Freaks City

Simple Graph Theory and Construction A Consider vertices with weight 2 as adding one to vertices with weight 1. Thus the problem is split into two parts: constructing the tree and adding one to vertices. In the first part, constructing the tree as balanced as possible is beneficial, as will be shown in the second step. Construction: Process DFS ...

Problem A - 4 Question With (n) horizontal lines and (m) vertical lines drawn on a plane, how many axis-aligned rectangles are formed that contain no interior lines? Solution Consider each dimension independent. Along any straight line, (n) distinct points partition the line into (n - 1) segments. These segments serve as the edges of our rectan ...