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: Memory Limit Exceeded)

#include<stdio.h>
#include<limits.h>


#define N 10001
#define true 1
#define false 0

int n;

int g[N][N];

int weight[N];
int us[N];

//prim
void prim(){

  int v;
  int i,j; 
  weight[0]=0;
  
  while(true){
    v=-1;
   
    for(i=0;i<n;i++){
      if(us[i]!=true && (v==-1 ||weight[i]<weight[v]))v=i;
    }

    if(v==-1)break;
    us[v]=true;
 

    for(i=0;i<n;i++){
      if(weight[i]>(g[v][i]+weight[v])){

        weight[i]=(g[v][i]+weight[v]);
        //      cout <<"fsafa"<<endl;
      }
    }
  }
 
}


int main(){

  int u,k1,c,v;
  int i,j;
 
  //load n
  //  cin >>n;
  scanf("%d",&n);
 
  for(i=0;i<n;i++){
    for(j=0;j<n;j++){
      g[i][j]=9953535;
    }
  }
 

  //load data
  for(i=0;i<n;i++){
    weight[i]=INT_MAX;
    us[i]=false;
    scanf("%d %d",&u,&k1);
    for(j=0;j<k1;j++){
      scanf("%d %d",&v,&c);
      g[u][v]=c;
      //    cout <<g[i][j]<<" ";
    }
    //    cout <<endl;
  }




  //print
  prim();

  for(i=0;i<n;i++){
    //  cout <<i<<" "<<weight[i]<<endl;
    printf("%d %d\n",i,weight[i]);
  }
  return 0;

}