Computation as a Universal and Fundamental Concept — Ergo

Kris Shamloo

A technical interviewer shares their approach to candidate evaluation using a simple but revealing coding question: implement a median function. The Python implementation is annotated with discussion points that probe deeper thinking — handling edge cases like empty lists, understanding pass-by-reference semantics (sorted() vs list.sort()), and avoiding over-engineering with unnecessary dependencies.

Count Substrings with More 1's than 0's

Bài viết giới thiệu thuật toán O(N log N) đếm số lượng substring nhị phân có nhiều số 1 hơn số 0 bằng cách chuyển đổi 1→+1, 0→-1, sử dụng prefix sums và Fenwick Tree. Thuật toán kết hợp nén tọa độ để tối ưu phạm vi prefix sum và đếm hiệu quả các cặp prefix sum thỏa điều kiện.

Lập trình viên nên đọc bài này để tìm hiểu cách tối ưu hóa giải quyết vấn đề đếm các chuỗi con trong chuỗi nhị phân với số '1' nhiều hơn '0' bằng thuật toán hiệu quả O(N log N) và công cụ như Fenwick Tree, giúp hiểu rõ về prefix sums, coordinate compression và ứng dụng của chúng trong xử lý dữ liệu hiệu quả.

MIT Complexity Theorist On Leetcode

MIT professor and Gödel Prize winner Ryan Williams discusses computational complexity theory in an interview that starts with the classic 3SUM LeetCode problem. He explains the O(N²) two-pointer solution and then describes how algorithms beating N² work via group-based finger search with preprocessing. The conversation covers fine-grained complexity theory, reductions between problems like Subset Sum and 2SUM, the Strong Exponential Time Hypothesis (SETH) and why Williams personally doubts it, hot takes on P vs NP (80% confidence they differ), EXP vs NEXP, and NEXP vs coNEXP. Williams also explains his breakthrough result showing any time-T algorithm can be simulated in space √T, building on Cook and Mertz's tree evaluation work using XOR-based memory tricks instead of write-to-blank-only approaches.

How a Bloom Filter Works: Build One From Scratch in Python

A hands-on tutorial building a Bloom filter from scratch in Python. Covers the core mechanics: a bit array plus multiple hash functions, the double-hashing trick for generating positions, and why false positives are an intentional trade-off for memory efficiency. Includes the math for sizing a filter given a target false positive rate and item count, a worked example showing ~1.2 MB for one million items at 1% error, and an explanation of why deletion requires a counting Bloom filter variant. Real-world use cases include databases (Cassandra, HBase), Chrome's safe browsing, CDN caching, and Bitcoin light clients.