Problem:
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Breadth First Search

Write a program which reads an directed graph $G = (V, E)$, and finds the shortest distance from vertex $1$ to each vertex (the number of edges in the shortest path). Vertices are identified by IDs $1, 2, ... n$.

Input

In the first line, an integer $n$ denoting the number of vertices, is given. In the next $n$ lines, adjacent lists of vertex $u$ are given in the following format:

$u$ $k$ $v_1$ $v_2$ ... $v_k$

$u$ is ID of the vertex and $k$ denotes its degree.$v_i$ are IDs of vertices adjacent to $u$.

Constraints

$1 \leq n \leq 100$

Output

For each vertex $u$, print $id$ and $d$ in a line. $id$ is ID of vertex $u$ and $d$ is the distance from vertex $1$ to vertex $u$. If there are no path from vertex $1$ to vertex $u$, print -1 as the shortest distance. Print in order of IDs.

Sample Input 1

4
1 2 2 4
2 1 4
3 0
4 1 3

Sample Output 1

1 0
2 1
3 2
4 1

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>
#include <stdlib.h>

void search(int **a, int n, int *d, int u, int t) {
  if(t > n) return;
  int i;
  if(d[u] == 0 || d[u] > t) d[u] = t;
  for (i = 1; i < n; i++) {
    if(a[u][i] == 1) {
      search(a,n,d,i,t+1);
    }
  }
}

int main()
{
  int i,j,n,**a,u,k,v;
  scanf("%d",&n);
  a = (int**)malloc(sizeof(int*) * n);
  for (i = 0; i < n; i++) {
    a[i] = (int*)malloc(sizeof(int) * n);
    for(j = 0; j < n; j++) a[i][j] = 0;
  }
  for (i = 0; i < n; i++) {
    scanf("%d",&u);
    scanf("%d", &k);
    for(j = 0; j < k; j++){
      scanf("%d",&v);
      a[u-1][v-1] = 1;
    }
  }

  int *d;
  d = (int*)calloc(n,sizeof(int));

  search(a,n,d,0,0);
  for (i = 1; i < n; i++) {
    if(d[i] == 0) d[i] = -1;
  }



  for (i = 0; i < n; i++) {
    printf("%d ", i+1);
    printf("%d\n", d[i]);
  }

  free(a);
  free(d);
  return 0;
}