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   INFTY 5000000
#define   WHITE 0
#define   GRAY 1
#define   BLACK 2

int n, M[MAX][MAX];

void dijkstra()
{
   int minv;
   int d[MAX], color[MAX];
   int i, v, u = -1;

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

   d[0] = 0;
   color[0] = GRAY;

   while (1){
      minv = INFTY;
      for (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 (v=0; v<n; v++){
         if (color[v]!=BLACK && M[u][v]!=INFTY){
            if (d[v] > d[u]+M[u][v]){
               d[v] = d[u] + M[u][v];
               color[v] = GRAY;
            }
         }
      }
   }

   for (i=0; i<n; i++){
      d[i] = INFTY ? -1 : d[i];
      if (i>0)
         printf(" ");
      printf("%d", d[i]);
   }
}

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

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

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

   dijkstra();

   return 0;
}