VisuAlgo contains many advanced algorithms that are discussed in Dr Steven Halim's book ('Competitive Programming', co-authored with his brother Dr Felix Halim and his friend Dr Suhendry Effendy) and beyond.

VisuAlgo was conceptualised in 2011 by Dr Steven Halim as a tool to help his students better understand data structures and algorithms, by allowing them to learn the basics on their own and at their own pace. This part runs in O( E) as we assume UFDS IsSameSet(u, v) and UnionSet(u, v) operations run in O( 1) for a relatively small graph. If IsSameSet(u, v) returns false, we greedily take this next smallest and legal edge e and call UnionSet(u, v) to prevent future cycles involving this edge. We use IsSameSet(u, v) to test if taking edge e with endpoints u and v will cause a cycle (same connected component - there is another path in the subtree that can connect u to v, thus adding edge (u, v) will cause a cycle) or not. Kruskal's main loop can be easily implemented using Union-Find Disjoint Sets data structure. This O( E log V) is the bottleneck part of Kruskal's algorithm as the second part is actually lighter, see below. We just store the graph using Edge List data structure and sort E edges using any O( E log E) = O( E log V) sorting algorithm (or just use C++/Python/Java sorting library routine) by non-decreasing weight, smaller vertex number, higher vertex number. There are two parts of Kruskal's algorithm: Sorting and the Kruskal's main loop.

Prim algorithm