Problem:
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Single Source Shortest Path

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

$1 \leq n \leq 100$

$0 \leq c_i \leq 100,000$

$|E| \leq 10,000$

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<string.h>
int moguru(int[][100],int);
int n,ans[100];
int main(){
  int i,j,a[100][100],mita[100],now,to,leng;
  scanf("%d",&n);
  for(i=0;i<n;i++){
    ans[i]=-1;
  }
  for(i=0;i<n;i++)
  for(j=0;j<n;j++)
    a[i][j] = -1;
  
  for(i=0;i<n;i++){
    scanf("%d",&now);
    scanf("%d",&now);
    for(j=0;j<now;j++){
      scanf("%d %d",&to,&leng);
      a[i][to] = leng;
    }
  }
  ans[0]=0;
  moguru(a,0);
  for(i=0;i<n;i++){
    printf("%d %d\n",i,ans[i]);
  }

}

int moguru(int a[][100],int now){
  int i;
  for(i=0;i<n;i++){
    if(a[now][i] == -1)
      continue;
    if(ans[now]+a[now][i] < ans[i] || ans[i] == -1){
      ans[i]= ans[now]+a[now][i];
      moguru(a,i);
    }
	
  }
  return 1;

}