Problem:
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Single Source Shortest Path II

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

$1 \leq n \leq 10,000$

$0 \leq c_i \leq 100,000$

$|E| < 500,000$

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 C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace ALDS1_12_C
{
    class Program
    {
        const int N = 10000;
        const int INFTY = int.MaxValue;
        const int white = 0;
        const int gray = 1;
        const int black = 2;
        static int n;
        static List<pair<int, int>>[] adj = Enumerable.Range(0, N).Select(n => new List<pair<int,int>>()).ToArray();
        
        static void dijkstra()
        {
            var d = Enumerable.Repeat(INFTY, n).ToArray();
            var color = Enumerable.Repeat(white, n).ToArray();
            var PQ = new PriorityQueue<pair<int,int>>(50000);

            d[0] = 0;
            PQ.Enqueue(new pair<int, int>(0, 0));
            color[0] = gray;

            while (PQ.Any())
            {
                pair<int, int> f = PQ.Peek();
                PQ.Dequeue();
                int u = f.Second;
                color[u] = black;

                if (d[u] < f.First * (-1)) continue;

                for (int i = 0; i < adj[u].Count; i++)
                {
                    int v = adj[u][i].First;
                    if (color[v] == black) continue;
                    if (d[v] <= d[u] + adj[u][i].Second) continue;

                    d[v] = d[u] + adj[u][i].Second;
                    PQ.Enqueue(new pair<int, int>(d[v] * (-1), v));
                    color[v] = gray;
                }             
            }
            var sb = new StringBuilder();
            foreach (var t in d.Select((i, j) => new { i, j}))
            {
                sb.AppendLine(t.j+ " " + ((t.i == INFTY) ? (-1) : t.i));
            }
            Console.Write(sb);
        }
        static void Main(string[] args)
        {
            n = scan()[0];
            for (int i = 0; i < n; i++)
            {
                var t = scan();
                for (int j = 0; j < t[1]; j++)
                    adj[t[0]].Add(new pair<int,int>(t[2 + j * 2], t[3 + j * 2]));
            }
            dijkstra();
        }

        static int[] scan()
        {
            return Console.ReadLine().Split().Select(int.Parse).ToArray();
        }
    }


    // #ref http://judge.u-aizu.ac.jp/onlinejudge/review.jsp?rid=1746876#1
    public class PriorityQueue<T> where T : IComparable
    {
        private T[] heap;
        private int size = 0;
        public PriorityQueue(int max){ heap = new T[max];}
        private int Compare(T x, T y){return y.CompareTo(x);}
    
        public void Enqueue(T x)
        {
            var i = size++;

            while (i > 0)
            {
                var p = (i - 1) >> 1;
                if (Compare(heap[p], x) <= 0) break;
                heap[i] = heap[p];
                i = p;
            }
            heap[i] = x;
        }

        public T Dequeue()
        {
            var ret = heap[0];
            var x = heap[--size];

            var i = 0;
            while ((i << 1) + 1 < size)
            {
                var a = (i << 1) + 1;
                var b = (i << 1) + 2;

                if (b < size && Compare(heap[b], heap[a]) < 0) a = b;
                if (Compare(heap[a], x) >= 0) break;

                heap[i] = heap[a];
                i = a;
            }
            heap[i] = x;
            return ret;
        }

        public int Count{get { return size; }}

        public bool Any(){return size > 0;}

        public T Peek(){return heap[0];}
    }

   
    public class pair<T, U> : IComparable where T : IComparable<T>
    {
        public pair()
        {
        }

        public pair(T first, U second)
        {
            this.First = first;
            this.Second = second;
        }

        public int CompareTo(Object obj)
        {
            pair<T, U> cast = (pair<T, U>)obj;
            return First.CompareTo(cast.First);
        }

        public T First { get; set; }

        public U Second { get; set; }

        public override string ToString()
        {
            return string.Format("{0} {1}?\n", First, Second);
        }
    }
}