Subarray Sum Equals K Using Hash Map in DSA Go - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main idea behind using a hash map to find subarrays with sum equals k?

We use a hash map to store the cumulative sums and their counts. This helps us quickly find if a previous cumulative sum exists such that the difference with the current sum is k, indicating a subarray with sum k.

beginner

In the context of subarray sum equals k, what does the cumulative sum represent?

The cumulative sum at index i is the sum of all elements from the start of the array up to index i. It helps track sums of subarrays efficiently.

intermediate

Why do we initialize the hash map with {0:1} before processing the array?

Initializing with {0:1} accounts for the case where a subarray starting from index 0 has a sum equal to k. It means the cumulative sum itself equals k without needing a previous sum.

intermediate

What is the time complexity of the hash map approach for finding subarray sum equals k?

The time complexity is O(n), where n is the number of elements in the array, because we traverse the array once and perform constant-time hash map operations.

advanced

How does the hash map help in counting multiple subarrays with sum k?

The hash map stores counts of cumulative sums. When the difference (current cumulative sum - k) appears multiple times, it means multiple subarrays ending at the current index have sum k, so we add all those counts.

What does the hash map store in the subarray sum equals k problem?

A Cumulative sums and their counts

B Individual elements and their indices

C Subarray lengths

D Sum of all elements

The hash map stores cumulative sums as keys and their counts as values to quickly find subarrays with sum k.

Why do we check if (current_sum - k) exists in the hash map?

A To count negative numbers

B To find the maximum element

C To find if a subarray ending at current index sums to k

D To reset the cumulative sum

If (current_sum - k) exists, it means a previous cumulative sum allows a subarray summing to k ending at current index.

What initial value do we put in the hash map before starting the iteration?

A {}

B {0:1}

C {k:1}

D {-k:1}

We initialize with {0:1} to handle subarrays starting at index 0 that sum to k.

What is the time complexity of the hash map solution for subarray sum equals k?

A O(n^2)

B O(1)

C O(log n)

D O(n)

The solution runs in O(n) time because it processes each element once with constant-time hash map operations.

If the array is [1, 2, 3] and k=3, how many subarrays sum to k?

A 2

B 1

C 3

D 0

Subarrays [1, 2] and [3] both sum to 3, so the answer is 2.

Explain how a hash map helps find the number of subarrays with sum equal to k.

Think about how previous sums relate to current sums to find subarrays.

Describe the steps to implement the subarray sum equals k solution using a hash map.

Focus on how cumulative sums and hash map interact during iteration.

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 store cumulative sums and their frequencies for quick lookup

D. To keep track of the maximum subarray length

Solution

1. Step 1: Understand the problem goal

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

2. Step 2: Role of hash map in solution

   A hash map stores cumulative sums seen so far and their counts, enabling quick checks if a previous sum exists that forms a subarray summing to k.

3. Final Answer:

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

4. Quick Check:

   Hash map = cumulative sums storage [OK]

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

Common Mistakes:

• Thinking hash map stores array elements as keys
• Assuming sorting is needed
• Confusing hash map with array for sums

2. Which of the following Go code snippets correctly initializes a hash map to store integer keys and values for the subarray sum problem?

easy

A. m := make([]int, 0)

B. m := make(map[int]int)

C. m := map[int]string{}

D. m := map[string]int{}

Solution

1. Step 1: Identify correct map type for keys and values

   We need a map with integer keys and integer values to store sums and counts.

2. Step 2: Check Go syntax for map initialization

   make(map[int]int) correctly creates a map with int keys and int values.

3. Final Answer:

   m := make(map[int]int) -> Option B

4. Quick Check:

   map[int]int = correct map type [OK]

Hint: Use make(map[int]int) for int keys and values [OK]

Common Mistakes:

• Using slice instead of map
• Wrong key or value types in map
• Using map with string keys incorrectly

3. What is the output of the following Go code snippet?

nums := []int{1, 2, 3}
k := 3
count := 0
sum := 0
m := make(map[int]int)
m[0] = 1
for _, v := range nums {
    sum += v
    if val, ok := m[sum-k]; ok {
        count += val
    }
    m[sum]++
}
fmt.Println(count)

medium

A. 1

B. 0

C. 3

D. 2

Solution

1. Step 1: Trace cumulative sums and map updates

   Iteration 1: sum=1, m[1]=1, sum-k=-2 not in map, count=0 Iteration 2: sum=3, sum-k=0 in map with count 1, count=1, m[3]=1 Iteration 3: sum=6, sum-k=3 in map with count 1, count=2, m[6]=1

2. Step 2: Final count after loop

   Count is 2 because two subarrays sum to k=3: [1,2] and [3].

3. Final Answer:

   2 -> Option D

4. Quick Check:

   Subarrays summing to 3 = 2 [OK]

Hint: Count increments when (sum-k) found in map [OK]

Common Mistakes:

• Not initializing m[0] = 1
• Forgetting to increment map count
• Miscounting subarrays

4. Identify the bug in the following Go code snippet for counting subarrays summing to k:

nums := []int{1, 1, 1}
k := 2
count := 0
sum := 0
m := make(map[int]int)
for _, v := range nums {
    sum += v
    if val, ok := m[sum-k]; ok {
        count += val
    }
    m[sum]++
}
fmt.Println(count)

medium

A. Missing initialization m[0] = 1 before loop

B. Incorrect increment of count variable

C. Wrong loop variable used

D. Using map with wrong key type

Solution

1. Step 1: Check map initialization

   The map m is used to store cumulative sums, but m[0] is not initialized to 1 before the loop.

2. Step 2: Effect of missing m[0] = 1

   Without m[0] = 1, subarrays starting from index 0 that sum to k are not counted, causing incorrect count.

3. Final Answer:

   Missing initialization m[0] = 1 before loop -> Option A

4. Quick Check:

   Initialize m[0]=1 to count subarrays from start [OK]

Hint: Always set m[0] = 1 before loop [OK]

Common Mistakes:

• Not initializing m[0]
• Incrementing count incorrectly
• Using wrong map key type

5. Given the array nums = []int{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 count.

hard

A. 4

B. 3

C. 6

D. 5

Solution

1. Step 1: Calculate cumulative sums and track counts

   Initialize m[0]=1, sum=0, count=0 Iterate nums: - sum=3, sum-k=-4 not in m, m[3]=1 - sum=7, sum-k=0 in m=1, count=1, m[7]=1 - sum=14, sum-k=7 in m=1, count=2, m[14]=1 - sum=16, sum-k=9 not in m, m[16]=1 - sum=13, sum-k=6 not in m, m[13]=1 - sum=14, sum-k=7 in m=1, count=3, m[14]=2 - sum=18, sum-k=11 not in m, m[18]=1 - sum=20, sum-k=13 in m=1, count=4, m[20]=1

2. Step 2: Verify subarrays

   The subarrays summing to 7 are: [3,4], [7], [7,2,-3,1], [1,4,2]. Total count = 4.

3. Final Answer:

   4 -> Option A

4. Quick Check:

   Count subarrays with sum k = 4 [OK]

Hint: Track cumulative sums and counts carefully [OK]

Common Mistakes:

• Missing m[0] initialization
• Miscounting overlapping subarrays
• Not updating map counts correctly