Shortest Path Algorithm With Updates

Question

There are N cities and there are M bidirectional roads connected to them , I have to find the shortest path between two fixed cities A and B.

But the problem is there are Q queries given such that path between two cities is blocked , i have to find the shortest path in each Q queries.

My time Complexity in my brute force Algorithm is O(QNlogN) which give me Time Limit Exceeded Error, How can i improve my solution please Help

Pseduo Code:

for u in Q:
  cin>>a>>b;
graph[a][b] = graph[b][a] = INFINITY VALUE
dijkstra algorithm();
cout<<Distance[D]<<endl;

Problem LINK

MY CODE Which Is giving me Time Limit Exceeded Error

Plese Help How can I improve my algorithm ?

There are plenty of posts here on this site that cover the Shortest Path or Djikstra's algorithm you should look them up, or go google. — David Coler, Dec 30 '14 at 20:12
possible duplicate of [the best shortest path algorithm](http://stackoverflow.com/questions/1846836/the-best-shortest-path-algorithm) — David Coler, Dec 30 '14 at 20:15
@DavidColer his time complexity shows that he is using Dijkstra's algorithm — Pham Trung, Dec 31 '14 at 03:36
@DavidColer please read the question carefully , it's is not about shortes path it's about how to Djikstra algorithm effect if one path is blocked — user4406103, Dec 31 '14 at 05:57
@PhamTrung yes but my question is little different please read it carefully — user4406103, Dec 31 '14 at 05:57

score 3 · Answer 1 · answered Dec 30 '14 at 20:18

The paper Vickrey Prices and Shortest Paths: What is an edge worth? by John Hershberger and Subhash Suri shows how to solve this problem in time O(NlogN+M) where N is the number of vertices, and M is the number of edges.

This allows you to precalculate the M answers depending on which road is blocked, so you can answer each query in O(1), for a total complexity of O(NlogN+M+Q).

Shortest Path Algorithm With Updates

1 Answers1