给定一个正整数 n，请输出 n 位格雷码序列。 第 i 个格雷码（i 从 0 开始编号）定义为 g(i) = i xor (i >> 1), 其中 xor 表示按位异或，>> 表示右移。请依次输出 i = 0, 1, ..., 2^n - 1 对应的 g(i)，每个格雷码用恰好 n 个字符的二进制串表示，不足 n 位时在高位（左侧）补 0。

有 n 个人，编号为 1 到 n。已知其中存在 m 对朋友关系，每对关系由两个编号 u 和 v 给出，表示 u 与 v 是朋友。 朋友关系是相互的，并且具有传递性：如果 A 与 B 是朋友，B 与 C 是朋友，那么 A 与 C 也属于同一个朋友圈。也就是说，只要两个人能通过若干条朋友 ...

You send a contract as a PDF, and the other party returns a PDF with their edits. This exchange does not leave a record like ...

A school math teacher refers to a dry textbook in response to a simple question, "What is a logarithm?" A familiar plot ...

When you stand in the machine learning section of a bookstore, you are met with specialized books full of mathematical ...

A search engine is a software system designed to search for information on the World Wide Web, identifying results relevant ...

A 450-task benchmark built from real CVEs shows even the best AI coding agent writes code that's both working and secure only ...

Learn how AI is used in trading, how to test ideas on a demo account and which risks to manage. A plain English guide with ...

Overview:  Computer Science, AI, and Data Science offer distinct career paths, although they share several technical skills ...

Researchers have derived a closed-form Fisher information decomposition to calculate sample sizes needed for precise, fair ...

A new Bayesian network framework predicts dropout risk in online continuing education with 88.9 percent cross-validated ...

Independent researcher Aman Sachan released MAPLE, a pruning method that removes 80 of 128 experts from Gemma 4 26B-A4B so the model fits entirely in a 6 GB laptop GPU. The speed and quality results ...