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 10000
#define INF 168435450

typedef struct node{
 int flg;
 int cost;
}node;

typedef struct edge{
 int p_id;
 int cost;
 struct edge *next;
}edge;


edge* makecell(int v,int cost){
edge* new;

new=malloc(sizeof(edge));
new->p_id=v;
new->cost=cost;
new->next=NULL;

return new;

}

void insert(edge* E[],int x,edge* new){
edge **p;

p=&E[x];

while((*p)!=NULL)p=&((*p)->next);

(*p)=new;


return;
}

int min(int a,int b){
if(a < b)return a;
return b;
}


int min_idx(node N[],int n){
int idx;
int i;
int mini=268435450;

for(i=0;i<n;i++){
 if(N[i].flg==0 && N[i].cost<mini){
   mini=N[i].cost;
   idx=i;
 }
}

return idx;
}



int main(){
int n,x,y,d;
int i,j,k,u;
node N[MAX];
edge *E[MAX];
edge *new;
edge *p;

scanf("%d",&n);

for(i=0;i<n;i++){
 N[i].flg=0; 
 N[i].cost=INF;
 E[i]=NULL;
}



for(i=0;i<n;i++){
 scanf("%d %d",&x,&k);
 for(j=0;j<k;j++){
  scanf("%d %d",&y,&d);
  new=makecell(y,d);
  insert(E,x,new);
 }
}


N[0].cost=0;

for(i=0;i<n;i++){
 u=min_idx(N,n);


 if(N[u].flg==0){
    N[u].flg=1;
    
    p=E[u];
    while(p!=NULL){
      j=p->p_id;
      N[j].cost=min(N[j].cost,N[u].cost+p->cost);
      p=p->next;
    }
    
 }

}


for(i=0;i<n;i++)
 printf("%d %d\n",i,N[i].cost);


return 0;
}