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: Accepted)

#include<stdio.h>
int N=10000;
int INFTY=(1<<21);
int W=0,G=1,B=2;

main(){
  int n,i,j,k,b,c=0,u,v,minv,M[500000][3];
  int d[N],color[N];

  scanf("%d",&n);
  for(i=0;i<n;i++){
    scanf("%d %d",&u,&k);
    for(j=0;j<k;j++){
      M[c][W] = u;
      scanf("%d %d",&v,&b);
      M[c][G] = v;
      M[c][B] = b;
      c++;
    }
  }
  color[u] = G;
  for(i=0;i<n;i++){
    d[i] = INFTY;
  }
  d[0] = 0;
  while(color[u] != 0){
    color[u] = W;
    for(v=0;v<c;v++){
      if(d[M[v][G]] > d[M[v][W]] + M[v][B]){
        d[M[v][G]] = d[M[v][W]] + M[v][B];
        color[u] = G;
      }
    }
  }
  for(i=0;i<n;i++){
    printf("%d %d\n",i,(d[i]==INFTY?-1:d[i]));
  }
  return 0;
}