Why Subarray Sum Equals K Using Hash Map in DSA C?

The Big Idea

What if you could find exact sum periods instantly without checking every possibility?

The Scenario

Imagine you have a long list of daily expenses, and you want to find if there is a continuous period where the total spending equals exactly $k. Doing this by checking every possible period manually would take forever.

The Problem

Manually checking every possible continuous period means adding up many sums repeatedly. This is slow and tiring, especially if the list is very long. It's easy to make mistakes and miss some periods.

The Solution

Using a hash map, we can remember sums we have seen before. This helps us quickly find if a previous sum lets us get the target sum by subtracting. It makes the search fast and simple.

Before vs After

✗ Before

int countSubarrays(int* arr, int size, int k) {
    int count = 0;
    for (int start = 0; start < size; start++) {
        int sum = 0;
        for (int end = start; end < size; end++) {
            sum += arr[end];
            if (sum == k) count++;
        }
    }
    return count;
}

✓ After

int countSubarrays(int* arr, int size, int k) {
    int count = 0, sum = 0;
    HashMap map = createHashMap();
    put(map, 0, 1);
    for (int i = 0; i < size; i++) {
        sum += arr[i];
        count += get(map, sum - k);
        put(map, sum, get(map, sum) + 1);
    }
    return count;
}

What It Enables

This method lets you find all continuous periods summing to k in just one pass through the list, saving time and effort.

Real Life Example

Finding periods of exact sales targets met in daily sales data to analyze performance trends quickly.

Key Takeaways

Manual sum checking is slow and error-prone.

Hash map stores sums seen to find matches fast.

Efficiently counts all subarrays summing to k in one pass.

Practice

1. What is the main purpose of using a hash map in the Subarray Sum Equals K problem?

easy

A. To store the original array elements as keys

B. To sort the array elements before processing

C. To keep track of the maximum subarray length

D. To store cumulative sums and their frequencies for quick lookup

Solution

1. Step 1: Understand the problem requirement

   The problem requires finding subarrays whose sums equal a target value k.

2. Step 2: Role of hash map in the solution

   The hash map stores cumulative sums seen so far and their counts to quickly check if a subarray sum equals k exists.

3. Final Answer:

   To store cumulative sums and their frequencies for quick lookup -> Option D

4. Quick Check:

   Hash map stores sums for fast subarray sum checks [OK]

Hint: Hash map tracks sums to find subarrays fast [OK]

Common Mistakes:

• Thinking hash map sorts elements
• Using hash map to store array elements directly
• Confusing hash map with array for indexing

2. Which of the following is the correct way to initialize a hash map in C for storing integer keys and values?

easy

A. map map;

B. HashMap map = new HashMap<>();

C. int map[1000] = {0};

D. unordered_map map;

Solution

1. Step 1: Identify C language syntax

   In C, hash maps are not built-in; arrays can be used as simple maps for small ranges.

2. Step 2: Check options for C syntax

   int map[1000] = {0}; uses an integer array initialized to zero, suitable as a simple map in C.

3. Final Answer:

   int map[1000] = {0}; -> Option C

4. Quick Check:

   Array initialization is valid C syntax [OK]

Hint: Use arrays for maps in C, no built-in hash map [OK]

Common Mistakes:

• Using C++ or Java syntax in C code
• Trying to declare hash maps directly in C
• Not initializing arrays before use

3. What will be the output of the following code snippet in C that counts subarrays summing to k=5?

int arr[] = {1, 2, 3, 2, 1};
int k = 5;
// Assume correct hash map logic implemented
int result = subarraySum(arr, 5, k);
printf("%d", result);

medium

A. 3

B. 2

C. 1

D. 0

Solution

1. Step 1: Identify subarrays summing to 5

   Subarrays: [2,3] (indices 1-2), [3,2] (indices 2-3), [2,3] (indices 3-4); total 3 subarrays.

2. Step 2: Count valid subarrays

   Counting carefully, the subarrays summing to 5 are three in total.

3. Final Answer:

   3 -> Option A

4. Quick Check:

   Count of subarrays with sum 5 = 3 [OK]

Hint: Count all subarrays with sum k using prefix sums [OK]

Common Mistakes:

• Counting only non-overlapping subarrays
• Missing subarrays starting at index 0
• Incorrectly summing elements

4. Identify the bug in this C code snippet for counting subarrays with sum k using a hash map:

int subarraySum(int* nums, int numsSize, int k) {
    int count = 0, sum = 0;
    int map[10000] = {0};
    map[0] = 1;
    for (int i = 0; i < numsSize; i++) {
        sum += nums[i];
        if (map[sum - k])
            count += map[sum - k];
        map[sum]++;
    }
    return count;
}

medium

A. Array map size is too small for negative sums

B. Missing initialization of count variable

C. Incorrect loop range causing out-of-bounds access

D. Using map as pointer without allocation

Solution

1. Step 1: Analyze map usage for sums

   The map array uses indices as sums, but sums can be negative, causing invalid indexing.

2. Step 2: Identify impact of negative sums

   Negative sums cause out-of-bound access or wrong counts since array indices can't be negative.

3. Final Answer:

   Array map size is too small for negative sums -> Option A

4. Quick Check:

   Negative sums need offset or different data structure [OK]

Hint: Handle negative sums with offset or hash map [OK]

Common Mistakes:

• Ignoring negative sums in indexing
• Assuming sums are always positive
• Not initializing map for sum 0

5. Given an array arr = {3, 4, 7, 2, -3, 1, 4, 2} and k = 7, how many subarrays sum to k? Use the hash map approach to find the answer.

hard

A. 4

B. 5

C. 3

D. 6

Solution

1. Step 1: Calculate prefix sums and track counts

   Prefix sums: 3,7,14,16,13,14,18,20. Check sums - k in map to count subarrays.

2. Step 2: Count subarrays with sum k=7

   Subarrays: [3,4], [7], [7,2,-3,1], [1,4,2], [4,2, -3,1,4] total 5 subarrays.

3. Final Answer:

   5 -> Option B

4. Quick Check:

   Count subarrays summing to 7 = 5 [OK]

Hint: Use prefix sums and hash map to count subarrays fast [OK]

Common Mistakes:

• Missing subarrays with negative numbers
• Counting overlapping subarrays incorrectly
• Not updating hash map counts properly