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 <limits.h>
#include <stdlib.h>
/*#include <math.h>*/
#include <string.h>

#define N 10005
#define INF 12345678
#define WHITE 0 
#define GRAY  1
#define BLACK 2
#define NIL -1

void create_generate_super_makeone_node(int, int, int );

struct node{
  struct node *next;
  // struct node *prev;
  int vertex;
  int omosa;
};

typedef struct node *NodePointer;
NodePointer nil;

NodePointer data[N];
//int adj[N][N];
int d[N];
int color[N];
//int check[N];
int pi[N];
//int n;
/*
  void MinHeapify(int );
  void BuildMinHeap(void );
  int  ExtractMin(void );
  void HeapDecreace(int, int );
  void dijkstra(int );
*/

int main(){
  int ex;
  int i,j;
  int n,u,k,vertex,c;
  int uid;
  int mincost;
  int r;

  for(i=0;i<10001;i++){
    data[i] = (NodePointer)malloc(sizeof(struct node));
    data[i]->vertex = INF;
    data[i]->omosa = INF;
    data[i]->next  = NULL;
    // d[i] = INF;
    // color[i] = WHITE;
    // pi[i] = NIL;
  }
  
  scanf("%d",&n);

  for(i=1;i<=n;i++){
    d[i] = INF;
    color[i] = WHITE;
    pi[i] = NIL;

    
    scanf("%d%d",&uid,&k);
    r = uid;
    for(j=0;j<k;j++){
      scanf("%d%d",&vertex,&c);
      create_generate_super_makeone_node(r,vertex,c);
    }
  }


  d[0] = 0;
  for(ex=0;;ex++){
    mincost = INF;
    for(j=0;j<n;j++){
      if(color[j] != BLACK && d[j] < mincost){
	mincost = d[j];
	u = j;
	  }
    }
  
  


    if(mincost == INF) break;

    color[u] = BLACK;
    
    nil = data[u]->next; 
    
    while(nil != NULL){
      // if(nil != NULL) break;

      if(color[nil->vertex] != BLACK && d[u]+nil->omosa<d[nil->vertex]){
	//	printf("aiueo\n\n");
	pi[nil->vertex] = u;
	d[nil->vertex] = nil->omosa+d[u];
      }
      //if(nil != NULL) break;
      nil = nil->next;
      // if(nil != NULL) break;
    }
  }
  for(i=0;i<n;i++){
    printf("%d %d\n",i,d[i]);
  }

  


  

  
    return 0;
}

void create_generate_super_makeone_node(int r, int vertex, int c){
  NodePointer n;
  n =(NodePointer)malloc(sizeof(struct node));
  n->vertex = vertex;
  n->omosa = c;
  n->next = data[r]->next;
  data[r]->next = n;

}