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

Recall & Review

beginner

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

Use a hash map to store numbers and their indices while iterating through the list. For each number, check if the complement (target - current number) exists in the map to find the pair.

beginner

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

A hash map allows quick lookup (average O(1) time) to check if the complement of the current number exists, making the solution efficient.

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 array, because each element is processed once and hash map lookups are O(1) on average.

beginner

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

The function returns an empty vector or a special value indicating no solution was found.

intermediate

Show the key steps of the Two Sum classic hash solution in C++.

1. Create an empty hash map. 2. Loop through each number in the array. 3. Calculate complement = target - current number. 4. Check if complement is in the map. 5. If yes, return indices. 6. Otherwise, add current number and index to the map. 7. Return empty if no pair found.

What data structure is used in the classic Two Sum hash solution to store numbers and indices?

A Stack

B Array

C Hash map

D Queue

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

What is the average time complexity of looking up an element in the hash map during the Two Sum solution?

A O(1)

B O(log n)

C O(n^2)

D O(n)

Hash maps provide average O(1) time complexity for lookups.

If the target is 9 and the current number is 2, what complement do we look for in the hash map?

A 7

B 11

C 2

D 9

Complement = target - current number = 9 - 2 = 7.

What should the Two Sum function return if no valid pair is found?

A Indices of the first two elements

B The input array

C The target value

D Empty vector or special value

Returning an empty vector indicates no pair sums to the target.

Which step is NOT part of the Two Sum classic hash solution?

A Iterate through the array once

B Sort the array before processing

C Check if complement exists in hash map

D Store current number and index in hash map

Sorting is not required in the classic hash solution.

Explain how the classic hash map solution solves the Two Sum problem step-by-step.

Think about how you find pairs quickly without checking all pairs.

Describe the advantages of using a hash map over a nested loop approach in the Two Sum problem.

Compare efficiency and speed.

Practice

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

easy

A. To store numbers and their indices for quick lookup

B. To sort the array before searching

C. To store the sum of all pairs

D. To reverse the array elements

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: Explain why quick lookup is needed

   Quick lookup helps find if the complement (target - current number) exists without scanning the entire array.

3. Final Answer:

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

4. Quick Check:

   Hash map = quick index lookup [OK]

Hint: Hash map stores values for instant complement search [OK]

Common Mistakes:

• Thinking hash map sorts the array
• Confusing hash map with storing sums
• Assuming hash map reverses elements

2. Which of the following C++ code snippets correctly declares the hash map used in the Two Sum problem to store integer keys and values?

easy

A. std::map<int> map;

B. std::unordered_map map;

C. std::unordered_map<int> map;

D. std::vector map;

Solution

1. Step 1: Identify correct hash map syntax

   std::unordered_map declares a hash map with int keys and int values.

2. Step 2: Explain why others are incorrect

   std::map<int> lacks value type; std::unordered_map<int> lacks value type; std::vector is invalid syntax.

3. Final Answer:

   std::unordered_map<int, int> map; -> Option B

4. Quick Check:

   Correct hash map syntax = std::unordered_map<int, int> [OK]

Hint: Use std::unordered_map<key, value> for hash maps in C++ [OK]

Common Mistakes:

• Omitting value type in map declaration
• Using std::vector instead of map
• Confusing std::map and std::unordered_map syntax

3. What will be the output of the following C++ code snippet for the input array nums = {2, 7, 11, 15} and target = 9?

std::vector<int> twoSum(std::vector<int>& nums, int target) {
    std::unordered_map<int, int> map;
    for (int i = 0; i < nums.size(); i++) {
        int complement = target - nums[i];
        if (map.find(complement) != map.end()) {
            return {map[complement], i};
        }
        map[nums[i]] = i;
    }
    return {};
}

int main() {
    auto result = twoSum({2, 7, 11, 15}, 9);
    for (int i : result) std::cout << i << " ";
}

medium

A. [1 0]

B. [2 3]

C. [0 1]

D. No output

Solution

1. Step 1: Trace the loop and map updates

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

2. Step 2: Return indices of complement and current

   Return {0,1} which prints as "0 1".

3. Final Answer:

   [0 1] -> Option C

4. Quick Check:

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

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

Common Mistakes:

• Returning indices in wrong order
• Not checking complement before insertion
• Confusing values with indices

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

std::vector<int> twoSum(std::vector<int>& nums, int target) {
    std::unordered_map<int, int> map;
    for (int i = 0; i < nums.size(); i++) {
        int complement = target - nums[i];
        if (map.find(complement) != map.end()) {
            return {i, map[complement]};
        }
        map[nums[i]] = i;
    }
    return {};
}

medium

A. Swap the return indices to {map[complement], i}

B. Change unordered_map to map

C. Insert nums[i] into map before checking complement

D. Return empty vector immediately

Solution

1. Step 1: Analyze the return statement order

   The function returns {i, map[complement]} but correct order is {map[complement], i} to match indices.

2. Step 2: Explain why swapping fixes the bug

   Swapping ensures the first index is of complement and second is current index, matching problem requirement.

3. Final Answer:

   Swap the return indices to {map[complement], i} -> Option A

4. Quick Check:

   Correct index order = complement index, current index [OK]

Hint: Return complement index first, then current index [OK]

Common Mistakes:

• Returning indices in wrong order
• Inserting before checking complement
• Changing map type unnecessarily

5. Given the input array nums = {3, 3, 4, 5} and target = 6, what will the classic Two Sum hash solution return and why?

std::vector<int> twoSum(std::vector<int>& nums, int target) {
    std::unordered_map<int, int> map;
    for (int i = 0; i < nums.size(); i++) {
        int complement = target - nums[i];
        if (map.find(complement) != map.end()) {
            return {map[complement], i};
        }
        map[nums[i]] = i;
    }
    return {};
}

hard

A. Empty vector because no two numbers sum to 6

B. [2 3] because 4 and 5 sum to 9, not 6

C. [1 0] because indices are reversed

D. [0 1] because first 3 and second 3 sum to 6

Solution

1. Step 1: Trace the loop with duplicates

   At i=0, map empty, insert (3,0). At i=1, complement=6-3=3 found at index 0.

2. Step 2: Return indices of first and second 3

   Return {0,1} because nums[0] + nums[1] = 3 + 3 = 6.

3. Final Answer:

   [0 1] because first 3 and second 3 sum to 6 -> Option D

4. Quick Check:

   Duplicates allowed, indices 0 and 1 sum to target [OK]

Hint: Duplicates can form valid pairs if sum matches target [OK]

Common Mistakes:

• Ignoring duplicates in map
• Assuming no pair sums to target
• Returning indices in wrong order