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>

#define UND_NODE -1

typedef struct {
//    int id;
    int firstChild;
    int nextSibling;
    int parent;
} BinaryNode;

//int nodeIndexFromId(BinaryNode nodes[], int length, int id) {
//    for (int i = 0; i < length; i++)
//        if(nodes[i].id == id)
//            return i;
//}

int nodeDepthFromId(BinaryNode nodes[], int length, int id) {
    int i = 0;
    while (nodes[id].parent != UND_NODE) {
        i++;
        id = nodes[id].parent;
    }
    return i;
}

void printArray(int array[], int length) {
    for (int i = 0; i < length; i++) {
        if (i) printf(", ");
        printf("%d", array[i]);
    }
}


int main(int argc, char** argv) {
    int nNodes, nChildren;
    scanf("%d", &nNodes);
    
    BinaryNode nodes[nNodes]; // Binary tree
    int i, j, parentNodeId, currentNodeId, incomingNodeId;
    
    for (i = 0; i < nNodes; i++)
        nodes[i].parent = nodes[i].firstChild = nodes[i].nextSibling = UND_NODE;
    
    for (i = 0; i < nNodes; i++) {
        scanf("%d", &(parentNodeId)); // id
        scanf("%d", &(nChildren)); // k, number of children

        for (j = 0; j < nChildren; j++) {
            scanf("%d", &(incomingNodeId));
            if (j == 0) {
//                printf("firstChild of %d will be %d", parentNodeId, incomingNodeId);
                nodes[parentNodeId].firstChild = incomingNodeId;
            }
            else {
//                printf("nextSibling of %d will be %d", currentNodeId, incomingNodeId);
                nodes[currentNodeId].nextSibling = incomingNodeId;
            }
            
            currentNodeId = incomingNodeId;
            
            nodes[incomingNodeId].parent = parentNodeId;
            
//            printf("parentNodeId: %d; currentNodeId: %d; incomingNodeId: %d\n", parentNodeId, currentNodeId, incomingNodeId);
//            printf("incoming;   node %d: parent = %d\n", incomingNodeId, nodes[incomingNodeId].parent);
//            printf("parentNode; node %d: parent = %d\n", parentNodeId, nodes[parentNodeId].parent);
        }
    }
    
    for (i = 0; i < nNodes; i++) {
        j = nodeDepthFromId(nodes, nNodes, i);
        
        printf("node %d: parent = %d, depth = %d, ", i, nodes[i].parent, j);
        
        // node types
        if (nodes[i].parent == UND_NODE)
            printf("root, ");
        else if (nodes[i].firstChild == UND_NODE)
            printf("leaf, ");
        else 
            printf("internal node, ");
        
        // children
        printf("[");
        if (nodes[i].firstChild != UND_NODE) {
            printf("%d", nodes[i].firstChild);
            j = nodes[i].firstChild;
            while (nodes[j].nextSibling != UND_NODE) {
                printf(", %d", j = nodes[j].nextSibling);
            }
        }
        printf("]\n");
    }
    

    return (EXIT_SUCCESS);
}