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 <string.h>
#include <stdlib.h>

struct ve{
        int num;
        int parent_num;
        int degree;
        int depth;
        char type[128];
        int *child;
};

int n;

int calc_depth(struct ve *, int, int);

int main(){
        int p, i, j, id, k, l, m, root;
        char f;
        struct ve *T;

        scanf("%d", &n);

        T = malloc(n * sizeof(struct ve));

        for(i = 0 ; i < n ;i++){
                T[i].parent_num = -1;
        }

        for(i = 0 ; i < n ; i++){
                m = 0;
                scanf("%d", &id);
                T[id].num = id;
                scanf("%d", &T[id].degree);
                if(T[id].degree == 0){
                        strcpy(T[id].type, "leaf");
                        continue;
                }
                T[id].child = malloc(T[id].degree * sizeof(int));
                for(j = 0 ; j < T[id].degree ; j++){
                        scanf("%d", &p);
                        T[id].child[m] = p;
                        T[p].parent_num = id;
                        m++;
                }
        }

        for(i = 0 ; i < n ; i++){
                if(n == 1)strcpy(T[i].type, "root");
                if(T[i].degree == 0)continue;
                if(T[i].parent_num == -1){
                        strcpy(T[i].type, "root");
                        root = i;                               
                }else strcpy(T[i].type, "internal node");
        }

        for(i = 0 ; i < n ; i++){
                T[i].depth = calc_depth(T, root, i);
        }
        
        for(i = 0 ; i < n ; i++){
                printf("node %d: parent = %d, depth = %d, %s, [", T[i].num, T[i].parent_num, T[i].depth, T[i].type);
                for(j = 0 ; j < T[i].degree ; j++){
                        printf("%d", T[i].child[j]);
                        if(j + 1 < T[i].degree)printf(", ");
                }
                printf("]\n");
        }

        for(i = 0 ; i < n ; i++){
                if(T[i].degree == 0)continue;
                else free(T[i].child);
        }
        free(T);
        return 0;
}

int calc_depth(struct ve *T, int root, int id){
        if(strcmp(T[id].type, "root") == 0)return 0;
        else{
                return 1 + calc_depth(T, root, T[id].parent_num);
        }
}