution in DSA Rust - Time & Space Complexity

Time Complexity: Two Sum Problem Classic Hash Solution

O(n)

Understanding Time Complexity

We want to understand how fast the Two Sum solution using a hash map runs as the input size grows.

Specifically, how does the time to find two numbers that add up to a target change when the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

use std::collections::HashMap;

fn two_sum(nums: &[i32], target: i32) -> Option<(usize, usize)> {
    let mut map = HashMap::new();
    for (i, &num) in nums.iter().enumerate() {
        let complement = target - num;
        if let Some(&j) = map.get(&complement) {
            return Some((j, i));
        }
        map.insert(num, i);
    }
    None
}
    

This code finds two numbers in the list that add up to the target using a hash map for quick lookups.

Identify Repeating Operations

• Primary operation: One loop over the input array.
• How many times: Exactly once for each element in the list.
• Inside the loop: Constant time hash map lookups and insertions.

How Execution Grows With Input

As the list size grows, the number of steps grows roughly the same amount.

Input Size (n)	Approx. Operations
10	About 10 lookups and inserts
100	About 100 lookups and inserts
1000	About 1000 lookups and inserts

Pattern observation: The work grows linearly with the input size.

Final Time Complexity

Time Complexity: O(n)

This means the time to find the two numbers grows in direct proportion to the size of the input list.

Common Mistake

[X] Wrong: "Because there is a loop inside a loop, the time is O(n²)."

[OK] Correct: The code only has one loop; hash map lookups are fast and do not add extra loops, so the time stays linear.

Interview Connect

Understanding this solution's time complexity helps you explain why hash maps speed up searching, a key skill in coding interviews.

Self-Check

"What if the input list was sorted and we used two pointers instead of a hash map? How would the time complexity change?"

Practice

1. What is the main purpose of using a hash map in the Two Sum problem classic hash solution?

easy

A. To reverse the array elements

B. To sort the array before searching

C. To store the sum of all pairs

D. To store numbers and their indices for quick lookup

Solution

1. Step 1: Understand the role of hash map

   The hash map stores each number as a key and its index as the value for quick access.

2. Step 2: Use hash map for complement lookup

   For each number, we check if the complement (target - number) exists in the hash map to find the pair.

3. Final Answer:

   To store numbers and their indices for quick lookup -> Option D

4. Quick Check:

   Hash map stores number:index pairs [OK]

Hint: Hash map helps find complements fast by storing indices [OK]

Common Mistakes:

• Thinking hash map sorts the array
• Trying to store sums instead of indices
• Using hash map to reverse elements

2. Which of the following Rust code snippets correctly declares a mutable hash map to solve the Two Sum problem?

easy

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

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

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

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

Solution

1. Step 1: Identify mutable hash map declaration

   To insert elements, the hash map must be mutable, so use 'let mut'.

2. Step 2: Use full path or import HashMap

   Using 'std::collections::HashMap::new()' is correct if HashMap is not imported.

3. Final Answer:

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

4. Quick Check:

   Mutable hash map declaration requires 'mut' [OK]

Hint: Use 'let mut' to allow inserting into hash map [OK]

Common Mistakes:

• Forgetting 'mut' keyword for mutable map
• Using HashMap without importing or full path
• Declaring map immutable when insertions needed

3. What will be the output of the following Rust code snippet for the Two Sum problem?

fn two_sum(nums: Vec<i32>, target: i32) -> Vec<i32> {
    let mut map = std::collections::HashMap::new();
    for (i, &num) in nums.iter().enumerate() {
        if let Some(&index) = map.get(&(target - num)) {
            return vec![index as i32, i as i32];
        }
        map.insert(num, i);
    }
    vec![]
}

fn main() {
    let result = two_sum(vec![2, 7, 11, 15], 9);
    println!("{:?}", result);
}

medium

A. [2, 3]

B. [1, 0]

C. [0, 1]

D. []

Solution

1. Step 1: Iterate and check complements

   At i=0, num=2, map empty, insert (2,0). At i=1, num=7, complement=9-7=2 found at index 0.

2. Step 2: Return indices of complement pair

   Return vector with indices [0,1] as the pair sums to target 9.

3. Final Answer:

   [0, 1] -> Option C

4. Quick Check:

   Indices of 2 and 7 are [0,1] [OK]

Hint: Check complement in map before inserting current number [OK]

Common Mistakes:

• Returning indices in wrong order
• Not casting usize to i32 for return
• Returning empty vector when pair exists

4. Identify the bug in this Rust Two Sum solution and select the fix:

fn two_sum(nums: Vec<i32>, target: i32) -> Vec<i32> {
    let mut map = std::collections::HashMap::new();
    for (i, num) in nums.iter().enumerate() {
        if let Some(&index) = map.get(&(target - num)) {
            return vec![index as i32, i as i32];
        }
        map.insert(num, i);
    }
    vec![]
}

medium

A. Change 'num' to '*num' in map.insert to match key type

B. Remove 'as i32' casts from return vector

C. Change 'map.get(&(target - num))' to 'map.get(&(target + num))'

D. Declare map as immutable instead of mutable

Solution

1. Step 1: Check key types in hash map

   Keys are i32 values, but 'num' is a reference (&i32), so insert needs dereferenced value.

2. Step 2: Fix insertion to use dereferenced num

   Change 'map.insert(num, i);' to 'map.insert(*num, i);' to insert i32 key, matching get() key type.

3. Final Answer:

   Change 'num' to '*num' in map.insert to match key type -> Option A

4. Quick Check:

   Dereference num when inserting key [OK]

Hint: Dereference iterator item before inserting into hash map [OK]

Common Mistakes:

• Inserting reference instead of value as key
• Changing target arithmetic incorrectly
• Making map immutable causing insert error

5. Given the input array [3, 3, 4, 5] and target 6, what will the Two Sum classic hash solution return and why?

hard

A. [0, 1] because the first two 3's sum to 6

B. [1, 2] because 3 and 4 sum to 7, closest to 6

C. [2, 3] because 4 and 5 sum to 9, which is greater than 6

D. [] because no two numbers sum exactly to 6

Solution

1. Step 1: Check pairs for target sum

   The first element 3 at index 0 is inserted. At index 1, num=3, complement=6-3=3 found at index 0.

2. Step 2: Return indices of first matching pair

   Return [0,1] because these two 3's sum exactly to 6.

3. Final Answer:

   [0, 1] because the first two 3's sum to 6 -> Option A

4. Quick Check:

   First pair summing to target returned [OK]

Hint: Return first found pair that sums to target [OK]

Common Mistakes:

• Choosing pairs that don't sum to target
• Ignoring duplicate values as valid pairs
• Returning empty vector incorrectly