基于堆的Python版Dijkstra算法实现输出异常，求调试修复

I've built a Dijkstra's shortest path algorithm using a custom priority dictionary backed by a heap. The priority dict has two core methods:

• smallest(): Only returns the smallest key that holds the minimum value in the dictionary
• pop_smallest(): Returns that same smallest key (with the minimum value) and removes it from the heap-backed dictionary

I've tested this implementation against a set of test cases from GitHub, but I'm getting mixed results—some tests pass perfectly, while others spit out wrong shortest path distances or select unexpected nodes during execution.

What I've Checked So Far #

I've verified basic heap operations (push/pop) work for simple standalone cases, and the smallest()/pop_smallest() methods behave as expected when tested in isolation. But when integrated into the full Dijkstra's workflow, something breaks.

Common Issues I'm Suspecting #

I'm wondering if any of these could be the root cause:

• Stale heap entries: When I update a node's distance (priority), the old, higher-distance entry is still left in the heap. Could this cause pop_smallest() to pick an outdated entry instead of the updated one?
• Key tie-breaking logic: When two nodes have the same minimum distance, does my code correctly return the numerically smaller key? I think I implemented this, but maybe there's an edge case I missed.
• Heap invariant maintenance: Am I properly re-heapifying the structure after updates or pops? Maybe the heap isn't staying in a valid state when the priority dictionary is modified.

I'd love any guidance on how to troubleshoot these possibilities, or other common mistakes in heap-based priority dictionaries for Dijkstra's that I might have overlooked.

内容的提问来源于stack exchange，提问作者georgeB