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;
 
public class Program
{
  static private readonly int MAX = 100;
  static private readonly int INFINITY = (1<<21);
  static private readonly int WHITE = 0;
  static private readonly int GRAY = 1;
  static private readonly int BLACK = 2;
 
  static private int n = -1;
  static private int[,] M = new int[MAX, MAX];
 
  private static void dijkstra()
  {
    int minv;
    int[] d = new int[n];
    int[] color = new int[n];
 
 //   Console.Write("n={0}, d.length={1}, color.length={2}\n", n, d.Length, color.Length);
 
    for(int i=0; i<n; i++)
    {
      d[i] = INFINITY;
      color[i] = WHITE;
    }
 
    d[0] = 0;
    color[0] = GRAY;
    while(true)
    {
      minv = INFINITY;
      int u = -1;
      for(int i=0; i<n; i++)
      {
        if(minv > d[i] && color[i] != BLACK)
    {
      u = i;
      minv = d[i];
    }
      }
 
      if(u == -1) { break; }
      color[u] = BLACK;
      for(int v=0; v<n; v++)
      {
    if(color[v] != BLACK && M[u,v] != INFINITY)
    {
      if(d[v] > d[u] + M[u,v])
      {
        d[v] = d[u] + M[u,v];
        color[v] = GRAY;
      }
    }
      }
    }
 
    for(int i=0; i<n; i++)
    {
      Console.Write("{0} {1}\n", i, (d[i] == INFINITY ? -1 : d[i]));
    }
  }
 
  public static void Main()
  {
    n = int.Parse(Console.ReadLine());
    M = new int[n, n];
 
    for(int i=0; i<n; i++)
    {
      for(int j=0; j<n; j++)
      {
    M[i,j] = INFINITY;
      }
    }
 
    int k, c, u, v;
    for(int i=0; i<n; i++)
    {
      int s=0;
      string [] str = Console.ReadLine().Split(' ');
      u = int.Parse(str[s++]);
      k = int.Parse(str[s++]);
//      Console.Write("{0}, {1}\n", u, k);
      for(int j=0; j<k; j++)
      {
    v = int.Parse(str[s++]);
    c = int.Parse(str[s++]);
    M[u,v] = c;
//  Console.Write("{0}, {1}\n", v, c);
      }
    }
 
    dijkstra();
  }
}