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: Time Limit Exceeded)

#include<stdio.h>
#define MAX 100
#define INF 100000
#define W 0
#define G 1
#define B 2

int n,M[MAX][MAX];

void dijkstra()
{
  int i,u,v,minv,d[MAX],color[MAX];

  for(i=0;i<n;i++)
    {
      d[i]=INF;
      color[i]=W;
    }

  d[0]=0;
  color[0]=G;

  while(1){
    minv=INF;
    u=-1;
    for(i=0;i<n;i++)
      {
	if(minv>d[i]&&color[i]!=B)
	  {
	    u=i;
	    minv=d[i];
	  }
      }
    if(u==i) break;
    color[u]=B;
    for(v=0;v<n;v++)
      {
	if(color[v]!=B&&M[u][v]!=INF)
	  {
	    if(d[v]>d[u]+M[u][v])
	      {
		d[v]=d[u]+M[u][v];
		color[v]=G;
	      }
	  }
      }
  }

  for(i=0;i<n;i++)
    {
      if(d[i]==INF) d[i]=-1;
      else d[i]=d[i];
      printf("%d %d\n",i,d[i]);
    }
}

int main()
{
  int i,j,k,c,u,v;

  scanf("%d",&n);
  for(i=0;i<n;i++)
    {
      for(j=0;j<n;j++)
	{
	  M[i][j]=INF;
	}
    }

  for(i=0;i<n;i++)
    {
      scanf("%d%d",&u,&k);
      for(j=0;j<n;j++)
	{
	  scanf("%d%d",&v,&c);
	}
    }

  dijkstra();

  return 0;
}