Finding articulation vertices is an application of DFS. In a nutshell, Apply DFS on a graph. Get the DFS tree. A node which is visited earlier is a “parent” of those nodes which are reached by it and visited later. If any child of a node does not have a path to any of the … Read more
I’ve found the answer to my question in this book. It is the same with Computer wiring problem which occurs repeatedly in the design of computers and other digital systems. The purpose is to minimize the total wire length. So, it is indeed a minimum length Hamiltonian path. What the book suggests is to create … Read more
Here is an academic paper which investigates this problem in great detail. There is also some sample code for the different algorithms in Section 8 towards the end. Verhoeff, T. (2004). Settling multiple debts efficiently : an invitation to computing science. Informatics in Education, 3(1), 105-126.
Your confusion is stemming from the fact that you apparently assume that DFS algorithm can be obtained from BFS algorithm by replacing the FIFO queue with a LIFO stack. This is a popular misconception – it is simply not true. The classic DFS algorithm cannot be obtained by replacing the BFS queue with a stack. … Read more
The reason for using decrease-key rather than reinserting nodes is to keep the number of nodes in the priority queue small, thus keeping the total number of priority queue dequeues small and the cost of each priority queue balance low. In an implementation of Dijkstra’s algorithm that reinserts nodes into the priority queue with their … Read more
All these data structures are used for solving different problems: Segment tree stores intervals, and optimized for “which of these intervals contains a given point” queries. Interval tree stores intervals as well, but optimized for “which of these intervals overlap with a given interval” queries. It can also be used for point queries – similar … Read more
This is a common graph theory problem algorithm In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. The problem of finding the shortest path between two intersections on a … Read more
The algorithm you have suggested will indeed find the shortest path in this graph, but not all graphs in general. For example, consider this graph: Let’s trace through the execution of your algorithm. First, you set d(A) to 0 and the other distances to ∞. You then expand out node A, setting d(B) to 1, … Read more
To fill your rectangle handle it as closed convex polygon (almost the same as triangle filling) order your points to match winding rule so there are lines AB BC CD DA or reverse create left and right buffer address is y-coordinate, its an array of x-positions and if needed also array of color,texture coordinates,…. for … Read more
I found this page in my search and since cycles are not same as strongly connected components, I kept on searching and finally, I found an efficient algorithm which lists all (elementary) cycles of a directed graph. It is from Donald B. Johnson and the paper can be found in the following link: http://www.cs.tufts.edu/comp/150GA/homeworks/hw1/Johnson%2075.PDF A … Read more