Dynamic Shortest Paths with Updates

Problem

Given a directed weighted graph with nodes labeled 0 to n - 1, an initial edge list edges, and a sequence of update operations, return the shortest path cost from source to target after each update. Each update changes the graph dynamically by adding a new edge, removing an existing edge, or changing an edge weight. If no path exists after an update, return -1 for that step.

Constraints

• 1 <= n <= 200
• 0 <= edges.length <= 5000
• 1 <= updates.length <= 1000
• 0 <= u, v < n
• 1 <= w <= 10^6
• Update type is one of "add", "remove", "update"