Code Is In Description:
Intuition:
The problem at hand requires determining the shortest path from city 0 to city n - 1 after each road addition query. The main challenge lies in efficiently updating the shortest path after each road is added. By leveraging Breadth-First Search (BFS), we can dynamically update the shortest path for each query.
Approach:
Initial Road Setup:
The cities are initially connected in a linear fashion: city 0 to city 1, city 1 to city 2, and so on up to city n - 2 to city n - 1.
Graph Representation:
Represent the cities and roads using an adjacency list. Each city points to its next city in the initial setup.
Breadth-First Search (BFS):
Use BFS to calculate the shortest path from city 0 to city n - 1.
BFS works well for finding the shortest path in an unweighted graph because it explores all nodes at the present depth level before moving on to nodes at the next depth level.
Processing Queries:
For each query that adds a new road, update the graph to include this new road.
Run BFS from city 0 to city n - 1 to determine the new shortest path after each road addition.
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