本文介绍了图的两种主要表示方法：邻接表和邻接矩阵，并分析了它们在稀疏图和稠密图中的应用。此外，还探讨了图遍历算法——广度优先搜索（BFS）和深度优先搜索（DFS）的实现细节与时间复杂度，包括如何通过这两种算法检测图中是否存在环。
1. Representation of graphs G=(V,E)
- adjacency lists—sparse graphs; directed, undirected, weighted; memory requiresθ(V+E);
- adjacency matrix—dense graph
2. Breadth-first search
Analysis
queue operations is O(V), scanning adjacency list is O(E), total running time of BFS is O(V+E).
3. Depth-first search
Analysis θ(V+E);
breadth-first search's predecessor subgraph forms a tree
depth-first search's predecessor is composed of several trees
a directed graph is acyclic if and only if a depth-first search yields no "back" edges
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