LeetCode 3825 — Longest Strictly Increasing Subsequence With Non-Zero Bitwise AND

LeetCode 3825 — Longest Strictly Increasing Subsequence With Non-Zero Bitwise AND
From Biweekly Contest 175

Problem Summary:

You are given an array nums.
You must find the length of the longest strictly increasing subsequence
whose bitwise AND of all elements is non-zero.

If no such subsequence exists, return 0.

Example:
[5,4,7] → answer = 2
because subsequence [5,7] has AND = 5 (non-zero)

Why this problem is tricky:

It looks like a normal LIS problem…
but with an extra bitwise constraint.

Brute force and DP explode quickly and cause TLE.

Key Insight:

For AND to stay non-zero,
at least one bit must remain 1 across all chosen elements.

So we flip the thinking:

Instead of choosing subsequences directly,
we choose a bit that must survive.

Strategy:

For each bit position (0 → 31):

1. Filter numbers that contain that bit
2. Run Longest Increasing Subsequence (LIS)
3. Take the maximum LIS length

This converts exponential search
into an efficient O(32 × n log n) solution.

Concepts used:

✔ Bit manipulation
✔ Longest Increasing Subsequence
✔ Greedy optimization
✔ Contest strategy thinking
✔ Pattern recognition

This is a perfect interview question combining
LIS + bit tricks + optimization insight.

Java implementation explained step-by-step in the video.

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