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?
- A connected undirected graph with no cycles
- What is a leaf node in a tree?
- A node with degree 1 (connected by exactly one edge)
- What is the height of a tree?
- The length of the longest path from the root to any leaf
- What is the depth of a node in a rooted tree?
- The number of edges from the root to that node
- How many edges does a tree with n vertices have?
- Exactly n - 1 edges
- What is a spanning tree of a connected graph G?
- A subgraph that is a tree and includes all vertices of G
- What is a minimum spanning tree (MST)?
- A spanning tree with the smallest possible sum of edge weights
- What problem does Dijkstra's algorithm solve?
- Finding the shortest path from a source vertex to all other vertices
- What problem does Kruskal's algorithm solve?
- Finding a minimum spanning tree
- What problem does Prim's algorithm solve?
- Finding a minimum spanning tree
- What is a binary tree?
- A tree where each node has at most two children
- What is a complete binary tree?
- 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)?
- O(V + E), where V is vertices and E is edges
- What is the time complexity of breadth-first search (BFS)?
- O(V + E), where V is vertices and E is edges
- What is a rooted tree?
- A tree with one distinguished node designated as the root
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