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 C# (judge verdict: Accepted)

using System;

class B12{
  const int max = 100;
  const int inf = (1<<21);
  const int white = 0;
  const int gray = 1;
  const int brack = 2;

  static int n;
  static int[,] m = new int[max,max];

  public static void Calc(){
    int min;
    int[] d = new int[max];
    int[] color = new int[max];

    for(int i = 0;i < n;i++){
      d[i] = inf;
      color[i] = white;
    }

    d[0] = 0;
    color[0] = gray;
    while(true){
      min = inf;
      int u = -1;
      for(int i = 0;i < n;i++){
        if(min > d[i] && color[i] != brack){
          u = i;
          min = d[i];
        }
      }
      if(u == -1) break;
      color[u] = brack;
      for(int v = 0;v < n;v++){
        if(color[v] != brack && m[u,v] != inf){
          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.WriteLine("{0} {1}",i,d[i] == inf ? -1 :d[i]);
    }
  }

  public static void Main(){
    n = int.Parse(Console.ReadLine());
    for(int i = 0;i < n;i++){
      for(int j = 0;j < n;j++){
        m[i,j] = inf;
      }
    }

    int k,c,u,v;
    for(int i = 0;i < n;i++){
      string[] str = Console.ReadLine().Split(' ');
      u = int.Parse(str[0]);
      k = int.Parse(str[1]);
      for(int j = 0;j < k;j++){
        v = int.Parse(str[2 + j * 2]);
        c = int.Parse(str[3 + j * 2]);
        m[u,v] = c;
      }
    }
    Calc();
  }
}