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>
#include<limits.h>

#define N 20001
#define nil -1
#define WHITE 0
#define BLACK 1
#define INF 9999999

int n,G[N][N],d[N];

void dijkstra(int , int);
void initializeSingleSource(int);

int main(){

  int i,j,u,k,c,v,w=INF,r;
  
  scanf("%d",&n);

  for(i=0;i<n;i++){
    for(j=0;j<n;j++){
      G[i][j]=-1;
    }
  }
  
  for(i=0;i<n;i++){
    scanf("%d %d",&u,&k);
    for(j=0;j<k;j++){
      scanf("%d %d",&c,&v);
      G[u][c]=v;
      if(v<w && u==0) w=v;
    }
  }
 
  dijkstra(w,0);

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


void dijkstra(int w , int s){

  int i,u,v,pi[N],color[N],mincost,sum=0;

 
  for(u=0;u<n;u++){
    d[u]=INF;
    pi[u]=nil;
    color[u]=WHITE;
  }
  d[s]=0;

  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(G[u][v]!=-1) w=G[u][v];
	else continue;
		
	if(color[v]!=BLACK && w+d[u]<d[v]){
	  pi[v]=u;
	  d[v]=w+d[u];
	}
      }
  }
  
}