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 MAX 10001
#define INF 2e8

struct node{
  int key;
  int weight;
  struct node *next;
};

typedef struct node *Node;
 
Node G[MAX];

Node cpy(int k,int w,Node n)
{
  Node x;
  
  x= (Node)malloc(sizeof(struct node));
  x->key = k;
  x->weight = w;
  x->next = n;
  
  return x;
}

void insert(int a,int b,int c)
{
  Node x;
  x=cpy(b,c,G[a]->next);
  G[a]->next=x;
}


int main()
{
  int i,j,n,count=0,u,k,v,c,color[MAX],d[MAX],pi[MAX],min,save;
  Node s;
 
  scanf("%d",&n);
  for(i=0; i<n; i++)
    G[i]=cpy(0,0,NULL);
    
  for(i=0; i<n; i++){
    scanf("%d%d",&u,&k);
    for(j=0; j<k; j++){
      scanf("%d%d",&v,&c);
      insert(i,v,c);
    }
  }
  
  for(i=0; i<n; i++){
    color[i] = 0;
    pi[i] = -1;
    d[i] = INF;
  }
  d[0] = 0;
  
  while(1){
    min = INF;
    for(i=0; i<n; i++){
      if(color[i]!=2 && d[i]<min){
        min=d[i];
        save = i;
      }
    }
    if(min == INF)
        break;
    color[save]=2;
    
    for(s=G[save]; s!=NULL; s=s->next){
      if(color[s->key]!=2 && (s->weight+d[save])<d[s->key]){
	    pi[s->key] = save;
	    d[s->key] = s->weight+d[save];
    	color[s->key]=1;
      }
    }
  }
  for(i=0; i<n; i++)
    printf("%d %d\n",i,d[i]);
  
  return 0;
}