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>
#define INF 100000000 
#define N 100

int n;
int size[N];
int to[N][N];
int cost[N][N];
int dist[N];
 
void DFS(int,int);
 
main(int argc,char *argv[]){
  int i, j;
  scanf("%d", &n);
  for(i=0;i<n;i++){
    int u;
    scanf("%d", &u);
    scanf("%d", &size[u]);
    for(j=0;j<size[u];j++){
      scanf("%d", &to[u][j]);
      scanf("%d", &cost[u][j]);
    }
  }
  for(i=0;i<n;i++) dist[i] = INF;
  DFS(0, 0);
  for(i=0;i<n;i++){
    printf("%d %d\n", i, dist[i]);
  }
  return 0;
}
void DFS(int p, int c){
  int i;
  dist[p] = c;
  for(i=0;i<size[p];i++){
    if(dist[to[p][i]] > c + cost[p][i])
      DFS(to[p][i], c + cost[p][i]);
  }
}