Space-Complexity

Weak Vertices The Problem In graph theory, the structural integrity of a network can often be analyzed by identifying fundamental shapes within it, such as triangles. A triangle provides rigidity and is a common motif in many applications. This problem asks us to identify vertices that are not part of any triangle. A vertex i is defined as being part of a triangle if it has two distinct neighbors, j and k, which are also neighbors of each other. Our task is to find all vertices that do not satisfy this condition, which the problem statement refers to as “weak vertices.” The graph is given to us in the form of an adjacency matrix. ...

Recount Problem The recent schoolboard elections were hotly contested: a proposal to swap school start times for elementary and high school students, a controversial new dress code proposal that bans athletic clothes in school, and a proposal to raise real-estate taxes to pay for a new football practice facility, and the list goes on and on. It is now hours after the polls have closed and a winner has yet to emerge! ...