Interview guides · MPW

MPW Software Engineer Interview Questions & Guide 2026

Caching practice for MPW software engineer prep: settle the staleness budget before choosing an invalidation strategy.

The 60-second brief

A Software Engineer at MPW serves as a vital contributor to the company’s technological infrastructure, bridging the gap between complex engineering challenges and practical, scalable solutions. Whether working on Cash Application systems or Electrical Systems, your role is centered on delivering robust code that supports the operational efficiency of MPW. You are expected to be a problem-solver who can translate high-level requirements into reliable, maintainable software.

The shape of the workload matters more for your prep than the industry label does. Read-heavy serving, write-heavy ingestion and scheduled batch processing have different binding constraints and fail in different places, so find out which one the team lives in before picking design topics.

Focus areas

Trace a symptom to a mechanism under load
Choose indexes from the query's access path
Detect concurrent edits instead of losing writes

Overview

This role is critical to the business because it directly impacts the tools and processes that keep MPW’s specialized services running. You will work in an environment that values practical application and collaborative problem-solving. While the work requires technical rigor, MPW fosters a culture where engineers are encouraged to contribute ideas, learn from their peers, and grow within a supportive, stable professional setting.

The environment at MPW is described as collaborative and approachable. Focus on demonstrating your ability to work well within a team, as interviewers value personality and cultural alignment alongside technical proficiency.

Where to focus your preparation

Treat the sections below as preparation areas and confirm the format with your recruiter.

Preparation focus

No round sequence has been reported for this company, so work the categories below and confirm the format with your recruiter.

What to demonstrate

Breadth across SQL, experimentation and product reasoning
Ability to state assumptions before choosing a method

How to prepare

Drill the practice exercises below and time yourself
Prepare three quantified stories about decisions you drove

Where candidates lose points

Running a schema change as though the lock lasts as long as the statement

In PostgreSQL an ALTER TABLE that needs an ACCESS EXCLUSIVE lock must first wait for every open transaction touching that table, and while it waits, later queries needing a conflicting lock queue behind it rather than overtaking it. A DDL statement that would execute in milliseconds, issued while a thirty-second analytics query is open, therefore stalls all traffic on that table for thirty seconds: the outage length is set by the longest open transaction, not by the change. The defences are specific and worth knowing by name - set lock_timeout low and retry rather than queue, add columns without a volatile default so no table rewrite occurs (from version 11 a non-volatile default is a metadata-only change), build indexes with CREATE INDEX CONCURRENTLY while accepting that it cannot run inside a transaction block and leaves an invalid index behind if it fails, and add constraints as NOT VALID followed by a separate VALIDATE CONSTRAINT, which takes a weaker lock.

Paginating with LIMIT/OFFSET over a set that changes while the client is reading it

OFFSET n makes the database produce and discard n rows before returning anything, so the cost of a page grows with its depth rather than with its size and page 500 costs five hundred pages of work. The correctness problem is worse than the cost: if a row is inserted or reordered between two page fetches, rows shift across the offset boundary and are either skipped entirely or returned twice, and neither outcome leaves any trace in the response for the client to detect. Keyset pagination - WHERE (sort_key, id) < ($last_sort_key, $last_id) ORDER BY sort_key DESC, id DESC LIMIT n, backed by an index in exactly that order - reads only the rows it returns and is stable against concurrent inserts. It requires the tie-break column: a timestamp is not unique, and duplicate sort keys straddling a page boundary reintroduce the skip it was adopted to remove.

A queue or buffer with no bound

Every producer-consumer boundary needs a capacity and a policy for reaching it: block the producer, shed load, or drop the oldest entry. Unbounded buffering converts a temporary slowdown into memory exhaustion and hides the backpressure signal that would have revealed the consumer was falling behind.

Sharing mutable state with no stated owner

Say which thread, request or task owns each mutable structure, and what protects it when the answer is more than one: a lock, a queue that hands ownership across, or an immutable copy per reader. A structure documented as safe for concurrent reads is usually not safe for a concurrent write alongside those reads.

Questions & practice

Given a snippet of code, identify potential bugs or logic errors.

Medium · data structures and algorithms

Approach

Restate the input: its shape, its size, and what is guaranteed about it.
Choose the data structure from the access pattern, not from familiarity.
State the target complexity and say which constraint rules the naive version out.

Follow-up

What is the worst case, and how likely is it on real data?
Which test case would catch an off-by-one here?

Walk us through a piece of code you’ve written: what would you improve?

Medium · data structures and algorithms

Approach

State the target complexity and say which constraint rules the naive version out.
Walk one small example through your approach before writing the whole thing.
Name the brute-force solution and its complexity before improving on it.

Follow-up

How does this change if the input no longer fits in memory?
Which test case would catch an off-by-one here?

Track a rolling failure rate per destination for circuit decisions

Easy · sliding window · ring buffer · circuit breaker

The egress service delivers about 1,500 webhooks per second across roughly 40,000 destinations, each call bounded by a 10 second timeout. Maintain, per destination, the failure rate over the trailing 60 seconds so a caller can ask before dispatch whether the circuit should open. Attempts arrive as (destination_id, finished_at_ms, outcome). Requirement: amortised O(1) per attempt, with total memory bounded by the destination count rather than by traffic. Give the structure, its exact memory, and the rule that stops a destination with three attempts from opening a circuit.

Approach

Name the exact-deque version and then reject it as the default. Holding timestamps and advancing a tail pointer past anything older than now minus 60 seconds is a correct two-pointer window at amortised O(1) per attempt, but its memory tracks in-window traffic, so one destination in a retry storm holds hundreds of thousands of entries while thousands of quiet destinations hold none.
Use a ring of 60 one-second buckets per destination, each bucket a pair of counters for attempts and failures. On an attempt, advance the ring by the elapsed whole seconds, zeroing at most min(elapsed, 60) buckets, then increment the head. That is amortised O(1) with a fixed footprint per destination.
State the footprint: 60 buckets times two 4-byte counters is 480 bytes of payload per destination, so 40,000 destinations is roughly 20 to 25 MB with per-entry overhead, bounded by the catalogue rather than by the rate. The cost is granularity, since the oldest bucket ages out in whole seconds, which is far tighter than the decision needs.
Require a minimum sample before the circuit may open. A destination with three attempts and three failures reads as 100 percent and is not evidence; a floor of roughly 20 attempts in the window makes the ratio meaningful, and below that floor use a run of consecutive failures as the trigger instead.
Expire idle destinations, or memory grows with every destination ever seen rather than with the live set. Hold the rings in a bounded LRU keyed on destination_id and treat a miss as no history, which is the correct default for an endpoint that has been silent for a minute.
Keep the half-open probe out of the window arithmetic. After the circuit opens, one probe per interval decides whether to close it, and folding that single success into a window that still holds a 100 percent failure history would reopen the destination on one data point.

Worked solution (20 min)

Define the bucket struct and the advance step: take floor(finished_at_ms / 1000), compare with the ring's current second, zero min(delta, 60) buckets forward, then write into the new head.
Trace a destination that receives 5 attempts, goes silent for 90 seconds, then receives one more, and confirm the rate is computed from one attempt rather than six.
Compute total memory for 40,000 destinations at 60 buckets of two 4-byte counters, and state what changes if the window widens to 300 seconds.
Write the open rule as a single predicate combining the minimum-attempt floor with the rate threshold.

Expected result: A per-destination ring of 60 one-second (attempts, failures) buckets advanced lazily for amortised O(1) cost, roughly 480 bytes of counters per destination and about 20 to 25 MB for 40,000 of them, an LRU bound on live rings, and an open rule requiring both a minimum attempt count in the window and a rate above threshold.

Verify it yourself

After 60 seconds of silence a destination's window holds zero attempts and cannot open a circuit.
Memory measured with one hot destination and 39,999 idle ones is indistinguishable from the reverse, which the deque version would fail.
Replaying the same attempt stream with the clock shifted by an hour yields the same final rate.

Follow-up

The fleet is 30 instances and each sees roughly a thirtieth of a destination's traffic. Where does the rate actually live, and what does a per-instance answer get wrong?
A destination answers in 9.5 seconds and succeeds. It is not failing but it is consuming your per-destination concurrency. What signal should open the circuit here?
How would you make the window survive a process restart, and is it worth the cost?

Write the update path that detects a concurrent edit

Medium · optimistic concurrency · transactional outbox · audit history

resource carries version INT NOT NULL DEFAULT 1. resource_revision holds revision_id, resource_id, version, actor_user_id, change_kind, patch JSONB, request_id, created_at with UNIQUE (resource_id, version). outbox_event holds aggregate_type, aggregate_id, aggregate_version, event_type, payload, status. A PUT carries the version the client read. Write the exact statements for the single transaction that applies the edit, records the revision and enqueues 'resource.updated', and give the handler's branch on zero affected rows. Then say what PostgreSQL 16 does under READ COMMITTED when two of these updates hit one row at once.

Approach

One transaction, three writes, no network call inside it: UPDATE resource SET title = $3, version = version + 1, updated_at = now() WHERE resource_id = $1 AND tenant_id = $4 AND version = $2; then INSERT the resource_revision row at version $2 + 1; then INSERT the outbox_event row at the same aggregate_version. The event goes to a table rather than a broker because no transaction spans both.
Branch on the affected-row count before doing anything else. Zero has three causes — stale version, wrong tenant, row gone — so re-read once and map to 409 carrying the current version, or 404 for an id outside the caller's tenant, which also stops the endpoint confirming that another tenant's id exists.
State the engine behaviour instead of assuming it. Under READ COMMITTED the second UPDATE blocks on the row lock, and when the first commits PostgreSQL re-evaluates the WHERE clause against the newly committed row, so the version predicate now fails and the statement reports zero rows. Under REPEATABLE READ the identical collision raises SQLSTATE 40001 instead, so the handler must fold both shapes into one conflict response.
Keep UNIQUE (resource_id, version) even though the predicate already serialises writers. It is what makes a lost update unwritable if any other path ever reaches the revision table, and it converts a logic bug into 23505 rather than into a silently missing history row.
Refuse to auto-retry the whole PUT. A retry re-reads the winner's state and reapplies an intent formed against data that no longer exists — the silent overwrite the version token was added to detect. Return the conflict; merge field-wise only if the patches are provably disjoint.
Note that now() is the transaction timestamp in PostgreSQL, so resource.updated_at, the revision's created_at and the outbox row share one instant, which is what later makes reconciliation between the three tables unambiguous.

Follow-up

A client sends the version it read ten minutes ago and the resource has moved three versions. What is in your 409 so it can resolve the conflict without a full re-fetch?
Two editors, two disjoint fields, no overlap. Does your answer still refuse the second write, and should it?
Every write now touches a second hot table. How do you keep the outbox insert and its partial index from becoming the write bottleneck at 1.2k writes/second?

Stop tag and share joins from fanning out a page

Medium · join fan-out · semi-joins · many-to-many

resource_tag is (resource_id, tag_id) with PK (resource_id, tag_id); resource_share is (resource_id, shared_with_user_id, permission). The tagged-and-shared listing inner-joins resource to both, filters tenant_id, tag_id = ANY($2) and shared_with_user_id = $3, orders by updated_at DESC and takes 50. Pages come back with fewer than 50 distinct resources and the total in the header is far too high. Explain the row multiplication, rewrite both the page query and the count query so each is correct, and name the index each one needs. PostgreSQL 16.

Approach

Do the arithmetic against the predicates that are actually there. An inner join emits one row per matching child row, and both joins are filtered: tag_id = ANY($2) admits only the requested tags, shared_with_user_id = $3 admits one user's share rows. So a resource holding three of the requested tags and shared with $3 once yields three rows, not one — the multiplier is its count of matching tags times its share rows for that single user, and that second factor is 1 unless the table admits duplicate (resource_id, shared_with_user_id) pairs. LIMIT 50 then limits rows rather than resources, and COUNT(*) counts pairs — the header is the product, not the population.
Reject DISTINCT as the fix. It deduplicates after the product has been built, so the planner must materialise and sort the fanned-out set before the LIMIT can apply, and it leaves any SUM or AVG in the same select list wrong.
Rewrite both filters as semi-joins, keeping resource as the only row source: AND EXISTS (SELECT 1 FROM resource_tag rt WHERE rt.resource_id = r.resource_id AND rt.tag_id = ANY($2)) and the same shape against resource_share. A semi-join stops at the first match per resource and preserves the driving index order, so ORDER BY updated_at DESC, resource_id DESC LIMIT 50 still stops after 50 rows.
Count with the same predicates and no join at all: SELECT count(*) FROM resource r WHERE r.tenant_id = $1 AND r.status = 'active' AND EXISTS (...) AND EXISTS (...). Nothing multiplies a resource, so the number is the population.
Attach the tags for display after the page has been cut — LEFT JOIN LATERAL (SELECT array_agg(rt.tag_id) FROM resource_tag rt WHERE rt.resource_id = p.resource_id) ON TRUE over the 50 returned rows. Aggregate over the page, never over the tenant.
Index both directions and say which query each serves: PK (resource_id, tag_id) serves the lateral lookup, (tag_id, resource_id) serves the EXISTS probe by tag, and resource_share needs (shared_with_user_id, resource_id) for the same reason. An index covering one direction only leaves the other as a scan.

Worked solution (30 min)

Build a tenant where each resource carries 0-5 tags from a 20-tag vocabulary and is shared with 0-4 distinct users, then bind $2 to three tags and $3 to a user holding shares on about half the resources. Run the joined query and compare its row count to the distinct resource count on page one.
Run COUNT(*) on the joined shape and on the EXISTS shape and compare both to a ground truth computed from distinct ids; then give $3 a second permission row on 10% of resources and record which of the two counts moves.
EXPLAIN both page queries and compare rows-read plus the presence of a Sort or HashAggregate node above the join.
Add (tag_id, resource_id), re-run the EXISTS probe, and record the plan change on the inner side.

Expected result: The EXISTS page returns exactly 50 distinct resources and reads about 50 driving rows with no aggregate above the join. The EXISTS count matches the ground truth. The joined COUNT(*) is larger by roughly the average number of matching tags per qualifying resource — the tags it holds from $2, not its total tag count — times its share rows for $3, which is 1 until the duplicate permission rows exist and rises with them afterwards. The EXISTS count is unchanged by those duplicates.

Verify it yourself

The page's resource_id list has no duplicates and is 50 long whenever at least 50 rows match.
count(*) from the rewrite equals count(DISTINCT r.resource_id) over the joined shape.
EXPLAIN shows a semi-join node on the inner side rather than a full join followed by a unique or aggregate step.

Follow-up

The filter changes from 'any of these tags' to 'all of these tags'. Rewrite it and state what it costs relative to the ANY form.
A resource can be shared with the same user twice under different permissions. Does your count change, and should it?
Where does the correct total come from when the tenant holds 4M resources and the header must not cost 200 ms?

Choose what to break when replication lag reaches forty seconds

Hard · replication lag · read-after-write · consistency vs availability · load shedding

Reads are served from two replicas: 14k requests/second, about 85% absorbed by cache, so roughly 2.1k reads/second reach the database. Writes go to the primary at 1.2k/second. A tenant's backfill drives replication lag from under 100 ms to 40 seconds and it is still climbing. Sessions that have just written are pinned to the primary. Decide, endpoint class by endpoint class, whether to serve stale, fail, or route to the primary, and justify each choice with the load it adds to the primary. Then state what you would have built beforehand.

Approach

Establish blast radius before cause, because mitigation and diagnosis have different deadlines. The decisive arithmetic is what happens if the database reads move to the primary: 2.1k reads/second on top of 1.2k writes/second roughly triples its operation count, on the node already absorbing the backfill that caused this. Reads and writes are not equal in cost, so treat that as an argument against a blanket move rather than as a capacity model - but it is enough to rule out routing everything to the primary.
Classify endpoints by what staleness costs, not by how important they feel. Reads whose staleness is invisible - listings, search, counters - stay on the replica and return the watermark so the client can tell. Reads that immediately follow that same session's write keep their primary pin, which is a small bounded slice of traffic rather than the whole 2.1k/second. Reads that feed a decision with a side effect - authorisation, quota, the read half of a read-modify-write - must not be stale at all, because a 40-second-old permission row is the stale-permission failure wearing a different costume; those go to the primary or fail.
Shed instead of queueing. If the must-be-fresh class alone exceeds the primary's headroom, refuse its lowest-value slice with 503 and a retry-after. A request queued behind a saturated primary holds a connection for a client that has already given up, and the retry storm that follows is what turns degradation into an outage. Bound the connection pool per role so the read fallback cannot consume the write path's connections - that bulkhead is the single decision that determines whether writes survive the next ten minutes.
Attack the cause in parallel, since it is the one thing that can be stopped. The backfill is the load generator. A backfill that reads replication lag as its throttle signal and pauses above a threshold would have made this a non-event, with batch sizes small enough that each batch's write volume is a fraction of what a replica can apply per second. That is most of the answer to what should have existed beforehand.
Name the mechanism you would prefer over session pinning. Capture the write position at commit and require the read path to be at or past it: compare the primary's pg_current_wal_lsn() at commit time against the replica's pg_last_wal_replay_lsn(), and fall back to the primary only for the specific request that is ahead of the replica. Session pinning is the cheap approximation and it over-pins - every read in the window goes to the primary whether or not it needed to, which is a share of the cost being paid right now.

Worked solution (35 min)

List the endpoints in three buckets - staleness invisible, staleness visible to the writer only, staleness unsafe - and attach the share of the 2.1k reads/second each bucket carries.
Compute the primary's operation count under each routing option and mark which options are arithmetically available.
Write the pin rule and its window, then the shed rule: which slice, what status code, what retry-after.
Write the backfill's throttle predicate against a measured lag value, including its pause threshold and resume condition.

Expected result: Staleness-invisible reads stay on the replica and return a watermark. Reads following the session's own write keep a bounded primary pin. Reads that gate a side effect go to the primary or fail, with the lowest-value slice shed as 503 plus retry-after if headroom runs out. Connection pools are bounded per role so the read fallback cannot starve writes. The backfill is throttled on measured replication lag. The durable fix is a commit-position token compared against the replica's replay position, replacing blanket session pinning.

Verify it yourself

The traffic routed to the primary under the plan is stated as a rate, not as a category.
No element of the plan increases the write path's connection usage.
The backfill throttle references a measured lag value and has an explicit resume condition.
Every endpoint left on a replica returns something with which a client can detect staleness.

Follow-up

Lag returns to normal in nine minutes. Which mitigation do you remove first, and which one stays permanently?
A user reports their change did not save, and the write committed. Trace the path that produces that report and name the signal that would have shown it before the report arrived.
The replica is 40 seconds behind but otherwise healthy. Do you take it out of rotation? What does that do to the other replica's lag?

Give the resource write endpoints a failure taxonomy clients can act on

Easy · error taxonomy · status codes · retries

Two callers use POST and PATCH /v1/resources: a server-side SDK that retries automatically, and a browser app that shows the user a message. Today every failure is a 500 carrying prose. Define the error contract for a malformed body, a field that fails validation, an expired token, a token whose auth_version no longer matches, a resource_id owned by another tenant, a version mismatch on update, an idempotency key reused with a different body, an exceeded tenant quota, and a read replica that has not caught up. Deliverable: the envelope, the status per case, and what each caller does.

Approach

Split the envelope by audience: a stable code enum for programs, a message documented as human-only and free to change wording, a request_id that joins to resource_revision.request_id and the trace, and a details array of field paths for validation failures. Publish the negative rules too - clients never branch on message, and an unrecognised code falls back to the status class.
Assign status by who has to change something. 400 for bytes that do not parse, 422 for a body that parses and violates a rule, 401 for a token that no longer authenticates - expiry and an auth_version mismatch are the same instruction, re-authenticate - 403 for a scope the principal lacks, 404 rather than 403 for another tenant's resource_id because 403 confirms the id exists, 412 for a failed If-Match (409 if the version travels in the body instead), 422 for a key reused with a different fingerprint, 429 for quota.
Derive retryability from whether the outcome is unknown, not from the status number. A timeout or a 5xx on a write is unknown - the transaction may have committed and the response lost - so the only safe retry is one carrying the same idempotency key. Every 4xx except 429 is deterministic, and retrying it only spends the caller's remaining deadline.
Refuse to model replica lag as an error. Read-after-write is held by pinning the session to the primary for a short window, not by a 404 the SDK retries into a loop; if staleness must be visible, expose it as a watermark on a 200, because a failure code invites a retry that cannot fix it.
Write both caller behaviours into the published contract: the SDK retries only 429, 503 and timeouts, with capped backoff and full jitter bounded by the deadline it was given; the browser stops and shows message, except on 412, where it must re-read the resource and rebase the edit rather than resubmit.

Follow-up

A customer reports two resources created from one click. Which of your status codes could have produced that, and what in the contract permitted the client's reading?
You need a tenth error code next quarter without a version bump. What must v1 already have said for that to be non-breaking?

Every query on one table stalls for forty seconds mid-deploy

Medium · lock contention · ddl · migrations · postgres

During a release on PostgreSQL, every query touching resource times out for about 40 seconds and then recovers with no intervention. The release ran one migration, ALTER TABLE resource ADD COLUMN archived_reason TEXT, and the migration log shows it completing in 6 ms. Unrelated tables showed no change in error rate. Explain how a 6 ms statement caused a 40-second stall, give the ordered checks you would run on a live system to confirm it, and give the migration procedure that prevents a repeat.

Approach

Separate the statement's duration from the lock's duration. ADD COLUMN with no default is a catalogue-only change and genuinely runs in milliseconds, but it requires ACCESS EXCLUSIVE, and it cannot acquire that until every transaction already touching the table has finished.
Account for the queueing, which is the part that surprises people. A lock request that is waiting blocks later requests for conflicting modes behind it rather than letting them overtake, so one long-open transaction holds the DDL and the DDL holds all the traffic. The stall length is set by the longest open transaction, not by the size of the change.
Confirm on a live system in this order: pg_stat_activity for that table ordered by xact_start, looking for the oldest transaction and specifically for state = idle in transaction; then pg_locks where granted = false to find the waiter; then join them on pid to name blocker and blocked. pg_blocking_pids() does that join for you and is the fastest single call.
Prevent rather than merely time it better. Set lock_timeout to a second or two on the migration session so the DDL abandons the queue after a bounded wait and is retried, instead of holding it for as long as the oldest transaction lives. Be exact about what that buys: queries arriving during the wait still queue behind the pending ACCESS EXCLUSIVE request, so each attempt costs them up to one lock_timeout of added latency. The outage goes from 40 seconds to about one second per attempt, not to zero. Also run migrations away from deploy-time peaks, and put a statement timeout and an idle-in-transaction timeout on the analytics role that opens the long transactions.
Know the lock each change takes, since the mitigation differs by change. A column with a non-volatile default is a metadata-only change from PostgreSQL 11 and still needs the brief ACCESS EXCLUSIVE; an index needs CREATE INDEX CONCURRENTLY, which cannot run inside a transaction block and leaves an INVALID index to drop if it fails; a check or foreign key is added NOT VALID and then VALIDATE CONSTRAINT as a separate statement under a weaker lock.

Follow-up

The same release also wants NOT NULL on that column. What is the sequence that gets there without a long lock?
Your lock_timeout retry fails ten times in a row because the analytics transaction is always open. What do you change?
How does this differ on MySQL with InnoDB online DDL, and what is the equivalent of the waiting-lock queue there?

Suggested practice checklist

For someone who has spent the last few years shipping features and reading other people's code, and who has not solved a timed problem from a blank file in a long time. Five days rebuild the primitives and the patterns that sit on them, working from invariants rather than remembered solutions, and the last two attach that back to the rest of the loop.

Day 1 — Rebuild the primitives by implementing them

Implement a dynamic array with doubling growth and an operation counter, then change the growth rule to add a fixed sixteen slots instead, and time both for n of ten thousand, a hundred thousand and a million. The fixed-increment version resizes n/16 times at O(n) each, so its total work is quadratic; doubling is what makes append amortised constant.
Implement a hash map with separate chaining and a load-factor resize, then insert ten thousand keys engineered to land in one bucket and record what happens to lookup time, so that average-case O(1) becomes a claim with a stated precondition rather than a reflex.
For dynamic-array append and hash-map insert, write down which cost is amortised rather than worst-case, which single operation pays the whole bill, and what a system with a hard per-operation deadline would have to do instead.

Deliverable: Two working implementations plus a timing table showing the input at which each structure's advertised complexity stops holding.

Day 2 — Arrays under an invariant: two pointers, sliding window, binary search

Solve longest-subarray-with-sum-at-most-K using a sliding window, then run it on an input containing negative numbers and watch it return the wrong answer: extending the window only moves the sum monotonically when every element is non-negative, and that precondition is the whole reason the technique works.
Write the binary search that finds the first index satisfying a predicate rather than an exact value, put the loop invariant above the loop in a comment, and verify termination on the two inputs that break careless versions: the empty range, and a range where every element satisfies the predicate.
Compute the midpoint as lo + (hi - lo) / 2 and write one line on why the obvious (lo + hi) / 2 is a genuine defect in a fixed-width integer type and a non-issue in a language with arbitrary-precision integers.

Deliverable: Three solved problems, each with its invariant written above the loop, plus one recorded input on which the sliding window is provably wrong.

Day 3 — Sorting, heaps, and the greedy argument that has to be proved

Solve one top-k problem three ways, by full sort, by a size-k heap, and by quickselect, then write the values of n and k at which each becomes the right choice, along with quickselect's quadratic worst case and why a randomised pivot makes that unlikely rather than impossible.
Implement bottom-up heapify and count sift-down steps to confirm it does linear work rather than n log n, because most nodes sit near the bottom of the tree and therefore move only a short distance.
Take interval scheduling by earliest finishing time and write the exchange argument out in full: given any optimal schedule, swapping in the earliest-finishing interval keeps it feasible and no smaller. Then construct the weighted variant where that same greedy fails and name what has to replace it.

Deliverable: A three-way top-k comparison with measured crossover points, one written exchange argument, and one counterexample to a greedy rule that looks almost identical.

Day 4 — Recursion, memoisation, and the step to a table

Take one problem with overlapping subproblems, such as edit distance or coin change, instrument the plain recursion with a call counter to show the blow-up, then add memoisation and re-count.
Convert the memoised version to a bottom-up table and state the two properties you relied on: each subproblem's result depends only on its arguments, and the dependencies form a DAG you can enumerate in order.
Rewrite one deep recursion with an explicit stack, then find the input length at which the original hits the interpreter's frame limit, which defaults to about a thousand frames in CPython, so you know when the rewrite is required rather than decorative.

Deliverable: One problem in three forms, naive, memoised and tabulated, with call counts for each and the input length at which recursion depth becomes the binding constraint.

Day 5 — Graphs, where most of the work is choosing the traversal

Implement BFS and DFS over one adjacency list, then answer for each which finds a shortest path in an unweighted graph and which you would use to detect a cycle in a directed graph, including why the in-progress versus finished distinction matters for the second.
Implement topological sort by in-degree, feed it a graph containing a cycle, and confirm the failure signature is that fewer than V nodes come out rather than an exception, then note that the order it produces is one of several valid ones.
Run a shortest-path search on a graph with a single negative edge weight and show the wrong answer, then write the precondition Dijkstra actually needs, non-negative weights, because it finalises a node's distance the first time that node is popped, and name the algorithm you would switch to and its own limit.

Deliverable: A small graph library with BFS, DFS and topological sort, plus two inputs that produce documented wrong answers under the wrong algorithm choice.

Day 6 — One day for everything that is not an algorithm

Sketch one system only to the depth a coding-heavy loop tends to reach: the endpoints, what the service stores, and the single query pattern that decides the schema. Stop at twenty-five minutes.
Prepare the project answer for an interviewer who codes, which means rehearsing the two levels they push to: the specific thing you built, and why you chose that approach over the alternative they will name. Open with a number and be ready to say what it excludes.
Prepare the answer to what you would do differently, choosing a real technical mistake with a specific fix rather than a complaint about process or staffing.

Deliverable: One design sketch at endpoint-and-schema depth, plus a project answer rehearsed to two levels of follow-up.

Day 7 — Solve out loud, under time

Do three timed problems at twenty-five minutes each in a plain editor with no autocomplete and no execution until the end, then tally separately the failures that were syntax and the ones that were approach, because those two numbers call for different fixes.
Narrate one solution from the first sentence, stating the approach and its complexity before writing any code, and rehearse the sentence you will use when you realise mid-solution that the approach is wrong.
Re-solve from blank the two problems you were slowest on this week and compare the times against the day they first appeared.

Deliverable: A recording of one fully narrated solution and a tally that separates syntax failures from approach failures.

Review and mentoring: what you let through

Counting review comments or mentees proves nothing. The useful version is a specific change you approved with a reservation you stated, or one you blocked and the delay that cost. Say which standard you were holding and why it was worth the friction. A mentoring story needs the thing the other person can now do without you.

Describe a project you are particularly proud of and why.

Medium · behavioural and engineering judgement

Approach

Give the blast radius: what could have broken, and what you measured.
Name the disagreement and how you resolved it with evidence.
Pick a story where you made the decision, not one where you watched it.

Follow-up

What did you decide not to do, and why?
What would you do differently if you ran that again?

Explain how you came to choosing software development.

Medium · behavioural and engineering judgement

Approach

Pick a story where you made the decision, not one where you watched it.
Name the disagreement and how you resolved it with evidence.
State the situation in two sentences and spend the rest on the reasoning.

Follow-up

What would you do differently if you ran that again?
How did you know your change caused the improvement?

How do you handle situations where you disagree with a technical decision?

Medium · behavioural and engineering judgement

Approach

Name the disagreement and how you resolved it with evidence.
State the situation in two sentences and spend the rest on the reasoning.
Pick a story where you made the decision, not one where you watched it.

Follow-up

How did you know your change caused the improvement?
What would you do differently if you ran that again?