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

Recall & Review

beginner

What is the main idea behind using a hash map to solve the Subarray Sum Equals K problem?

We use a hash map to store the cumulative sums and their frequencies. This helps us quickly find if there is a previous cumulative sum that, when subtracted from the current cumulative sum, equals k, indicating a subarray summing to k.

beginner

In the Subarray Sum Equals K problem, what does the key in the hash map represent?

The key represents a cumulative sum of elements from the start of the array up to a certain index.

intermediate

Why do we initialize the hash map with {0:1} in the Subarray Sum Equals K solution?

We initialize with {0:1} to handle the case where a subarray starting from index 0 sums exactly to k. It means the cumulative sum equals k at that point.

intermediate

What is the time complexity of the Subarray Sum Equals K solution using a hash map?

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 that sum to k?

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

What does the cumulative sum represent in the Subarray Sum Equals K problem?

A Sum of elements from start to current index

B Sum of elements from current index to end

C Sum of all elements in the array

D Sum of elements excluding current index

Cumulative sum is the sum of elements from the start of the array up to the current index.

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

A To count total elements processed

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

C To reset the cumulative sum

D To find the maximum sum subarray

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

What initial value is stored in the hash map before processing the array?

A {} (empty)

B {k:1}

C {0:1}

D {sum:0}

We start with {0:1} to count subarrays that start from index 0 and sum to k.

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

A O(n^2)

B O(1)

C O(log n)

D O(n)

The hash map can store up to n cumulative sums, so space complexity is O(n).

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.

Explain how a hash map is used to find the number of subarrays that sum to k.

Think about how previous sums help identify subarrays ending at current index.

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

Focus on how each element updates the cumulative sum and hash map.