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

Recall & Review

beginner

What is a subarray in an array?

A subarray is a continuous part of an array. For example, in [1, 2, 3, 4], [2, 3] is a subarray but [1, 3] is not because elements are not continuous.

beginner

What does the problem 'Subarray Sum Equals K' ask for?

It asks to find how many continuous subarrays in an array have a sum equal to a given number k.

intermediate

Why do we use a hash map in the 'Subarray Sum Equals K' problem?

We use a hash map to store the counts of prefix sums seen so far. This helps us quickly find if there is a previous prefix sum that when subtracted from the current prefix sum equals k.

beginner

What is a prefix sum?

A prefix sum at index i is the sum of all elements from the start of the array up to index i.

intermediate

How does the hash map help find the count of subarrays summing to k?

For each prefix sum, we check if (prefix sum - k) exists in the hash map. If yes, it means a subarray ending at current index sums to k. We add the count of such prefix sums to the result.

What does the hash map store in the 'Subarray Sum Equals K' solution?

A Counts of prefix sums seen so far

B Indexes of all elements

C Sum of all subarrays

D Values of k

The hash map stores counts of prefix sums to quickly find if a subarray sum equals k.

What is the time complexity of the hash map approach for 'Subarray Sum Equals K'?

A O(n^3)

B O(n^2)

C O(log n)

D O(n)

Using a hash map with prefix sums allows us to solve the problem in linear time O(n).

If prefixSum[i] is the sum of elements up to index i, what does prefixSum[i] - k represent?

A The sum of the entire array

B A previous prefix sum needed to form a subarray summing to k

C The value of k itself

D The index of the subarray start

If prefixSum[i] - k exists in the hash map, it means a subarray sums to k.

What initial value should be added to the hash map before processing the array?

A prefix sum k with count 1

B empty hash map

C prefix sum 0 with count 1

D prefix sum of first element

We add prefix sum 0 with count 1 to handle subarrays starting at index 0.

Which of these is NOT true about the 'Subarray Sum Equals K' problem?

A The hash map stores all subarrays explicitly

B We can use prefix sums to optimize

C Subarrays must be continuous

D The problem counts how many subarrays sum to k

The hash map stores counts of prefix sums, not all subarrays explicitly.

Explain how prefix sums and a hash map work together to find the count of subarrays summing to k.

Think about how subtracting prefix sums helps find subarrays.

Describe the step-by-step process to solve 'Subarray Sum Equals K' using a hash map.

Focus on how the prefix sums and hash map update 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 cumulative sums and their frequencies for quick lookup

B. To sort the array elements before processing

C. To store the original array elements as keys

D. To reverse the array for easier traversal

Solution

1. Step 1: Understand the problem goal

   The problem wants to find subarrays whose sums equal a target value k.

2. Step 2: Role of hash map in solution

   The hash map stores cumulative sums seen so far and how many times they occurred, enabling quick checks for needed sums.

3. Final Answer:

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

4. Quick Check:

   Hash map stores sums = A [OK]

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

Common Mistakes:

• Thinking hash map stores array elements directly
• Assuming sorting is needed
• Using hash map to reverse array

2. Which of the following is the correct way to declare a hash map (Dictionary) in C# to store cumulative sums and their counts?

easy

A. Dictionary sumCounts = new Dictionary();

B. HashMap sumCounts = new HashMap();

C. Map sumCounts = new Map();

D. Dictionary sumCounts = new Dictionary();

Solution

1. Step 1: Identify correct C# dictionary syntax

   C# uses Dictionary<TKey, TValue> with new Dictionary<TKey, TValue>() to declare hash maps.

2. Step 2: Check each option

   Dictionary sumCounts = new Dictionary(); uses correct generic syntax. Options B and C use Java-like syntax. Dictionary sumCounts = new Dictionary(); misses generic types.

3. Final Answer:

   Dictionary sumCounts = new Dictionary(); -> Option A

4. Quick Check:

   C# Dictionary syntax = A [OK]

Hint: Use Dictionary in C# for hash maps [OK]

Common Mistakes:

• Using Java HashMap syntax in C#
• Omitting generic type parameters
• Using non-existent Map type in C#

3. What is the output of the following C# code snippet?

int[] nums = {1, 2, 3};
int k = 3;
int count = 0;
Dictionary sumCounts = new Dictionary();
sumCounts[0] = 1;
int sum = 0;
foreach (int num in nums) {
    sum += num;
    if (sumCounts.ContainsKey(sum - k)) {
        count += sumCounts[sum - k];
    }
    if (sumCounts.ContainsKey(sum)) {
        sumCounts[sum]++;
    } else {
        sumCounts[sum] = 1;
    }
}
Console.WriteLine(count);

medium

A. 1

B. 0

C. 3

D. 2

Solution

1. Step 1: Calculate cumulative sums and check counts

   nums = [1,2,3], k=3. sumCounts starts with {0:1}. - sum=1: sum-k= -2 (not in sumCounts), count=0, sumCounts={0:1,1:1} - sum=3: sum-k=0 (in sumCounts=1), count=1, sumCounts={0:1,1:1,3:1} - sum=6: sum-k=3 (in sumCounts=1), count=2, sumCounts={0:1,1:1,3:1,6:1}

2. Step 2: Final count of subarrays with sum k

   Count is 2 because subarrays [1,2] and [3] sum to 3.

3. Final Answer:

   2 -> Option D

4. Quick Check:

   Subarrays count = 2 [OK]

Hint: Track cumulative sums and check sum-k in map [OK]

Common Mistakes:

• Not initializing sumCounts with {0:1}
• Forgetting to update count correctly
• Misunderstanding sum-k lookup

4. Identify the bug in this C# code snippet for counting subarrays summing to k:

int[] nums = {1, 1, 1};
int k = 2;
int count = 0;
Dictionary sumCounts = new Dictionary();
int sum = 0;
foreach (int num in nums) {
    sum += num;
    if (sumCounts.ContainsKey(sum - k)) {
        count += sumCounts[sum - k];
    }
    sumCounts[sum] = 1;
}
Console.WriteLine(count);

medium

A. nums array is empty

B. sumCounts is not initialized with sum 0 count 1

C. count is not incremented correctly

D. sum variable is not updated inside the loop

Solution

1. Step 1: Check initialization of sumCounts

   sumCounts should start with {0:1} to count subarrays starting at index 0, but here it is empty.

2. Step 2: Check updating sumCounts inside loop

   sumCounts[sum] = 1 overwrites counts instead of incrementing, but main bug is missing initial {0:1}.

3. Final Answer:

   sumCounts is not initialized with sum 0 count 1 -> Option B

4. Quick Check:

   Initialize sumCounts[0] = 1 [OK]

Hint: Always initialize sumCounts with {0:1} before loop [OK]

Common Mistakes:

• Not initializing sumCounts with {0:1}
• Overwriting counts instead of incrementing
• Ignoring sum-k lookup logic

5. Given the array nums = {3, 4, 7, 2, -3, 1, 4, 2} and k = 7, how many subarrays sum to k using the hash map approach?

hard

A. 5

B. 3

C. 4

D. 6

Solution

1. Step 1: Calculate cumulative sums and track counts

   Initialize sumCounts = {0:1}, sum=0, count=0. - i=0: sum=3, sum-k=-4(not found), count=0, sumCounts={0:1,3:1} - i=1: sum=7, sum-k=0(found=1), count=1, sumCounts={0:1,3:1,7:1} - i=2: sum=14, sum-k=7(found=1), count=2, sumCounts={0:1,3:1,7:1,14:1} - i=3: sum=16, sum-k=9(not found), count=2, sumCounts={0:1,3:1,7:1,14:1,16:1} - i=4: sum=13, sum-k=6(not found), count=2, sumCounts={0:1,3:1,7:1,14:1,16:1,13:1} - i=5: sum=14, sum-k=7(found=1), count=3, sumCounts[14]=2 - i=6: sum=18, sum-k=11(not found), count=3, sumCounts={0:1,3:1,7:1,14:2,16:1,13:1,18:1} - i=7: sum=20, sum-k=13(found=1), count=4, sumCounts={0:1,3:1,7:1,14:2,16:1,13:1,18:1,20:1}

2. Step 2: Verify the counted subarrays

   Subarrays summing to 7 are: - [3,4] - [7] - [7,2,-3,1] - [1,4,2] Count is 4 total.

3. Final Answer:

   4 -> Option C

4. Quick Check:

   Count subarrays with sum k = 4 [OK]

Hint: Track sums and counts carefully to find all subarrays [OK]

Common Mistakes:

• Missing subarrays with negative numbers
• Not updating counts when sum repeats
• Forgetting to initialize sumCounts with {0:1}