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B+tree height after delete: PostgreSQL fast root

Many databases use B+tree indexes, but they all differ. It's a sorted structure. The leaf pages are logically sorted so that a specific key value belongs to one page. A lookup by value reaches a single leaf page and either directly finds an entry for that value or immediately knows there's no entry with that key. When a page becomes full, it is split into two pages, each covering its own dedicated range. To find the right page, an internal page holds the range of values for the pages below. This internal page can become full, and a new level is added above it. Finally, at the highest level, there's a single internal page that is the root. A lookup always starts at the root and goes down to the leaves, following the branches of internal pages. In a traditional B+tree lookup, the cost is proportional to the height of the tree because the search starts at the root and descends to a leaf: 1 page to read when all fits in one leaf that is also the root (0 levels of internal pages, total height is 1). With small keys, this level can typically index hundreds of rows. 2 pages to read when there's one root that can list all leaf pages (1 level of internal page, total height is 2). With small keys, this level can typically index tens or hundreds of thousands of rows. 3 pages to read when there's one level of branches under the root (so 2 levels of internal pages, total height is 3). With small keys, this level can typically index millions of rows. This means that finding one key within ten million rows may require traversing 3 index pages, where most of them are probably in cache given the small number of branches compared to the leaves. For a given index size, whatever the value you are looking for, it's always the same number of pages to read because the index is balanced (the commonly accepted meaning of the B in B+tree). This property is maintained because any page can split, but only splitting the root adds another level. I've described how the height of an index can incr

2026-07-24 原文 →
开发者

I Spent 3 Weeks Debugging Rate Limits Before I Realized the Problem Wasn't My Code

Ever chased a bug for days, only to discover the "bug" was actually the platform working exactly as designed? That happened to me building a client reporting pipeline. The lesson stuck. Here's what nobody tells you about pulling marketing data from multiple ad platforms: the hard part was never the dashboard. It was everything underneath it. The Setup That Looked Simple on Paper The brief sounded easy. Pull spend, clicks, and conversions from Google Ads and Meta. Store it. Display it in a chart. A junior dev could knock this out in a sprint, I figured. Reality disagreed. Google Ads API enforces operation quotas per developer token, and those quotas scale differently depending on account tier. Meanwhile, Meta's Marketing API throttles based on a rolling usage score tied to the ad account itself, not your app. Two platforms. Two completely different throttling philosophies. Neither documented in a way that made the actual limits obvious until you hit them in production. Where Things Actually Broke My first version polled every client account every hour. Fine for three clients. Then we onboarded client number twelve, and Meta started returning 429s intermittently. Not consistently — intermittently. That's the worst kind of bug. I initially assumed it was a code issue. Retry logic, maybe a race condition in my job scheduler. I spent three weeks going down that path. Eventually, I found the real cause: cumulative API call volume across all client accounts was tripping Meta's app-level rate limit, not the individual account limit. The fix wasn't more retries. It was a request queue with exponential backoff, plus a priority system so active dashboards refreshed before idle ones. Simple in hindsight. Expensive in dev hours. The Real Architecture Behind Multi-Platform Reporting If you're building this yourself, here's what a production-grade pipeline actually needs, based on what broke for me. A Queue, Not a Cron Job Don't just fire off API calls on a schedule and hope for t

2026-07-24 原文 →
AI 资讯

I keep finding out about API breaking changes from production errors, so I'm building a changelog watcher

I build products solo. Every single one of them sits on top of somebody else's API — Stripe for payments, OpenAI and Anthropic for AI features, Meta for ads, print-on-demand APIs, map APIs. My code is maybe half of what actually runs in production. The other half belongs to vendors, and it changes whenever they decide it changes. Twice this year the first notice I got about a breaking change was a production error. Not an email, not a warning. An error, and then me digging through the vendor's changelog trying to figure out what they changed and when. The information was public the whole time. It was sitting in a changelog page I never visit, because nobody visits changelog pages until something is on fire. So I'm building the thing I wanted to exist BreakWatch is simple: you tell it which APIs your product depends on, and it reads their public changelogs for you. It fetches each changelog page once a day Diffs it against yesterday's snapshot Classifies the real changes: breaking (endpoint removed, field deprecated, "migrate by September") vs. informational (new feature, docs clarification — stuff you can ignore) Alerts you only when something looks like it will break an existing integration Keeps everything in a searchable timeline, so six months later "what changed on their side right before this broke" takes ten seconds instead of an afternoon No SDK, no credentials, nothing installed in your codebase. It only reads public pages. What I tested this week I ran it against the real changelogs of the ten APIs I'm watching first: Stripe, Twilio, OpenAI, Anthropic, Shopify, GitHub, Slack, Cloudflare, Google Maps and Plaid. Some honest findings: 10/10 scrape cleanly now, but it took fixes. Stripe's changelog page alone is 3.3 MB. SendGrid's standalone changelog doesn't exist anymore (it merged into Twilio's). PayPal's developer site serves a JavaScript shell with an HTTP 404 to anything that isn't a full browser, so it's out until I add rendering. The thing I was most a

2026-07-24 原文 →
AI 资讯

Six queries, three runs, every mean 8 — and the fine-tune wasn't why

The bar we set We approved a plan on 2026-07-10 with an acceptance test we weren't sure was reachable. Six drafted analyst-memo queries against Nigerian economic data, scored 0-10 across five dimensions — named-entity density, citation quality, sector-specific detail, honest-gap acknowledgement, decision-usefulness. The strict pass criterion: every query's mean score across three temperature=0.2 runs must be ≥8/10, with no query below 6 in any single run. At approval time the aggregate was somewhere around 30/60 across the six queries — a system that produced grounded but generic answers, and refused competently but not always. The gap to the bar was real. We gave it 4-5 weeks. What we shipped Phase 1 — retrieval breadth. Kind-diversity enforcement across the top-K result set so a "start a fintech" query stopped collapsing into 12 CBN circulars and started pulling BOI, NEXIM, PayStack, Flutterwave, and the World Bank agribusiness chapters in the same context window. Named-entity boost when the query mentions "factory", "startup", "invest", "loan". Deduplication so a briefing about the same fact doesn't crowd out its own primary source. Phase 2 — a six-class rule-based intent classifier and memo templates. Sub-millisecond routing on regex patterns: venture\_feasibility\ , strategic\_forecasting\ , credit\_risk\ , regulatory\_analysis\ , market\_sizing\ , general\_qa\ . Each intent gets a memo template — a section-headed scaffold with a named-entity mandate, an honest-gaps section, and a 1000-1500 word target. The general\_qa\ template stays empty (no memo shape) so genuinely-general questions don't get forced into a memo they don't need. Phase 3 — composition quality. Two changes did most of the work here: 1. A CITATION PREFERENCE: PRIMARY OVER BRIEFING\ block in the system prompt. Primary sources — CBN circulars, NAICOM regulations, NBS reports, textbook chapters, IMF Article IV, press coverage of specific events — get cited over daily briefings when both are presen

2026-07-24 原文 →
AI 资讯

Why I Chose Slot Hashes Over VRF for Fair Random Selection on Solana

When I set out to build a provably-fair random selection system on Solana, the obvious choice for randomness was a VRF (Verifiable Random Function). Instead, I built the system around Solana's SlotHashes sysvar with a commit-reveal scheme. Here's why, and what I gave up to get there. The problem A fair-selection system needs a winner (or set of winners) chosen in a way that's fair, and just as important that participants can check for themselves without taking anyone's word for it. VRF services (Switchboard, ORAO, etc.) solve the fairness part well: they produce randomness that's unpredictable in advance and cryptographically provable after the fact. But they come with a dependency on an oracle, a fee per request, and a proof that most users will never actually verify they'll trust it because the crypto math says they can, not because they did. I wanted something a participant with no crypto background could check in a browser console. The approach: commit-reveal with slot hashes The core idea: commit to the participant list before you know the randomness, then derive the randomness from a slot hash you couldn't have predicted at commit time. rust fn derive_randomness(target_hash: &[u8; 32], participant_root: &[u8; 32]) -> [u8; 32] { let mut combined_seed = [0u8; 64]; combined_seed[..32].copy_from_slice(target_hash); // slot hash at reveal combined_seed[32..].copy_from_slice(participant_root); // Merkle root, locked at commit solana_keccak_hasher::hash(&combined_seed).to_bytes() } The flow: Commit: participant list is finalized and hashed into a Merkle root; this is written on-chain. Wait: a target slot in the future is chosen as the reveal point. Reveal: once that slot passes, its hash is pulled from SlotHashes and combined with the committed root to derive the randomness. Select: the randomness deterministically picks winners from the participant set; winners get their own Merkle root and proofs. Every draw ends up with an audit record like: rust pub struct AuditR

2026-07-24 原文 →
产品设计

NeurIPS E and D, Average rating 3 and average confidence 4, I can rebuttal and address all their concerns? Do I still have a decent shot or unlikely ?[R]

NeurIPS E and D track review are out today and the average rating I received is a 3 and confidence is a 4. I can correct and address all their concerns. Do I still have a genuine shot of getting in or is it basically impossible at this point since none of my scores are a 4 or 5? Should I withdraw? submitted by /u/Ok-Ball-2546 [link] [留言]

2026-07-24 原文 →
AI 资讯

Namecheap Gave My Account to an Unverified Third Party Just Because They Asked

I’ve been a NameCheap customer for 13 years. I’ve also helped out an old college club paying for a .com they use (that is registered to me under my name, address, and phone number). During a recent leadership transition, the incoming club lead wanted to make changes to the DNS and didn’t know to contact me. They figured out the domain name was parked at NameCheap, so they initiated a password reset using the domain name. I got a password reset email and immediately filed a NameCheap support tick

2026-07-24 原文 →
AI 资讯

houhou — Resilience Policies for TypeScript Async Functions

The problem Most resilience libraries in the TypeScript ecosystem are tied to HTTP clients (axios-retry, p-retry, Polly.js) or require wrapping your function in a class with a .execute() ceremony. What if you just want to wrap any async function — a database query, an internal service call, a file operation — with retry logic, a timeout, and a circuit breaker, without pulling in heavy dependencies? Enter houhou . What is houhou? Houhou is a zero-dependency TypeScript library (~500 LOC) that wraps any async function with composable resilience policies. The wrapped function keeps the exact same signature — you call it like the original. import { task } from ' houhou ' const charge = task ( chargeCard ) . retry ( 3 ) . timeout ( 10 _000 ) . fallback (() => ({ status : ' pending ' })) await charge ( account , amount ) Policies at a glance Retry Re-execute on failure with fixed or exponential backoff: task ( fetchUser ). retry ( 3 ) // shorthand task ( fetchUser ). retry ({ attempts : 5 , backoff : ' exponential ' , jitter : true , delay : 500 }) Timeout Reject if the function doesn't complete in time: task ( fetchUser ). timeout ( 5000 ) Fallback Run an alternative function on failure: task ( fetchUser ). fallback (() => loadFromCache ( id )) Circuit Breaker Prevent repeated calls to an unhealthy service: task ( queryDb ). circuitBreaker ({ failureThreshold : 5 , successThreshold : 2 , resetTimeout : 30 _000 }) Delay Wait before execution: task ( syncData ). delay ( 1000 ) Policy ordering matters Policies are nested : the last method called wraps the previous ones. Execution order is reverse of declaration order. task ( fn ). retry ( 3 ). timeout ( 1000 ) // → timeout wraps retry // → function runs → retry on failure (up to 3 times) → 1s total timeout // → if the timeout fires, there are no more retries task ( fn ). timeout ( 1000 ). retry ( 3 ) // → retry wraps timeout // → function runs → 1s timeout → if timeout fires, retry catches it // → the whole cycle repeats up

2026-07-24 原文 →
AI 资讯

2 Free Browser-Based Tools I Use Instead of Installing CLI/Desktop Converters

As developers, we end up needing to convert or resize a file constantly — a screenshot that needs to be a PNG for docs, an asset that needs to hit exact social-preview dimensions, a PDF that needs merging before a demo. Reaching for ffmpeg , imagemagick , or a paid SaaS every time is overkill for a one-off task. Here are two free, no-signup web tools that cover most of that day-to-day friction. 1. FreelyConvert — general-purpose file conversion freelyconvert.com A browser-based converter covering documents, images, video, and audio: 500+ formats — PDF, DOC/DOCX, images (JPG/PNG/GIF/BMP/SVG/WEBP), video (MP4/AVI/MOV/MKV), audio (MP3/WAV/FLAC/AAC), spreadsheets, presentations No account/signup — upload, convert, download Batch conversion for multiple files in one pass Auto-delete after 24 hours and SSL encryption in transit Useful specifically for: PDF ↔ image conversions ( pdf-to-jpg , images-to-pdf ) Merging PDFs without touching a CLI tool Compressing video/audio for quick sharing Quick image compression when you don't want to script it 2. ImageResizer.dev — client-side image resizing/conversion imageresizer.dev This one's worth calling out for devs specifically: it runs entirely client-side via the Canvas API — nothing is uploaded to a server. That's a real difference if you're resizing anything you'd rather not send off-device, and it also means it's fast (no upload/download round trip). Features: Exact dimension presets for social platforms (Instagram, LinkedIn, X/Twitter, YouTube, TikTok, Pinterest, WhatsApp) — handy for generating OG images or social preview assets without hardcoding dimensions yourself Format conversion across JPG, PNG, WebP, AVIF, BMP, GIF, SVG Crop, flip, upscale , plus bulk resize/compress for batches Aspect-ratio locking to avoid distortion No account, no watermark Good fit for generating og:image assets, favicon prep, or resizing screenshots for a README without spinning up a script. Why bother mentioning these Neither requires an accoun

2026-07-24 原文 →
AI 资讯

Two credentials, two threat models: auth for a content API

A headless content API has two kinds of callers, and it's tempting to secure them the same way. That's the mistake. There's a human logging into an admin UI to edit content, and there's a machine — a website, a build step — pulling published content through a delivery endpoint. They authenticate with different credentials, and those credentials have opposite properties. Treat them identically and you either make the machine path painfully slow or the human path dangerously weak. I built a small headless content API ( Depot ) partly to get this boundary right. Here's the reasoning. The two credentials A session proves "this human is logged in." Short-lived, rides in an httpOnly cookie, checked on management routes. A delivery token proves "this machine may read this account's published content." Long-lived, sent as a Bearer header, checked on every public read. Two auth surfaces, kept explicit: /** * - requireUser() — admin session (httpOnly JWT cookie) for the management API. * - requireToken() — a `depot_…` bearer token for the public delivery API. */ Why they get different hashing Here's the part people get wrong. Both credentials get stored as hashes — never plaintext — but not the same kind of hash , and the reason is entropy. Passwords are low-entropy. Humans pick summer2024 . An attacker who steals your DB will brute-force guesses against the stored hashes, so you want hashing to be deliberately slow — that's exactly what bcrypt's cost factor buys you: import bcrypt from " bcryptjs " ; const ROUNDS = 10 ; // deliberately slow — the point is to resist brute force export function hashPassword ( plain : string ): Promise < string > { return bcrypt . hash ( plain , ROUNDS ); } export function verifyPassword ( plain : string , hash : string ): Promise < boolean > { return bcrypt . compare ( plain , hash ); } Tokens are high-entropy. I generate them — 32 random bytes — so there's nothing to guess. A stolen hash can't be reversed by brute force because the keyspace i

2026-07-24 原文 →