Find Subarrays With Equal Sum

Find Subarrays With Equal Sum

What is this problem about?

The Find Subarrays With Equal Sum interview question is a simple search for patterns within an array. You are asked to determine if there exist at least two different subarrays of length exactly 2 that have the same sum. The subarrays do not need to be non-overlapping; they just need to start at different indices.

Why is this asked in interviews?

Companies like Morgan Stanley and Bloomberg use the Find Subarrays With Equal Sum coding problem as a warm-up to check for basic knowledge of Hash Table interview patterns. It tests whether you can identify a "Two-Sum" style problem and use a Set to find duplicates in a single pass. It’s a test of choosing the right data structure for the job.

Algorithmic pattern used

This problem follows the Hash Set for Duplicate Detection pattern.

1. Iterate: Traverse the array from index 0 to $n-2$.
2. Calculate: For each index i, find the sum of the pair: nums[i] + nums[i+1].
3. Check: Check if this sum has been seen before in a HashSet.
4. Store: If not seen, add the sum to the set. If seen, you've found a duplicate sum, so return true.

Example explanation

Array: [4, 2, 4]

1. Pair 1: 4 + 2 = 6. Set: {6}.
2. Pair 2: 2 + 4 = 6. Sum 6 is already in the set! Result: True. Array: [1, 2, 3, 4]
3. Pair 1: $1+2=3$. Set: {3}.
4. Pair 2: $2+3=5$. Set: {3, 5}.
5. Pair 3: $3+4=7$. Set: {3, 5, 7}. Result: False.

Common mistakes candidates make

• Nested Loops: Using two loops to compare every pair of sums ($O(N^2)$), which is less efficient than the $O(N)$ set-based approach.
• Subsequence Confusion: Mistakenly looking for subsequences instead of contiguous subarrays.
• Off-by-one: Stopping the loop at n-1, which causes an index out of bounds error when trying to access i+1.

Interview preparation tip

Whenever you need to find "if any two X are the same," your first instinct should be to use a Hash Set. This pattern reduces the time complexity from quadratic to linear in almost every case.