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>
#define INF 1000000001
typedef struct vertice
{
  int cost;
  int status;
  int numOfAdj;
  int *adjList;
  int *costList;
} ver;
ver *v;
int n;//the number of vertices
void init();
void setArray(int);
void dijkstra(void);
int main(void)
{
  int i,j;//counter
  int key;
  scanf("%d",&n);
  init();
  for(i=0;i<n;i++)
    {
      scanf("%d",&key);
      scanf("%d",&v[key].numOfAdj);
      setArray(key);
      for(j=0;j<v[key].numOfAdj;j++) scanf("%d%d",&v[key].adjList[j],&v[key].costList[j]);
    }
  dijkstra();
  free(v);
  return 0;
}
void init(void)
{
  int i;//counter
  v=(ver*)malloc(sizeof(ver)*n);
  for(i=0;i<n;i++)
    {
      v[i].numOfAdj=0;
      v[i].status=0;
      v[i].cost=INF;
    }
}
void setArray(int key)
{
  v[key].adjList=(int*)malloc(sizeof(int)*v[key].numOfAdj);
  v[key].costList=(int*)malloc(sizeof(int)*v[key].numOfAdj);
}
void dijkstra(void)
{
  int i;//count
  int current=0;
  int viewing;
  int next;
  int minCost;
  v[0].cost=0;
  for(;;)
    {
      v[current].status=1;
      minCost=INF;
      for(i=0;i<v[current].numOfAdj;i++)
	{
	  viewing=v[current].adjList[i];
	  if(v[viewing].status==0)
	    {
	      if(v[current].cost+v[current].costList[i]<v[viewing].cost)
		{
     		  v[viewing].cost=v[current].cost+v[current].costList[i];
		  //printf("v[%d].cost=%d\n",viewing,v[viewing].cost);
		}
	    }
	}
      for(viewing=0;viewing<n;viewing++)
	{
	  if(v[viewing].status==0&&v[viewing].cost<minCost)
	    {
	      minCost=v[viewing].cost;
	      next=viewing;
	    }
	}
      if(minCost==INF) break;
      //printf("next->%d\n",next);
      current=next;
    }
  for(i=0;i<n;i++) printf("%d %d\n",i,v[i].cost);
}