在无权有向图中使用A*求最短路径是否合理？最优算法探讨

Let's break down your questions clearly and practically:

Is using A* for shortest paths in unweighted directed graphs reasonable? #

Honestly, it’s technically feasible but rarely worth the effort. Here’s the breakdown:

• A*’s core advantage comes from an admissible heuristic (a function that never overestimates the remaining distance to the target). For unweighted graphs, you could theoretically use a heuristic like the minimum number of edges needed to reach the target—but in most general unweighted directed graphs, calculating that heuristic isn’t straightforward. If you default to a trivial heuristic like h(n) = 0, A* just reduces to Dijkstra’s algorithm, which is less efficient than BFS for unweighted scenarios.
• As you pointed out, A* carries higher memory overhead: it requires maintaining a priority queue and tracking state cost estimates, which is unnecessary extra baggage when simpler, more efficient algorithms exist.

What’s the optimal/lowest-overhead algorithm for unweighted directed graph shortest paths? #

Plain BFS (Breadth-First Search) is absolutely your best choice here, and here’s why it’s optimal:

• BFS explores nodes level by level, where each level corresponds to the number of edges from the start node. The first time you reach the target node, you’ve found the shortest path—any later path would require more edges, making it longer.
• It runs in O(V + E) time (V = number of vertices, E = number of edges) and uses O(V) space for the queue and visited set, which is as efficient as it gets for this problem.
• Unlike A*, you don’t need to spend time designing or validating a heuristic function—no extra work, no guesswork.

A quick side note: If your graph had non-negative weighted edges, Dijkstra’s would be the go-to, and A* could add value if you had a solid heuristic. But for unweighted directed graphs, BFS is the simplest, most efficient option by far.

内容的提问来源于stack exchange，提问作者user8571142