Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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: Time Limit Exceeded)

#include <stdio.h>
  
#define INF 1e9
#define MAX 1000
 
int min(int a,int b){
  if(a<b) return a;
  return b;
}
  
int main(){
  int n,i,u,k,j,v,c;
  int d[MAX][MAX];
  
  for(i = 0 ; i < MAX ; i++){
    for(j = 0 ; j < MAX ; j++){
      d[i][j] = INF;
    }
    d[i][i] = 0;
  }
  
  scanf("%d",&n);
   
  for(i = 0 ; i < n ; i++){
    scanf("%d%d" ,&u ,&k);
     
    for(j = 0 ; j < k ; j++){
      scanf("%d%d" ,&v ,&c);
      d[u][v] = c;
    }
  }
  
  for(k = 0 ; k < n ; k++){
    for(i = 0 ; i < n ; i++){
      for(j = 0 ; j < n ; j++){
    d[i][j] = min(d[i][j],d[i][k]+d[k][j]);
      }
    }
  }
  
  for(i = 0 ; i < n ; i++){
    printf("%d %d\n" ,i ,d[0][i]);
  }
  
  return 0;
}