Problem:
Single Source Shortest Path

For a given weighted graph G(V, E) and a source r, find the source shortest path to each vertex from the source (SSSP: Single Source Shortest Path).

Input

An edge-weighted graph G (V, E) and the source r.

|V| |E| r
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1

|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively. r is the source of the graph.

si and ti represent source and target vertices of i-th edge (directed) and di represents the cost of the i-th edge.

Output

Print the costs of SSSP in the following format.

c0
c1
:
c|V|-1

The output consists of |V| lines. Print the cost of the shortest path from the source r to each vertex 0, 1, ... |V|-1 in order. If there is no path from the source to a vertex, print INF.

Constraints

1 ≤ |V| ≤ 100000

0 ≤ di ≤ 10000

0 ≤ |E| ≤ 500000

There are no parallel edges

There are no self-loops

Sample Input 1

4 5 0
0 1 1
0 2 4
1 2 2
2 3 1
1 3 5

Sample Output 1

0
1
3
4

Sample Input 2

4 6 1
0 1 1
0 2 4
2 0 1
1 2 2
3 1 1
3 2 5

Sample Output 2

3
0
2
INF

Solution in Haskell (judge verdict: Accepted)

import Control.Applicative
import Control.Monad
import qualified Data.ByteString.Char8 as B
import Data.List
import Data.IntMap ((!))
import qualified Data.IntMap as M
import Data.Maybe
import qualified Data.Set as S
import qualified Data.Tuple as T

dijkstra graph source = dijkstra' graph (S.singleton (0, source)) (M.singleton source 0)

dijkstra' graph pq res
    | S.null pq = res
    | otherwise = dijkstra' graph pq'' res'
    where
      ((d,v), pq') = S.deleteFindMin pq
      pq''= foldl' (\acc (x,e) -> S.insert (d+e,x) acc) pq' update
      res' = foldl' (\acc (x,e) -> M.insert x (d+e) acc) res update
      update = filter (\(x,e) -> M.notMember x res || d+e < res!x) (M.findWithDefault [] v graph)

buildGraph edges =
 let g = groupBy (\ (x, _, _) (y, _, _) -> x == y) edges
 in M.fromDistinctAscList (map (\x -> (f1 $ head x, map (\ (_, y, z) -> (y, z)) x)) g)

readInt = fst . fromJust . B.readInt
f1 (x, _, _) = x
f3 (_, _, x) = x

main = do
  ((nv,_,r):edges) <- map (\[x,y,z]->(x,y,z)) . map (map readInt . B.words) . B.lines <$> B.getContents
  let g = buildGraph (sort edges)
  let res = dijkstra g r
  mapM_ (putStrLn . maybe "INF" show . flip M.lookup res) [0..nv-1]