Find the next greater element for every element in O(n)

A strong answer

A strong candidate frames Find the next greater element for every element in O(n) around the exact memory layout, compiler semantics, and hardware execution model covered in Deques and monotonic stacks. Solve it with a monotonic stack, explain why it is linear, and adapt it to related questions.

A deque, short for double-ended queue and pronounced "deck", combines a stack and a queue: it supports push and pop at both the front and the back, all in O(1). The ring buffer from the previous lesson already has everything needed. Moving head backward, (head − 1) % capacity, adds at the front, just as moving forward removed from it. Java's ArrayDeque and Rust's VecDeque are growable ring buffers; Python's collections.deque stores items in a chain of fixed-size blocks instead.

Because a deque can behave as a stack, a queue or both, it is often the most useful single structure in this module. Java's documentation even recommends ArrayDeque over its older Stack class. Its main limitation is the same as a queue's: reading the middle is slower or unavailable.

In a production interview, always connect the specification rule to its concrete runtime consequence: state what lives on the stack versus the heap or static storage segment, how the compiler or operating system validates alignments, lifetimes, and error codes, and what happens under adversarial or boundary inputs (such as zero-length buffers, integer overflow, concurrent mutation, or partial I/O). Backing your explanation with a small trace of register/memory state transitions immediately separates senior systems engineers from candidates who only memorized syntax.

What the interviewer is listening for

• Mastery of core invariant: Use a deque for O(1) operations at both ends.
• Mastery of core invariant: Find the next greater element for every position in O(n) with a monotonic stack.
• Mastery of core invariant: Explain why each element is pushed and popped at most once, and extend the idea to a sliding-window maximum.
• Hardware and ABI awareness: Explaining how sizes, alignments, calling conventions, or kernel boundaries behave on real 64-bit targets rather than relying on implementation-defined assumptions.
• Defensive engineering: Naming the exact compiler flags (-Wall -Wextra -Werror), static analyzers, or runtime sanitizers (-fsanitize=address,undefined,thread) that verify correctness in CI.

Common mistakes

• Explaining only surface syntax without tracing the underlying memory addresses, ownership lifetime, or kernel/user-space state transitions.
• Assuming undefined behavior (such as signed overflow, uninitialized reads, strict-aliasing violations, or dangling pointers) will "just work" because it passed an unoptimized -O0 debug build.
• Ignoring return codes, partial reads/writes, alignment padding, or cleanup paths when an allocation or syscall fails midway through a function.