Programming Fundamentals Questions

Direct answer
A pure function's output depends only on its inputs, and calling it produces no observable effect outside its own return value, no mutation of external state, no I/O, no reliance on anything that could change between calls. A function with side effects does at least one of those things: it might mutate a variable outside its own scope, write to a file, or return a different result for the same input depending on some external state.

Structured elaboration

• Same input, same output, always: this is the defining property. math.sqrt(4) is pure, it returns 2.0 every single time. A function that reads the current time, a global counter, or a mutable default argument that accumulates across calls is not pure, its output can differ across calls even with identical arguments.
• No observable effects outside the return value: a pure function doesn't print, doesn't write to a database, doesn't mutate an object passed into it, doesn't increment a counter defined outside itself. If you could delete every call to it (assuming nothing used the return value) and the rest of the program's behavior would be unchanged, that's a strong sign of purity; if deleting a call changes behavior beyond 'the return value is no longer available', something impure happened inside it.
• Why purity matters for testing: a pure function needs no setup beyond its arguments and no teardown, you call it, you assert on the return value, done. An impure function's test has to also arrange whatever external state it reads, and verify whatever external state it mutates, which multiplies both the setup complexity and the number of ways the test can be wrong or flaky.
• Why purity matters for parallel execution: if a function only reads its inputs and produces a return value, calling it concurrently from multiple threads for different inputs is automatically safe, there's no shared mutable state for two calls to race on. An impure function that mutates shared state needs explicit synchronization (locks) to be safe under concurrency, or it will produce wrong results or crashes under load in a way that's notoriously hard to reproduce.

Worked example

def add_tax_pure(price, rate):
    return price * (1 + rate)          # no side effects

total_calls = {"count": 0}
def add_tax_impure(price, rate):
    total_calls["count"] += 1          # side effect: mutates external state
    return price * (1 + rate)

Verified: add_tax_pure(100, 0.08) returns 108.0 every time it's called, and calling it twice does not change anything else observable in the program. add_tax_impure(100, 0.08) returns the same 108.0, but after two calls total_calls["count"] has become 2, a change visible to any OTHER code that also reads total_calls, which is exactly the kind of hidden coupling purity avoids: two unrelated pieces of code that both happen to call add_tax_impure now silently affect each other's view of total_calls.

Trade-offs & pitfalls
Purity isn't free, and most real programs need SOME side effects (writing output, updating a database) somewhere; the useful discipline is not 'eliminate all side effects everywhere' but 'push side effects to the edges of the system and keep the core computation (the actual business logic, the actual data transformation) pure', so the large majority of the code gets the testing and concurrency benefits, and the necessarily-impure parts are small, isolated, and easy to reason about individually.

Direct answer
An immutable object's state can never change after construction, any operation that looks like a modification actually produces a new object; a mutable object's state can be changed in place through the same reference. The trade-off is safety and reasoning simplicity (immutable) versus avoided copying and lower memory churn (mutable).

Structured elaboration

• What immutability buys you: once you hold a reference to an immutable object, nobody else holding a different reference to the SAME object can surprise you by changing it out from under you. This matters most where a value is shared: as a dict/set key (see the containers discussion), as a default function argument, and across threads.
• Why it helps concurrency specifically: a data race requires at least one thread to write while another reads (or writes) the same memory. If the object literally cannot be written to after construction, that half of the race is structurally impossible, so immutable data can be freely shared across threads with zero synchronization (no locks needed) for reads. This is a much stronger guarantee than 'we were careful with locking'.
• What it costs: every 'modification' allocates a new object and (for anything nontrivial) copies the parts that didn't logically change. For a small string this is free; for a large data structure updated in a tight loop, allocating a full new copy per update can dominate runtime and memory traffic, this is the performance problem immutability can become.
• Java's concrete example: String is immutable, every apparent concatenation makes a new String object; repeatedly concatenating in a loop is a classic O(n^2) performance trap for exactly this reason, which is why StringBuilder (a mutable, purpose-built accumulator) exists as the escape hatch. Python's tuple vs list is the same shape: tuple gives you the sharing-safety and hashability of immutability, list gives you cheap in-place growth when you know you own the only reference.

Worked example

name = "engineer"
upper_name = name.upper()   # returns a NEW string; name itself is untouched
assert name == "engineer"
assert upper_name == "ENGINEER"

nums = [1, 2, 3]
nums.append(4)              # mutates the SAME list object in place
assert nums == [1, 2, 3, 4]

(both assertions verified). name.upper() cannot change name because Python strings are immutable, there is no operation that mutates a str in place; nums.append(4) changes the exact object nums refers to, so any other variable that also referenced that list would see the appended 4 too, that aliasing behavior is the concrete risk mutable shared state introduces.

Trade-offs & pitfalls
The practical decision is rarely 'immutability is always better', it's 'default to immutable for anything shared or used as a key, and reach for mutable structures deliberately, in the narrow scope where you know you own the only reference and the update pattern is hot enough that copy-on-write would actually cost something measurable'. Treating one choice as universally correct, in either direction, is the mistake.

Direct answer
try marks a block whose exceptions you want to intercept; except runs only if a matching exception is raised inside the try; finally always runs, whether or not an exception occurred and whether or not it was caught, and it runs even if the exception propagates past this block entirely.

Structured elaboration

• No exception: the try block runs to completion, every except clause is skipped, then finally runs. Nothing unusual happens.
• Exception raised and caught: execution jumps out of the try block the instant the exception is raised (any code after the raising line in try does NOT run), the first matching except clause runs, then finally runs.
• Exception raised and NOT caught (no except clause matches its type): the matching-except search fails, finally still runs (this is the part people get wrong: finally is not conditional on being caught), and only after finally completes does the exception continue propagating up to the caller.
• The consequence that matters in practice: finally is the correct place for resource cleanup that must happen unconditionally, closing a file handle, releasing a lock, rolling back a partially-started operation, precisely because it is the one block guaranteed to run on every exit path from the try.

Worked example

def no_exception():
    order = []
    try:
        order.append('try')
    except ValueError:
        order.append('except')
    finally:
        order.append('finally')
    return order

def caught_exception():
    order = []
    try:
        order.append('try')
        raise ValueError('boom')
    except ValueError:
        order.append('except')
    finally:
        order.append('finally')
    return order

Running both (verified): no_exception() returns ['try', 'finally'] (the except clause never runs), caught_exception() returns ['try', 'except', 'finally']. A third case with a TypeError raised where only ValueError is caught confirms finally still runs before the TypeError propagates out to the caller, exactly as described above.

For the file-I/O case, opening a file and guaranteeing it closes even on a mid-read failure:

def read_lines(path):
    f = open(path, 'r')
    try:
        return f.readlines()
    finally:
        f.close()   # runs whether readlines() succeeds, raises, or the caller's except re-raises

This is exactly what a with open(path) as f: block (or Java's try-with-resources) does under the hood, they are sugar over a try/finally that closes the resource. In this pattern, whether to re-raise the error after logging it or return a sentinel value to the caller depends on whether the caller can meaningfully continue: propagate (let the exception continue, possibly after logging) when the caller cannot proceed without the data; return a sentinel only when the caller has a genuine, documented fallback.

Trade-offs & pitfalls
The most common mechanical mistake is assuming finally only runs when an exception was caught, when in fact it runs on every exit from try (normal completion, caught exception, uncaught exception, even a return inside the try block). The second most common mistake is putting cleanup code after the try/except instead of in finally, which silently skips cleanup on any path that doesn't hit that exact line, exactly the bug that finally exists to prevent.

Direct answer
The four core built-in containers split along two axes: mutability (can you change it after creation?) and whether elements need to be ordered/duplicable versus unique/hashable. A list is a mutable ordered sequence, a tuple is an immutable ordered sequence, a set is a mutable unordered collection of unique hashable elements, and a dict is a mutable unordered mapping of unique hashable keys to values.

Structured elaboration

The O(1)-average / O(n)-worst-case split for set/dict comes from hashing: normally a hash lookup goes straight to (approximately) the right bucket, but if many keys collide into the same bucket, resolving the collision degenerates toward a linear scan. list/tuple index access is O(1) because the underlying storage is one contiguous block, computing an offset from the index is arithmetic, not a search; searching a list BY VALUE (x in my_list) is O(n) because there's no shortcut, every element may need to be checked.

Worked example
Hashability is the concrete reason tuples, not lists, can be dict keys or set members: {(1, 2): 'a point'} works because a tuple's contents can't change after creation, so its hash value is stable for its lifetime; {[1, 2]: 'a point'} raises TypeError: unhashable type: 'list' because a list's contents CAN change, so Python refuses to let it serve as a hash key at all (verified: t = (1, 2, 3) then t[0] = 99 raises TypeError: 'tuple' object does not support item assignment; {1, 2, 2, 3} == {1, 2, 3}, confirming a set silently drops the duplicate 2).

Trade-offs & pitfalls
The most common mistake is choosing list by default and doing repeated x in my_list membership checks in a hot path, that's O(n) per check and O(n*m) over m checks; switching to a set for membership-only use cases is one of the cheapest performance wins available. The second is using a mutable default in a spot that implicitly needs hashability (trying to use a list as a dict key, or storing lists inside a set) and hitting a TypeError that a tuple would have avoided entirely.

Direct answer
Convert the recursive walk into an explicit loop that maintains its own stack (a plain list/array), pushing left children as you descend and popping/visiting/moving right exactly where the recursive calls would have happened, so the traversal order is identical but the call depth is no longer tied to the language's function-call stack.

Structured elaboration
The recursive in-order traversal is: recurse left, visit the node, recurse right. Each recursive call pushes a real stack frame, so a left-skewed tree of depth d uses O(d) frames and blows the interpreter's recursion limit once d exceeds it (Python's default is 1000). The iterative version replaces those implicit call-stack frames with an explicit stack you manage yourself, which lives on the heap and has no language-imposed depth limit (bounded only by available memory, not by a fixed call-depth ceiling):

1. Walk left as far as possible, pushing every node visited onto the stack (mirrors descending through the left-recursion calls without visiting yet).
2. Pop the top of the stack, that's the next node to visit, in the exact order the recursive version would have visited it.
3. Move to that node's right child and repeat from step 1 (mirrors the recurse-right call).
4. Stop when the stack is empty and there's no current node left to descend into.

Worked example

def inorder_iterative(root):
    out = []
    stack = []
    node = root
    while stack or node is not None:
        while node is not None:
            stack.append(node)
            node = node.left
        node = stack.pop()
        out.append(node.val)
        node = node.right
    return out

Verified against a known small balanced tree (root 4, left subtree 2 with children 1 and 3, right subtree 6 with children 5 and 7): both the recursive version and this iterative version return [1, 2, 3, 4, 5, 6, 7], identical order. Verified against a deliberately pathological case, a left-skewed tree of depth 3000 (each node's left child is the next node down, no right children): the recursive version raises RecursionError: maximum recursion depth exceeded at Python's default limit of 1000, while the iterative version completes and returns all 3000 values in order (len(result) == 3000, result == list(range(1, 3001))), confirming it has no equivalent depth ceiling.

Trade-offs & pitfalls
The iterative version is not simply 'better', it trades the recursive version's direct correspondence to the problem's structure (which makes it easy to verify by inspection) for an explicit stack whose invariant (everything on the stack is an ancestor of the current node, still awaiting its visit-and-descend-right) is easy to get subtly wrong, common bugs are popping before fully descending left, or forgetting to move to node.right after visiting and looping forever on the same node. This conversion is worth doing specifically when input depth is attacker- or user-controlled and therefore cannot be assumed small (a request-driven tree/graph walk), not as a blanket 'recursion is bad' rule for every tree operation.