Longest Even Odd Subarray With Threshold

Longest Even Odd Subarray With Threshold

What is this problem about?

The Longest Even Odd Subarray With Threshold problem provides an integer array and an integer threshold. You need to find the length of the longest contiguous subarray that follows strict rules: it must start with an even number, every adjacent pair of numbers in the subarray must have different parities (even, odd, even, odd, etc.), and every number in the subarray must be less than or equal to the threshold.

Why is this asked in interviews?

This is a great, highly logical array traversal question often seen in mid-level interviews. It tests a candidate's ability to track multiple simultaneous constraints (parity alternation, threshold limit, starting condition) without creating deeply nested, unreadable loops. It evaluates whether you can use a sliding window or a state-machine approach cleanly and concisely.

Algorithmic pattern used

This problem is best solved using a Single Pass / Sliding Window (or State Machine) pattern. You iterate through the array once, maintaining a counter for the current valid sequence length. If you encounter a valid even number $\le$ threshold, you start counting. As you move forward, as long as the threshold rule and the alternating parity rule are satisfied, you increment the count. If a rule is broken, you record the max length and reset the state.

Example explanation

Array: [3, 2, 5, 4, 8], Threshold: 5.

• Index 0 (3): It's odd, cannot start a sequence. Max = 0.
• Index 1 (2): Even and $2 \le 5$. We start! current_len = 1.
• Index 2 (5): Odd (different from 2) and $5 \le 5$. Valid! current_len = 2.
• Index 3 (4): Even (different from 5) and $4 \le 5$. Valid! current_len = 3.
• Index 4 (8): $8 > 5$. Fails the threshold! The sequence breaks. The longest valid sequence is [2, 5, 4], with a length of 3. Note that since 8 is $> 5$, it cannot even start a new sequence despite being even.

Common mistakes candidates make

A very common mistake is improperly managing the "reset" logic when a sequence breaks. If a sequence breaks because two adjacent numbers have the same parity, candidates sometimes reset the counter to zero. However, if the current number is an even number $\le$ threshold, it can actually act as the start of a brand new sequence of length 1! Failing to start the new sequence immediately causes candidates to miss valid subarrays.

Interview preparation tip

For the Longest Even Odd Subarray With Threshold coding problem, focus heavily on the "else" conditions of your loop. When your valid chain is broken, explicitly evaluate the current number. Ask yourself: "Can this element that broke my previous chain serve as the beginning of a new chain?" Implementing this logic cleanly prevents the need to back-track pointers and keeps your algorithm linear.