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

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++14 (judge verdict: Time Limit Exceeded)

#include<bits/stdc++.h>
#define INF 10000000
using namespace std;

int z[100],n;
int a[100][100];

void bfs(){
  int m;
  z[0]=0;
  queue<int> q;
  q.push(0);
  while(!q.empty()){
    m=q.front();
    q.pop();
    for(int i=0;i<n;i++){
      if(a[m][i]==1){
	q.push(i);
	z[i]=min(z[i],z[m]+1);
      }
    }
  }
}


int main(){
  int p,x;
  for(int i=0;i<100;i++){
    z[i]=INF;
    for(int j=0;j<100;j++) a[i][j]=0;
  }
  cin>>n;
  for(int i=0;i<n;i++){
    cin>>p>>p;
    for(int j=0;j<p;j++){
      cin>>x;
      a[i][x-1]=1;
    }
  }
  bfs();
  for(int i=0;i<n;i++){
    if(z[i]!=INF) cout<<i+1<<" "<<z[i]<<endl;
    else cout<<i+1<<" "<<-1<<endl;
  }
  return 0;
}