Problem:
Rooted Trees

A graph G = (V, E) is a data structure where V is a finite set of vertices and E is a binary relation on V represented by a set of edges. Fig. 1 illustrates an example of a graph (or graphs).

Fig. 1

A free tree is a connnected, acyclic, undirected graph. A rooted tree is a free tree in which one of the vertices is distinguished from the others. A vertex of a rooted tree is called "node."

Your task is to write a program which reports the following information for each node u of a given rooted tree T:

node ID of u

parent of u

depth of u

node type (root, internal node or leaf)

a list of chidlren of u

If the last edge on the path from the root r of a tree T to a node x is (p, x), then p is the parent of x, and x is a child of p. The root is the only node in T with no parent.

A node with no children is an external node or leaf. A nonleaf node is an internal node

The number of children of a node x in a rooted tree T is called the degree of x.

The length of the path from the root r to a node x is the depth of x in T.

Here, the given tree consists of n nodes and evey node has a unique ID from 0 to n-1.

Fig. 2 shows an example of rooted trees where ID of each node is indicated by a number in a circle (node). The example corresponds to the first sample input.

Fig. 2

Input

The first line of the input includes an integer n, the number of nodes of the tree.

In the next n lines, the information of each node u is given in the following format:

id k c1 c2 ... ck

where id is the node ID of u, k is the degree of u, c1 ... ck are node IDs of 1st, ... kth child of u. If the node does not have a child, the k is 0.

Output

Print the information of each node in the following format ordered by IDs:

node id: parent = p, depth = d, type, [c1...ck]

p is ID of its parent. If the node does not have a parent, print -1.

d is depth of the node.

type is a type of nodes represented by a string (root, internal node or leaf). If the root can be considered as a leaf or an internal node, print root.

c1...ck is the list of children as a ordered tree.

Please follow the format presented in a sample output below.

Constraints

1 ≤ n ≤ 100000

Sample Input 1

13
0 3 1 4 10
1 2 2 3
2 0
3 0
4 3 5 6 7
5 0
6 0
7 2 8 9
8 0
9 0
10 2 11 12
11 0
12 0

Sample Output 1

node 0: parent = -1, depth = 0, root, [1, 4, 10]
node 1: parent = 0, depth = 1, internal node, [2, 3]
node 2: parent = 1, depth = 2, leaf, []
node 3: parent = 1, depth = 2, leaf, []
node 4: parent = 0, depth = 1, internal node, [5, 6, 7]
node 5: parent = 4, depth = 2, leaf, []
node 6: parent = 4, depth = 2, leaf, []
node 7: parent = 4, depth = 2, internal node, [8, 9]
node 8: parent = 7, depth = 3, leaf, []
node 9: parent = 7, depth = 3, leaf, []
node 10: parent = 0, depth = 1, internal node, [11, 12]
node 11: parent = 10, depth = 2, leaf, []
node 12: parent = 10, depth = 2, leaf, []

Sample Input 2

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

Sample Output 2

node 0: parent = 1, depth = 1, leaf, []
node 1: parent = -1, depth = 0, root, [3, 2, 0]
node 2: parent = 1, depth = 1, leaf, []
node 3: parent = 1, depth = 1, leaf, []

Note

You can use a left-child, right-sibling representation to implement a tree which has the following data:

the parent of u

the leftmost child of u

the immediate right sibling of u

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<stdlib.h>
typedef struct node
{
  int id;
  struct node *parent;
  struct node *leftMostChild;
  struct node *rightSibling;
} *nodePointer;
nodePointer make1node(void);
void printNode(nodePointer);
int getDepth(nodePointer);
void printType(nodePointer);
void printChild(nodePointer);
nodePointer init(int);
nodePointer head;
int main(void)
{
  int i,j;//counter
  int n;//the number of nodes
  int id;//id of each node
  int k;//the number of children
  int c1,c2;//id of children
  nodePointer p1,p2;
  nodePointer *arr;
  head=init(-1);
  scanf("%d",&n);
  arr=(nodePointer*)malloc(sizeof(nodePointer)*n);
  for(i=0;i<n;i++) arr[i]=init(i);
  for(i=0;i<n;i++)
    {
      scanf("%d",&id);
      scanf("%d",&k);
      for(j=0;j<k;j++)
        {
          scanf("%d",&c1);
          if(j==0)
            {
              arr[id]->leftMostChild=arr[c1];
            }
          else
            {
              arr[c2]->rightSibling=arr[c1];
            }
          arr[c1]->parent=arr[id];
          c2=c1;
        }
    }
  for(i=0;i<n;i++) printNode(arr[i]);
  return 0;
}
nodePointer init(int id)
{
  nodePointer p;
  p=make1node();
  p->id=id;
  p->parent=NULL;
  p->leftMostChild=NULL;
  p->rightSibling=NULL;
  return p;
}
void printNode(nodePointer p)
{
  printf("node %d: ",p->id);
  if(p->parent!=NULL) printf("parent = %d, ",p->parent->id);
  else printf("parent = -1, ");
  printf("depth = %d, ",getDepth(p));
  printType(p);
  printf(", ");
  printChild(p);
  printf("\n");
}
nodePointer make1node(void)
{
  nodePointer p=(nodePointer)malloc(sizeof(struct node));
  return p;
}
int getDepth(nodePointer p)
{
  int depth;
  for(depth=0;p->parent!=NULL;p=p->parent) depth++;
  return depth;
}
void printType(nodePointer p)
{
  if(p->parent==NULL) printf("root");
  else if(p->leftMostChild==NULL) printf("leaf");
  else printf("internal node");
}
void printChild(nodePointer p)
{
  printf("[");
  if(p->leftMostChild!=NULL)
    {
      p=p->leftMostChild;
      printf("%d",p->id);
      for(;p->rightSibling!=NULL;p=p->rightSibling) printf(", %d",p->rightSibling->id);
    }
  printf("]");
}