Given four positive integers (x, y, z, H), the goal is to count the number of integers (d) in the range ([0, H]) that can be expressed as (d = a x + b y + c z), where (a, b, c) are non-negative integers. If a value (k) can be written as (k = b y + c z) with non-negative (b) and (c), then (k) is a va...
Graphs are non-linear data structures consisting of vertices (nodes) and edges that connect them. Formally denoted as $G = (V, E)$, where $V$ represents the set of vertices and $E$ represents the set of edges, graphs are widely utilized to model relationships in computer networks, logistics, and soc...
DFS Trees in Graph Theory A DFS tree is formed during a depth-first search traversal of a graph or tree structure. Starting from a root vertex, the algorithm explores as far as possible along each branch before backtracking. In this process, edges traversed to unvisited nodes become tree edges, whil...