Stage-by-stage summaries, dense pseudocode, complexity, and the discussion follow-ups. Skim end-to-end first, then drill the three you flagged as priority: image processor, web crawler, LRU.
Given a start URL and a provider with get_links(url), return every URL reachable that shares the start's hostname. Then make it parallel.
Approach. Standard BFS — queue + visited set. Mark visited at enqueue time, not at pop (otherwise duplicates leak in). Strip # and ? before comparing. Skip off-host links.
from collections import deque def crawl_same_host(start_url, provider): target_host = provider.get_hostname(start_url) visited = {start_url} queue = deque([start_url]) while queue: url = queue.popleft() for link in provider.get_links(url): link = link.split("#", 1)[0].split("?", 1)[0] if provider.get_hostname(link) != target_host: continue if link in visited: continue visited.add(link) queue.append(link) return visited
Time O(V + E) Space O(V)
The hard part is termination. "Queue empty" is NOT a stop signal — a worker can pull the last URL, then enqueue children before another worker checks. Track in-flight work, not just queue depth.
queue.Queue — already thread-safe per put/get.threading.Lock around visited set (Python set isn't thread-safe).in_flight counter + lock + threading.Event for done signal.ThreadPoolExecutor(max_workers=N) for bounded parallelism.from concurrent.futures import ThreadPoolExecutor from queue import Queue, Empty import threading def crawl_same_host_mt(start_url, provider, num_workers=4): target_host = provider.get_hostname(start_url) visited = {start_url} visited_lock = threading.Lock() in_flight = [1] in_flight_lock = threading.Lock() done_event = threading.Event() q = Queue() q.put(start_url) def worker(): while not done_event.is_set(): try: url = q.get(timeout=0.05) except Empty: continue try: for link in provider.get_links(url): link = link.split("#", 1)[0].split("?", 1)[0] if provider.get_hostname(link) != target_host: continue with visited_lock: if link in visited: continue visited.add(link) with in_flight_lock: in_flight[0] += 1 q.put(link) finally: with in_flight_lock: in_flight[0] -= 1 if in_flight[0] == 0: done_event.set() with ThreadPoolExecutor(max_workers=num_workers) as ex: futures = [ex.submit(worker) for _ in range(num_workers)] done_event.wait() for f in futures: f.result() return visited
queue.get(timeout=...) not blocking get (need to poll done_event); always try/finally around the body so the in_flight decrement runs even on exception; in_flight = [1] not plain int (closure mutation), OR use nonlocal.Time O(V + E) Wall-clock ≈ /num_workers
<link rel="canonical">).Apply each transform JSON to each image. 6 transform types (3 with params). Helper get_output_path(image, transform) tells you where to save. Then parallelize.
Library: Pillow (easiest). Approach: enumerate image files, enumerate transforms, for each pair apply transforms in order, save.
Image.open(path) → imageImageOps.grayscale(img) → mode 'L' (single channel — .convert('RGB') if next op expects RGB or saving as JPEG)ImageOps.mirror(img) — flip horizontalImageOps.flip(img) — flip verticalImageOps.scale(img, factor) — scale by factorimg.filter(ImageFilter.GaussianBlur(radius))img.rotate(angle, expand=True) — expand=True to swap dims on 90°from PIL import Image, ImageOps, ImageFilter import os, json def apply_transform(image_path, transform_path): with open(transform_path) as f: data = json.load(f) img = Image.open(image_path).copy() for t in data["transformations"]: kind = t["type"] if kind == "grayscale": img = ImageOps.grayscale(img) elif kind == "flip_horizontal": img = ImageOps.mirror(img) elif kind == "flip_vertical": img = ImageOps.flip(img) elif kind == "scale": img = ImageOps.scale(img, t["factor"]) elif kind == "blur": img = img.filter(ImageFilter.GaussianBlur(t["radius"])) elif kind == "rotate": img = img.rotate(t["angle"], expand=True) return img def process_images(image_dir, transformation_dir, output_dir, get_output_path): transforms = [os.path.join(transformation_dir, f) for f in os.listdir(transformation_dir) if f.lower().endswith(".json")] images = [os.path.join(image_dir, f) for f in os.listdir(image_dir) if f.lower().endswith((".png", ".jpg", ".jpeg"))] for image in images: for transform in transforms: result = apply_transform(image, transform) output = get_output_path(image, transform) os.makedirs(os.path.dirname(output), exist_ok=True) result.save(output)
rotate defaults to expand=False (crops back to original canvas); .lower().endswith() for case-insensitive extension match; os.makedirs(os.path.dirname(out), exist_ok=True) before save (handles nested output paths); open(transform_path) not json.load(transform_path) — pass file object, not path.This is CPU-bound (pixel ops). Use ProcessPoolExecutor, not threads. Each (image, transform) pair is independent. Worker MUST be module-scope (pickling) and should ship paths only — never decoded image buffers (huge IPC cost).
from concurrent.futures import ProcessPoolExecutor # MODULE SCOPE — must be importable by name, not nested or lambda def _worker(args): image_path, transform_path, output_path = args result = apply_transform(image_path, transform_path) os.makedirs(os.path.dirname(output_path), exist_ok=True) result.save(output_path) def process_images_parallel(image_dir, transformation_dir, output_dir, get_output_path, max_workers=None): jobs = [(img, tf, get_output_path(img, tf)) for img in images for tf in transforms] with ProcessPoolExecutor(max_workers=max_workers) as ex: list(ex.map(_worker, jobs)) # list() forces exceptions to surface
ex.map(...) returns a lazy iterator. Work IS submitted eagerly but exceptions from workers only surface as you iterate. list(...) drains the iterator → propagates errors.try/except, log, continue. Return success/failure manifest.call(func, *args, **kwargs) memoizes. Capacity-bounded. Survives crashes — same entries AND same recency after restart.
Bugs to find:
hash(args) fails on lists/dicts/sets. kwargs is itself a dict.func.__name__ collides across classes — use __qualname__ + __module__.move_to_end on cache hit (recency not maintained).func() invoked while holding the lock → serializes all calls.def _normalize(v): if isinstance(v, dict): return tuple(sorted((k, _normalize(x)) for k, x in v.items())) if isinstance(v, (set, frozenset)): return tuple(sorted(_normalize(x) for x in v)) if isinstance(v, (list, tuple)): return tuple(_normalize(x) for x in v) return v def generate_key(func, *args, **kwargs): canonical = (f"{func.__module__}.{func.__qualname__}", _normalize(args), _normalize(kwargs)) return json.dumps(canonical) # string key — JSON-roundtrip safe
def call(self, func, *args, **kwargs): key = self.generate_key(func, *args, **kwargs) with self._lock: if key in self._cache: self._cache.move_to_end(key) return self._cache[key] value = func(*args, **kwargs) # outside lock — parallel computes OK with self._lock: if key in self._cache: # re-check race return self._cache[key] self._cache[key] = value if len(self._cache) > self.capacity: evicted_key, _ = self._cache.popitem(last=False) # LRU = oldest return value
O(1) per call (OrderedDict ops are O(1))
Three event types — and HIT matters. PUT alone gives correct entries but wrong order; HIT records replay recency.
def _append_journal(self, record): with open(self.path, "a") as f: f.write(json.dumps(record) + "\n") f.flush() # Python buffer → OS os.fsync(f.fileno()) # OS page cache → physical disk def _recover(self): if not os.path.exists(self.path): return with open(self.path) as f: for line in f: line = line.strip() if not line: continue try: rec = json.loads(line) except json.JSONDecodeError: break # torn last line op = rec[0] if op == "PUT": self._cache[rec[1]] = rec[2] self._cache.move_to_end(rec[1]) while len(self._cache) > self.capacity: self._cache.popitem(last=False) elif op == "HIT": if rec[1] in self._cache: self._cache.move_to_end(rec[1]) elif op == "EVICT": self._cache.pop(rec[1], None) # safe pop
generate_key return json.dumps(canonical) from the start. Now keys are strings that survive the disk roundtrip cleanly.write → Python buffer. flush → OS page cache. fsync → physical disk. Without fsync, power loss can lose "successful" writes.test_compute_outside_lock test exercises this.Profiler gives time-sorted samples of (ts, stack) where stack is outermost → innermost. Output start/end events suitable for a flame graph.
Key insight: compute LCP between prev and current stacks. Frames at index ≥ LCP in prev ended (deepest first). Frames at index ≥ LCP in current started (outer to inner).
def common_prefix_len(a, b): n = 0 for x, y in zip(a, b): if x != y: return n n += 1 return n def convert_samples_to_events(samples): prev = [] events = [] for sample in samples: cur = sample.stack cp = common_prefix_len(prev, cur) # end disappeared frames, deepest first for i in range(len(prev) - 1, cp - 1, -1): events.append(Event("end", sample.ts, prev[i])) # start new frames, outer to inner for i in range(cp, len(cur)): events.append(Event("start", sample.ts, cur[i])) prev = cur return events
range(start, stop, -1) is exclusive on stop. To include index cp in the end loop, stop at cp - 1. Start loop is straightforward — range(cp, len(cur)) is naturally exclusive.Time O(S × D) Space O(D) — S samples, D max stack depth
Per-frame state parallel to prev_stack. Streak count for each frame. Continuing frame: streak += 1 → emit start at streak == N. New frame: streak = 1. Ends only for confirmed frames (streak ≥ N).
def convert_samples_to_debounced_events(samples, n): prev, streaks, events = [], [], [] for sample in samples: cur = sample.stack cp = common_prefix_len(prev, cur) # ends — only for confirmed frames for i in range(len(prev) - 1, cp - 1, -1): if streaks[i] >= n: events.append(Event("end", sample.ts, prev[i])) new_streaks = [] # continuing frames — bump streak, emit start on crossing N for i in range(cp): s = streaks[i] + 1 new_streaks.append(s) if s == n: events.append(Event("start", sample.ts, cur[i])) # new frames — streak = 1, immediate emit only if n == 1 for i in range(cp, len(cur)): new_streaks.append(1) if n == 1: events.append(Event("start", sample.ts, cur[i])) prev, streaks = cur, new_streaks return events
["a", "b"] → ["c", "b", "a"]. The "b" in sample 2 is NOT a continuation — its parent changed from "a" to "c". Common prefix is 0; streaks reset.work regardless of caller." Belongs in the analysis layer (over emitted events), not in event emission. Chrome trace, perfetto, pprof, perf — all prefix.Given a root dir, return all groups of files with identical content. Recurse. Group by content, not name. Filter singletons.
import hashlib, os from collections import defaultdict def hash_file(path, chunk_size=64*1024): h = hashlib.sha256() with open(path, "rb") as f: while chunk := f.read(chunk_size): # walrus + chunks h.update(chunk) return h.hexdigest() def find_duplicate_files(root_path): groups = defaultdict(list) for dirpath, _, filenames in os.walk(root_path): for f in filenames: path = os.path.join(dirpath, f) try: groups[hash_file(path)].append(path) except OSError: continue # skip unreadable return [g for g in groups.values() if len(g) > 1]
Time O(total bytes) — reads every file in full
Each stage filters down the candidate set. Skip singletons between stages so you only pay the next stage's cost on actual candidates.
def hash_partial(path, n_bytes=4*1024): with open(path, "rb") as f: return hashlib.sha256(f.read(n_bytes)).hexdigest() def find_duplicate_files_optimized(root_path): # Stage A: group by size (pure metadata, no I/O) by_size = defaultdict(list) for dirpath, _, filenames in os.walk(root_path): for f in filenames: path = os.path.join(dirpath, f) try: by_size[os.path.getsize(path)].append(path) except OSError: continue # Stage B: group by partial (first 4KB) hash by_partial = defaultdict(list) for paths in by_size.values(): if len(paths) < 2: continue for p in paths: try: by_partial[hash_partial(p)].append(p) except OSError: continue # Stage C: group by full hash by_full = defaultdict(list) for paths in by_partial.values(): if len(paths) < 2: continue for p in paths: try: by_full[hash_file(p)].append(p) except OSError: continue return [g for g in by_full.values() if len(g) > 1]
Best O(N files) all unique sizes — metadata only. Worst O(total bytes) all same content. Average: way better than Stage 1.
hash → [paths], path → hash. Reverse index for cheap deletes. Notify via message queue.N workers, each with a slice. send(target, data), recv() primitives. Compute global aggregates without funneling all data to one worker (hotspot).
The trick: shuffle by key % num_workers so identical keys land on the same worker, but keys distribute. All workers send AND receive in parallel — no hotspot.
Counter(local_data). No communication.
key % num_workers. Send each bucket to its target. Receive from N-1 others. Keep own bucket.
from collections import Counter, defaultdict def find_mode(local_data, worker_id, num_workers, send, recv): # Phase 1 local = Counter(local_data) # Phase 2 — shuffle buckets = defaultdict(list) for k, c in local.items(): buckets[k % num_workers].append((k, c)) for t in range(num_workers): if t != worker_id: send(t, buckets[t]) received = list(buckets[worker_id]) for _ in range(num_workers - 1): received.extend(recv()) # Phase 3 agg = Counter() for k, c in received: agg[k] += c if agg: # maximize count, then minimize key on tie local_top = max(agg.items(), key=lambda kv: (kv[1], -kv[0])) else: local_top = (None, 0) # Phase 4 if worker_id != 0: send(0, local_top) return None best_k, best_c = local_top for _ in range(num_workers - 1): rk, rc = recv() if rc > best_c or (rc == best_c and rk is not None and (best_k is None or rk < best_k)): best_k, best_c = rk, rc return best_k
Reuse phases 1-2 to build a distributed histogram. Then coordinator-led binary search over the value range.
total_count (all → 0 → broadcast).min/max for the search range.less + equal w.r.t. pivot; worker 0 aggregates + narrows range; broadcast.low == high.# After building histogram + total_count + global_min/max: target = total_count // 2 # for even count, upper middle low, high = global_min, global_max while low < high: if worker_id == 0: pivot = (low + high) // 2 for i in range(1, num_workers): send(i, pivot) else: pivot = recv() less = sum(c for v, c in histogram.items() if v < pivot) equal = histogram.get(pivot, 0) if worker_id == 0: tl, te = less, equal for _ in range(num_workers - 1): rl, re = recv(); tl += rl; te += re if target < tl: new = (low, pivot - 1) elif target < tl + te: new = (pivot, pivot) else: new = (pivot + 1, high) for i in range(1, num_workers): send(i, new) low, high = new else: send(0, (less, equal)) low, high = recv() return low if worker_id == 0 else None
Mode: O(distinct values) shipped Median: O(log value_range) rounds × tiny messages
key % num_workers uniform only if keys are uniform. Better hashes: MurmurHash, xxHash. Salted hash defeats adversarial keys. Two-level partitioning + dynamic rebalancing for severe skew.Convert text ↔ token IDs against a vocab dict. Handle unknowns with an UNK token. Stage 1 = bug-fix the starter. Stage 2 = optimal segmentation via DP.
Bugs in the starter:
Fix: add the "no possible match" check — if no vocab key starts with the current accumulated key, emit UNK + reset. After loop, if key non-empty, one more UNK.
def tokenize(text, vocab): tokens, key = [], "" for ch in text: key += ch if key in vocab: tokens.append(vocab[key]) key = "" elif not any(k.startswith(key) for k in vocab): tokens.append(vocab.get("UNK", -1)) key = "" if key: tokens.append(vocab.get("UNK", -1)) return tokens def detokenize(tokens, vocab): rev = {v: k for k, v in vocab.items()} return "".join(rev.get(t, "?") for t in tokens)
any(...): generators short-circuit on first True — any(k.startswith(key) for k in vocab) stops as soon as one match is found. With any([...]) the list is materialized first → full V scan even if first match is at index 0.O(N × V × L) — N text length, V vocab size, L avg key length. Trie optimization → O(N × L).
Greedy is wrong when longer matches exist. vocab = {"ab":1, "abc":2, "c":3, "UNK":-1}, text = "abc": greedy gives [1, 3] but optimal is [2].
Recurrence: best(i) = optimal segmentation of text[i:]. At each position, try every vocab key matching there; also try UNK (consume 1 char). Compare candidates by (unks, tokens) lexicographically.
from functools import lru_cache def tokenize_optimal(text, vocab): unk_id = vocab.get("UNK", -1) @lru_cache(maxsize=None) def best(i): if i == len(text): return (0, 0, ()) # (unks, tokens, segmentation) candidates = [] for k, v in vocab.items(): if k == "UNK": continue if text[i:i+len(k)] == k: su, st, ss = best(i + len(k)) candidates.append((su, st + 1, (v,) + ss)) # UNK option — consume 1 char su, st, ss = best(i + 1) candidates.append((su + 1, st + 1, (unk_id,) + ss)) # lex min: fewer unks first, then fewer tokens return min(candidates, key=lambda c: (c[0], c[1])) return list(best(0)[2])
lru_cache returns the same object on hit. If anyone mutated the returned list, the cache is corrupted. Tuples are immutable, safe by default. Convert to list only at the final return.O(N × L) instead of O(N × V × L). The two checks ("is current key in vocab?" / "could it still grow?") become O(1) node lookups.list(ex.map(...)) to surface exceptions.write → buffer; flush → OS page cache; fsync → physical disk. All three needed for real durability.best(i) = optimal of text[i:].Good luck. You've already coded all of these once tonight — your hands know the shape. Trust the prep.