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

Time Complexity: Two Sum Problem Classic Hash Solution

O(n)

Understanding Time Complexity

We want to know how the time needed to find two numbers that add up to a target grows as the list gets bigger.

How does the solution's speed change when the input size increases?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

#include <stdio.h>
#include <stdlib.h>

int* twoSum(int* nums, int numsSize, int target, int* returnSize) {
    int* map = (int*)calloc(2048, sizeof(int));
    int* result = (int*)malloc(2 * sizeof(int));
    for (int i = 0; i < numsSize; i++) {
        int complement = target - nums[i];
        if (map[complement & 2047]) {
            result[0] = map[complement & 2047] - 1;
            result[1] = i;
            *returnSize = 2;
            free(map);
            return result;
        }
        map[nums[i] & 2047] = i + 1;
    }
    *returnSize = 0;
    free(map);
    return NULL;
}

This code finds two numbers in an array that add up to a target using a simple hash map for quick lookups.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: A single loop through the array once.
• How many times: Exactly once for each element in the input array.

How Execution Grows With Input

Each new number is checked and stored once, so the work grows steadily as the list grows.

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

Pattern observation: The number of operations grows directly with input size, doubling input roughly doubles work.

Final Time Complexity

Time Complexity: O(n)

This means the time to find the two numbers grows in a straight line with the size of the input list.

Common Mistake

[X] Wrong: "The hash map lookup inside the loop makes this solution slower than a simple double loop."

[OK] Correct: Hash map lookups are very fast and happen in constant time, so the overall time stays linear, unlike the double loop which grows much faster.

Interview Connect

Understanding this solution's time complexity shows you can use smart data structures to speed up searching, a key skill in many coding challenges.

Self-Check

"What if we used a sorted array and binary search 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 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