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>

#define MAX 100

int n,M[MAX][MAX];
int d[MAX];
int Q[MAX+1];
int head = 1, tail;

void enqueue(int x){
   
  Q[tail] = x;
 
  if((tail +1) == MAX)
    tail = 0;
  else
    tail++;
 
}
 
int dequeue(){
 
  int x;
  x = Q[head];
  if((head + 1) == MAX)
    head = 0;
  else
    head++;
   
  return x; 
 
}
 
int Q_empty(){
  int i;
  for(i=0;i<MAX+1;i++)
    if(Q[i]!=-777) return 777;
  return 0;
}

void Breadth_First_Search(int s){
  int i,u,v,count=0,flag=1;
     
  enqueue(s);
  for(i=0;i<n;i++) d[i] = (1<<21);
  d[s]=0;
  
 
  while(1){
    if(Q_empty()==0)break;
    
    for(i=count;i<MAX+1;i++){
      u=dequeue();
      if(u!=-777) break;
    }
     if(u==-777) break;
    count=i;
    for(v=0;v<n;v++){
      if(M[u][v]==0) continue;
      if(d[v]!= (1<<21))continue;
      d[v]=d[u]+1;
      enqueue(v);
    }
  }

  for(i=0;i<n;i++){
    printf("%d",i+1);
    if(d[i]==(1<<21)) printf(" %d\n",-1);
    else printf(" %d\n",d[i]);
  }


}

int main(){
  int u,k,v,i,j;

  for(i=0;i<MAX+1;i++){
    Q[i]=-777;
  }
  
  scanf("%d",&n);
  for(i=0;i<n;i++){
    for(j=0;j<n;j++){
      M[i][j]=0;
    }
  }

  for(i=0;i<n;i++){
    scanf("%d%d",&u,&k);
    u--;
    for(j=0;j<k;j++){
      scanf("%d",&v);
      v--;
      M[u][v]=1;
    }
  }
  Breadth_First_Search(0);
  return 0;
}