Problem:
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Single Source Shortest Path

For a given weighted graph $G = (V, E)$, find the shortest path from a source to each vertex. For each vertex $u$, print the total weight of edges on the shortest path from vertex $0$ to $u$.

Input

In the first line, an integer $n$ denoting the number of vertices in $G$ is given. In the following $n$ lines, adjacency lists for each vertex $u$ are respectively given in the following format:

$u$ $k$ $v_1$ $c_1$ $v_2$ $c_2$ ... $v_k$ $c_k$

Vertices in $G$ are named with IDs $0, 1, ..., n-1$. $u$ is ID of the target vertex and $k$ denotes its degree. $v_i (i = 1, 2, ... k)$ denote IDs of vertices adjacent to $u$ and $c_i$ denotes the weight of a directed edge connecting $u$ and $v_i$ (from $u$ to $v_i$).

Output

For each vertex, print its ID and the distance separated by a space character in a line respectively. Print in order of vertex IDs.

Constraints

$1 \leq n \leq 100$

$0 \leq c_i \leq 100,000$

$|E| \leq 10,000$

All vertices are reachable from vertex $0$

Sample Input 1

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

Sample Output 1

0 0
1 2
2 2
3 1
4 3

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in Haskell (judge verdict: Accepted)

import           Control.Monad
import           Data.Functor
import           Data.List
import qualified Data.Map.Strict as Map
import           Debug.Trace

--main :: IO ()
main = do
  n <- readLn
  am <- replicateM n $ map read . words <$> getLine :: IO([[Int]])
  --print $ toAdjList am
  forM_ (Map.toList . solve . toAdjList $ am) (\(node, distance) -> putStrLn $ show node ++ " " ++ show distance)

type Node = Int
type Weight = Int
type AdjList = [Map.Map Node Weight]
toAdjList :: [[Int]] -> [Map.Map Node Weight]
toAdjList [] = []
toAdjList (a:as) = (adjacents a):(toAdjList as)
  where
    adjacents :: [Int] -> Map.Map Node Weight
    adjacents (i:n:bs) = Map.fromList $ toPair bs
    toPair :: [Int] -> [(Node, Weight)]
    toPair [] = []
    toPair (x:y:zs) = (x, y):toPair zs


solve :: AdjList -> Map.Map Node Int
--solve _ = Map.fromList [(1,2), (3,4)]
solve al = dijkstra al $ Map.singleton 0 0
  where
    dijkstra :: AdjList -> Map.Map Node Int -> Map.Map Node Int
    dijkstra al ss
      | length al <= Map.size ss = ss
      | otherwise = dijkstra al $ Map.insert i d ss
      -- | otherwise = trace ("adj = " ++ show adjacents) dijkstra al $ Map.insert i d ss
      where
        adjacents = join [[(j, ss Map.! i + (al !! i) Map.! j) | j <- Map.keys (al !! i), j `notElem` Map.keys ss]
            | i <- [0..(length al - 1)], i `elem` Map.keys ss]
        (i, d) = minimumBy (\x y -> compare (snd x) (snd y)) adjacents