Fix LC 787: Correct SPFA time complexity and harden test suite

[peizhao1]

• File(s) Modified: articles/cheapest-flight-path.md
• Language(s) Used: markdown
• Submission URL: N/A (Documentation/Article update)

Description

This PR addresses Issues #5796 and #5797 by correcting the time complexity analysis in the written article for LC 787 and providing an additional test case to strengthen backend test coverage.

1. Article Update (#5797)
Updated the time complexity analysis for the Shortest Path Faster Algorithm (SPFA) solution. The article previously stated the time complexity was $O(n \cdot k)$. This has been corrected to $O(m \cdot k)$ (where $m$ is the number of edges/flights), as the algorithm iterates through all edges connected to the current node at each level up to $k$ times.

2. Backend Action Required: Hardening Test Coverage (#5796)
The current backend test suite is missing a test case to catch incorrect Dijkstra implementations. Specifically, solutions that permanently track visited nodes using a shortest dictionary (e.g., if node not in shortest: shortest[node] = w) will incorrectly block valid paths that reach a node with a higher cost but fewer stops.

Please add the following test case to the private execution engine database to properly fail these incorrect submissions:

Input: n = 5
flights = [[0,1,1],[1,2,1],[2,3,1],[3,4,1],[0,2,10]]
src = 0
dst = 4
k = 2

Expected Output: 12

Resolves #5796, Resolves #5797