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: Memory Limit Exceeded)

#include<stdio.h>
#define MAX 10002
#define INF 1000000
#define NIL -1
#define WHITE 0
#define BLACK 1

int n,G[MAX][MAX],d[MAX],mincost,color[MAX];

void initializeSingleSource(){
  int v;
  for( v = 0 ; v < n ; v++ ){
    d[v] = INF;
    color[v] = WHITE;
  }
  d[0] = 0;
}

void dijkstra(){
  int i,v,u;
  initializeSingleSource();

  while(1){
    mincost = INF;
    for( i = 0 ; i < n ;i ++ )
      {
	if( color[i] != BLACK && d[i] < mincost ){
	  mincost = d[i];
	  u = i;
	}
      }
    
    if( mincost == INF ) break;

    color[u] = BLACK;

    for( v = 0 ; v < n ; v++ ){
      if( color[v] != BLACK && G[u][v] != INF ){
	if(( d[u] + G[u][v] ) < d[v] ){
	  d[v] = d[u] + G[u][v];
	}
      }
    }


  }
}

int main(){
  int i,j,u,v,k;
  scanf("%d",&n);

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

  dijkstra();

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