Two Sum Problem Classic Hash Solution in DSA C++ - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Two Sum Classic Hash Solution

What is the output of the following C++ code that solves the Two Sum problem using a hash map?

DSA C++

#include <iostream>
#include <vector>
#include <unordered_map>

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

int main() {
    std::vector<int> nums = {2, 7, 11, 15};
    int target = 9;
    std::vector<int> result = twoSum(nums, target);
    for (int index : result) {
        std::cout << index << " ";
    }
    return 0;
}

A No output

B 0 1

C 2 3

D 1 0

💡 Hint

Think about which two numbers add up to the target and their indices.

The code finds two numbers in the vector that add up to the target 9. The numbers 2 and 7 at indices 0 and 1 add up to 9, so the output is '0 1 '.

🧠 Conceptual

intermediate

Understanding Hash Map Usage in Two Sum

In the classic Two Sum hash solution, why do we check if the complement exists in the hash map before inserting the current number?

A To avoid using extra space for the hash map.

B To insert all numbers first and then search for pairs later.

C To sort the array before searching for pairs.

D To find the pair indices immediately when the complement is found, avoiding duplicates.

💡 Hint

Think about how the algorithm finds the pair efficiently in one pass.

Checking for the complement before inserting the current number allows the algorithm to find the pair as soon as possible and prevents using the same element twice.

❓ Predict Output

advanced

Output with Duplicate Numbers in Two Sum

What is the output of this modified Two Sum code when the input vector contains duplicates?

DSA C++

#include <iostream>
#include <vector>
#include <unordered_map>

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

int main() {
    std::vector<int> nums = {3, 3, 4, 5};
    int target = 6;
    std::vector<int> result = twoSum(nums, target);
    for (int index : result) {
        std::cout << index << " ";
    }
    return 0;
}

A 2 3

B 1 2

C 0 1

D No output

💡 Hint

Look for the first pair that sums to the target.

The first two elements are both 3, and 3 + 3 = 6, so the output is indices 0 and 1.

🔧 Debug

advanced

Identify the Error in Two Sum Implementation

What error will this code produce when compiled and run?

DSA C++

#include <iostream>
#include <vector>
#include <unordered_map>

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

int main() {
    std::vector<int> nums = {1, 2, 3};
    int target = 10;
    std::vector<int> result = twoSum(nums, target);
    for (int index : result) {
        std::cout << index << " ";
    }
    return 0;
}

A Runtime error: out_of_range exception

B Compilation error: missing semicolon

C Logical error: returns empty vector

D No error, outputs '0 2 '

💡 Hint

Check the loop condition carefully.

The loop uses i <= nums.size(), which causes an out-of-range access on the last iteration, leading to a runtime error.

🚀 Application

expert

Number of Unique Pairs Summing to Target

Given the Two Sum hash solution approach, how many unique pairs of indices (i, j) with i < j exist in the array nums = {1, 2, 3, 4, 3} that sum to target = 6?

A 2

B 3

C 1

D 4

💡 Hint

List all pairs that sum to 6 and count unique index pairs.

Pairs that sum to 6 are (2,4) at indices (1,3) and (3,3) at indices (2,4). So total unique pairs are 2.

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