Two Sum Problem Classic Hash Solution in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main idea behind the Two Sum problem classic hash solution?

Use a hash map (dictionary) to store numbers and their indices while checking if the complement (target - current number) exists in the map to find the pair quickly.

beginner

Why do we use a hash map in the Two Sum problem?

A hash map allows us to check if the complement number exists in constant time, making the solution efficient with O(n) time complexity.

intermediate

What is the time complexity of the classic hash solution for Two Sum?

O(n), where n is the number of elements in the input list, because each element is processed once and hash map lookups are O(1).

beginner

In the Two Sum hash solution, what does the complement represent?

The complement is the number needed to add to the current number to reach the target sum (complement = target - current number).

beginner

What happens if no two numbers add up to the target in the Two Sum hash solution?

The function returns an empty list indicating that no valid pair exists after checking all elements.

What data structure is primarily used in the classic Two Sum hash solution?

A Stack

B Array

C Queue

D Hash map (dictionary)

The hash map stores numbers and their indices for quick lookup of complements.

What is the time complexity of the Two Sum classic hash solution?

A O(n)

B O(n log n)

C O(n^2)

D O(log n)

Each element is processed once, and hash map lookups are O(1), so total is O(n).

In the Two Sum problem, what does the complement equal?

A target + current number

B current number - target

C target - current number

D current number * target

Complement is the number needed to reach the target sum with the current number.

If the input list is [2, 7, 11, 15] and target is 9, what pair indices does the Two Sum solution return?

A [0, 1]

B [1, 2]

C [2, 3]

D []

2 + 7 = 9, so indices 0 and 1 are returned.

What does the Two Sum hash solution return if no pair sums to the target?

A Indices of first two elements

B Empty list

C Null

D Error

It returns an empty list indicating no valid pair found.

Explain how the classic hash solution for the Two Sum problem works step-by-step.

Think about storing numbers and checking complements while looping.

Why is the hash map approach better than a nested loop for the Two Sum problem?

Compare time complexity and lookup speed.

Practice

1. What is the main idea behind the classic hash solution for the Two Sum Problem?

easy

A. Use a dictionary to store numbers and their indices for quick lookup

B. Sort the array and use two pointers to find the sum

C. Use nested loops to check every pair of numbers

D. Use recursion to find pairs that add up to the target

Solution

1. Step 1: Understand the problem requirement

   The Two Sum problem asks to find two numbers in an array that add up to a target value.

2. Step 2: Explain the hash solution approach

   Using a dictionary (hash map) allows storing each number's index and checking if the complement (target - current number) exists quickly.

3. Final Answer:

   Use a dictionary to store numbers and their indices for quick lookup -> Option A

4. Quick Check:

   Hash map lookup = fast pair finding [OK]

Hint: Use a dictionary to find complements quickly [OK]

Common Mistakes:

• Trying to sort the array which changes indices
• Using nested loops causing slow performance
• Not storing indices, only values

2. Which of the following is the correct syntax to check if a key exists in a Python dictionary named seen?

easy

A. if key exists in seen:

B. if key in seen:

C. if seen.has_key(key):

D. if key inside seen:

Solution

1. Step 1: Recall Python dictionary membership syntax

   In Python, to check if a key exists in a dictionary, use the syntax if key in dict:.

2. Step 2: Identify correct option

   if key in seen: uses the correct syntax. if key exists in seen: and D are invalid syntax. if seen.has_key(key): is legacy and removed in Python 3.

3. Final Answer:

   if key in seen: -> Option B

4. Quick Check:

   Python dict key check = if key in dict [OK]

Hint: Use 'in' keyword to check dictionary keys [OK]

Common Mistakes:

• Using outdated has_key() method
• Writing invalid syntax like 'exists in'
• Confusing keys with values

3. What will be the output of the following code?

def two_sum(nums, target):
    seen = {}
    for i, num in enumerate(nums):
        complement = target - num
        if complement in seen:
            return [seen[complement], i]
        seen[num] = i
    return []

print(two_sum([2, 7, 11, 15], 9))

medium

A. [0, 1]

B. [1, 2]

C. [2, 3]

D. []

Solution

1. Step 1: Trace the loop and dictionary updates

   Iteration 0: num=2, complement=7, seen={}, complement not in seen, add 2:0.
   Iteration 1: num=7, complement=2, complement 2 in seen at index 0, return [0,1].

2. Step 2: Determine returned indices

   The function returns indices [0,1] where nums[0]+nums[1]=2+7=9.

3. Final Answer:

   [0, 1] -> Option A

4. Quick Check:

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

Hint: Check complement in dict before adding current number [OK]

Common Mistakes:

• Returning values instead of indices
• Adding current number before checking complement
• Returning empty list incorrectly

4. The following code tries to solve the Two Sum problem but has a bug. What is the bug?

def two_sum(nums, target):
    seen = {}
    for i, num in enumerate(nums):
        if num in seen:
            return [seen[num], i]
        complement = target - num
        seen[complement] = i
    return []

medium

A. It does not check for complement in dictionary

B. It returns indices in wrong order

C. It stores complement as key instead of the number itself

D. It uses enumerate incorrectly

Solution

1. Step 1: Analyze dictionary key storage

   The code stores complement as key with current index, but it should store the number as key to check complement later.

2. Step 2: Identify impact of wrong key storage

   Because complement is stored as key, the lookup for num in seen fails to find correct pairs, causing wrong or no results.

3. Final Answer:

   It stores complement as key instead of the number itself -> Option C

4. Quick Check:

   Store number as key, not complement [OK]

Hint: Store numbers as keys, check for complement [OK]

Common Mistakes:

• Swapping complement and number keys
• Returning indices before checking complement
• Not using enumerate properly

5. Given the list nums = [3, 3, 4, 5] and target = 6, what will the classic hash solution return?
Consider the code:

def two_sum(nums, target):
    seen = {}
    for i, num in enumerate(nums):
        complement = target - num
        if complement in seen:
            return [seen[complement], i]
        seen[num] = i
    return []

print(two_sum(nums, target))

hard

A. []

B. [1, 2]

C. [2, 3]

D. [0, 1]

Solution

1. Step 1: Trace the loop with duplicates

   Iteration 0: num=3, complement=3, seen={}, complement not in seen, add 3:0.
   Iteration 1: num=3, complement=3, complement 3 in seen at index 0, return [0,1].

2. Step 2: Understand duplicate handling

   The solution correctly finds the two 3's at indices 0 and 1 that sum to 6.

3. Final Answer:

   [0, 1] -> Option D

4. Quick Check:

   Two 3's indices = [0, 1] [OK]

Hint: Duplicates allowed; first pair found is returned [OK]

Common Mistakes:

• Ignoring duplicates and returning empty list
• Returning wrong indices due to overwriting
• Assuming no pair exists when duplicates present