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 table (dictionary) to store numbers and their indices while checking if the complement (target - current number) exists. This allows finding the pair in one pass efficiently.

beginner

Why is a hash table useful in the Two Sum problem?

It provides fast lookup (average O(1) time) to check if the complement of the current number exists, avoiding nested loops and reducing time complexity from O(n²) to O(n).

beginner

In the Two Sum problem, what does the 'complement' mean?

The complement is the number that, when added to the current number, equals the target sum. It is calculated as target - current number.

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 lookups are O(1) on average.

beginner

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

The function returns an empty result or indication that no valid pair exists, after checking all elements without finding a complement.

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

A Linked list

B Stack

C Queue

D Hash table (dictionary)

The hash table allows quick lookup of complements to find pairs efficiently.

What is the complement of number 3 if the target sum is 9?

A 6

B 12

C 3

D 9

Complement = target - current number = 9 - 3 = 6.

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

A O(n log n)

B O(n)

C O(n²)

D O(1)

Each element is processed once with O(1) average lookup, so total O(n).

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

A [0, 1]

B [1, 2]

C [2, 3]

D No pair

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

What happens if the complement is found in the hash table during iteration?

A Clear the hash table

B Continue searching

C Return the indices of the complement and current number

D Ignore the complement

Finding the complement means the pair is found, so return their indices immediately.

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

Think about how you find pairs quickly without checking every pair.

Describe why the hash table approach is more efficient than the brute force method for Two Sum.

Focus on how lookup speed changes the overall work.

Practice

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

easy

A. To store all pairs of numbers

B. To sort the array before searching

C. To store numbers and their indices for quick lookup

D. To reverse the array elements

Solution

1. Step 1: Understand the role of hash map in Two Sum

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

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 again.

3. Final Answer:

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

4. Quick Check:

   Hash map = quick lookup [OK]

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

Common Mistakes:

• Thinking hash map sorts the array
• Assuming hash map stores all pairs
• Confusing hash map with array reversal

2. Which of the following is the correct syntax to declare a hash map (dictionary) in C for the Two Sum problem?

easy

A. unordered_map hashmap;

B. int hashmap[1000];

C. map hashmap = new map();

D. dict hashmap = {};

Solution

1. Step 1: Identify C++ STL syntax for hash map

   In C++, unordered_map is used for hash maps with integer keys and values.

2. Step 2: Check other options for correctness

   int hashmap[1000]; is a fixed-size array, not a hash map. map hashmap = new map(); is invalid syntax. dict hashmap = {}; is Python syntax.

3. Final Answer:

   unordered_map hashmap; -> Option A

4. Quick Check:

   unordered_map = hash map in C++ [OK]

Hint: Use unordered_map for hash map in C++ [OK]

Common Mistakes:

• Using array instead of hash map
• Confusing Python or Java syntax with C++
• Incorrect map declaration syntax

3. What will be the output of the following code snippet for input nums = [2, 7, 11, 15], target = 9?

int* twoSum(int* nums, int numsSize, int target, int* returnSize) {
    unordered_map map;
    for (int i = 0; i < numsSize; i++) {
        int complement = target - nums[i];
        if (map.find(complement) != map.end()) {
            int* result = (int*)malloc(2 * sizeof(int));
            result[0] = map[complement];
            result[1] = i;
            *returnSize = 2;
            return result;
        }
        map[nums[i]] = i;
    }
    *returnSize = 0;
    return NULL;
}

medium

A. [1, 0]

B. [0, 1]

C. [2, 3]

D. NULL

Solution

1. Step 1: Trace the loop and hash map insertions

   At i=0, map = {2:0}. At i=1, complement = 9-7=2 found in map at index 0.

2. Step 2: Return indices of complement and current number

   Return [0,1] as the pair that sums to 9.

3. Final Answer:

   [0, 1] -> Option B

4. Quick Check:

   nums[0]+nums[1] = 2+7 = 9 [OK]

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

Common Mistakes:

• Returning indices in wrong order
• Not checking complement before insertion
• Returning NULL when pair exists

4. Identify the bug in this Two Sum hash map solution snippet:

for (int i = 0; i < numsSize; i++) {
    map[nums[i]] = i;
    int complement = target - nums[i];
    if (map.find(complement) != map.end()) {
        return {map[complement], i};
    }
}

medium

A. Loop should start from i = 1

B. map should store complement instead of current number

C. Return statement syntax is invalid in C

D. Complement check should happen before inserting current number

Solution

1. Step 1: Analyze order of operations in loop

   Current number is inserted before checking complement, causing false positive when complement equals current number.

2. Step 2: Correct order to check complement before insertion

   Check if complement exists in map first, then insert current number to avoid matching with itself.

3. Final Answer:

   Complement check should happen before inserting current number -> Option D

4. Quick Check:

   Check complement before insert [OK]

Hint: Check complement before adding current number to map [OK]

Common Mistakes:

• Inserting before checking complement
• Wrong return syntax in C
• Starting loop from wrong index

5. Given an array nums = [3, 3, 4, 5] and target = 6, what will the Two Sum hash map solution return and why?

hard

A. [0, 1] because nums[0] + nums[1] = 3 + 3 = 6

B. [2, 3] because nums[2] + nums[3] = 4 + 5 = 9

C. NULL because no two numbers sum to 6

D. [1, 0] because indices order is reversed

Solution

1. Step 1: Trace the hash map insertions and complement checks

   At i=0, map = {3:0}. At i=1, complement = 6-3=3 found at index 0.

2. Step 2: Return indices of the first valid pair

   Return [0,1] as the pair that sums to 6.

3. Final Answer:

   [0, 1] because nums[0] + nums[1] = 3 + 3 = 6 -> Option A

4. Quick Check:

   3 + 3 = 6 [OK]

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

Common Mistakes:

• Ignoring duplicate values
• Returning wrong indices order
• Assuming no pair exists when duplicates present