Tree structures and basic graph algorithms such as shortest path and minimum spanning tree, from an intro discrete mathematics course.
29 cards · basic cards · AI-written, checked twice. Edit anything.
- What is a tree in graph theory?
Show answer
A connected undirected graph with no cycles- What is a leaf node in a tree?
Show answer
A node with degree 1 (connected by exactly one edge)- What is the height of a tree?
Show answer
The length of the longest path from the root to any leaf- What is the depth of a node in a rooted tree?
Show answer
The number of edges from the root to that node- How many edges does a tree with n vertices have?
Show answer
Exactly n - 1 edges- What is a spanning tree of a connected graph G?
Show answer
A subgraph that is a tree and includes all vertices of G- What is a minimum spanning tree (MST)?
Show answer
A spanning tree with the smallest possible sum of edge weights- What problem does Dijkstra's algorithm solve?
Show answer
Finding the shortest path from a source vertex to all other vertices- What problem does Kruskal's algorithm solve?
Show answer
Finding a minimum spanning tree- What problem does Prim's algorithm solve?
Show answer
Finding a minimum spanning tree- What is a binary tree?
Show answer
A tree where each node has at most two children- What is a complete binary tree?
Show answer
A binary tree where all levels are fully filled except the last, which fills from left to right- What is the time complexity of depth-first search (DFS)?
Show answer
O(V + E), where V is vertices and E is edges- What is the time complexity of breadth-first search (BFS)?
Show answer
O(V + E), where V is vertices and E is edges- What is a rooted tree?
Show answer
A tree with one distinguished node designated as the root
FlashKeepers