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>
#include <stdlib.h>
#include <limits.h>

typedef struct point {
  int x, ver, length;
} GVE;

int main(){
  GVE G[500000];
  int n,i,j,g,c,a = 1,size = 0,d[10000];

  scanf("%d",&n);

  for(i = 0;i < n;i++){
    scanf("%d",&c);
    scanf("%d",&g);

    for(j = 1;j <= g;j++){
      G[size].x = c;
      scanf("%d %d",&G[size].ver,&G[size].length);
      size++;
    }
  }

  for(i = 1;i < n;i++){
    d[i]=INT_MAX;
  }
  while(a){
    a = 0;
    for(i = 0; i < size; i++) {
      if(d[G[i].x] !=INT_MAX && d[G[i].x]+G[i].length < d[G[i].ver]) {
        d[G[i].ver] = d[G[i].x]+G[i].length;
        a++;
      }
    }
  }
  for(i = 0; i < n; i++){
    printf("%d %d\n",i,d[i]);
  }
  return 0;
}