Advanced Binary Search

Advanced problems combine binary search with segment trees, graphs, or DP state space. Still: find monotone structure, isolate check.

Try this in Python

def first_position_bit_pattern(n: int) -> int:
    """Toy: smallest i in [0,n) where (i ^ (i>>1)) & 1 == 0 — pattern demo only."""
    lo, hi = 0, n
    while lo < hi:
        mid = (lo + hi) // 2
        ok = ((mid ^ (mid >> 1)) & 1) == 0
        if ok:
            hi = mid
        else:
            lo = mid + 1
    return lo


print(first_position_bit_pattern(20))

Key takeaways

• Advanced means harder check, not harder binary search loop.
• Decompose: prove monotonicity on paper.
• Reuse library bisect when applicable.