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>

#define INF 1000000000
#define MAX 500000

typedef struct{
  int next;
  int back;
  int cost;
} Edge;

int main(){
  int i,j,n,k,u,v,c,count=0,flag=1;
  Edge E[MAX];
  int w[10000];

  scanf("%d",&n);

for(i=0;i<n;i++){
  scanf("%d %d",&u,&k);
  for(j=0;j<k;j++){
    E[count].back=u;
    scanf("%d %d",&v,&c);
    E[count].next=v;
    E[count].cost=c;
    count++;
    }
  }

for(i=0;i<n;i++){
  w[i]=INF;
}

w[0]=0;

while(flag!=0){
  flag=0;
  for(i=0;i<count;i++){
    if((E[i].cost+w[E[i].back])<w[E[i].next]){
      flag=1;
      w[E[i].next]=E[i].cost+w[E[i].back];
    }
  }
}


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

return 0;
}