To understand dominator trees, we first define the concept of dominance within a directed graph containing a designated entry node \(s\). For any two nodes \(u\) and \(v\), if every possible path from \(s\) to \(u\) must traverse \(v\), then \(v\) is considered a dominator of \(u\). Alternatively, t...
We are given an undirected graph containing N vertices, initial containing no edges. The system must process Q online queries of two distinct types: Type 1: Establish an undirected edge between vertices u and v. Type 2: Identify the k-th largest vertex identifier within the connected component conta...
Problem A: Symmetric Pair Removal Given a binary string of length n, repeatedly remove a pair of characters from opposite ends if they differ (one is '0' and the other is '1'). Calculate the remaining length after no more valid pairs can be removed. A two-pointer technique efficiently solves this pr...