Problem:
Tree Walk

Binary trees are defined recursively. A binary tree T is a structure defined on a finite set of nodes that either

contains no nodes, or

is composed of three disjoint sets of nodes:

- a root node.

- a binary tree called its left subtree.

- a binary tree called its right subtree.

Your task is to write a program which perform tree walks (systematically traverse all nodes in a tree) based on the following algorithms:

Print the root, the left subtree and right subtree (preorder).

Print the left subtree, the root and right subtree (inorder).

Print the left subtree, right subtree and the root (postorder).

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

Input

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

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

id left right

id is the node ID, left is ID of the left child and right is ID of the right child. If the node does not have the left (right) child, the left(right) is indicated by -1

Output

In the 1st line, print "Preorder", and in the 2nd line print a list of node IDs obtained by the preorder tree walk.

In the 3rd line, print "Inorder", and in the 4th line print a list of node IDs obtained by the inorder tree walk.

In the 5th line, print "Postorder", and in the 6th line print a list of node IDs obtained by the postorder tree walk.

Print a space character before each node ID.

Constraints

1 ≤ n ≤ 25

Sample Input 1

9
0 1 4
1 2 3
2 -1 -1
3 -1 -1
4 5 8
5 6 7
6 -1 -1
7 -1 -1
8 -1 -1

Sample Output 1

Preorder
0 1 2 3 4 5 6 7 8
Inorder
2 1 3 0 6 5 7 4 8
Postorder
2 3 1 6 7 5 8 4 0

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in JAVA (judge verdict: WA: Presentation Error)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.io.StreamTokenizer;
import java.util.InputMismatchException;


public class Main {

	public static Node[] nodes;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in); 
		Printer pr = new Printer(System.out);

		int n = sc.nextInt();
		nodes = new Node[n];
		
    	for (int i = 0; i < n; i++) {
    		int id = sc.nextInt();
    		nodes[id] = new Node(id, sc.nextInt(), sc.nextInt());
    	}

    	for (int i = 0; i < n; i++) {
    		setParent(i);
    	}
    	int root = seekRoot();

//    	setDepth(root, 0);
//    	for (int i = 0; i < n; i++) {
//        	setHeight(i);
//    	}


//    	for (int i = 0; i < n; i++) {
//    		pr.println(nodes[i].toString());
//    	}

    	int[] order = new int[n];
    	// Preorder
    	if (preorder(root, order, 0) != n) {
    		pr.println("Error");
    	}
    	
    	pr.println("Preorder");
    	pr.printArray(order);
    	
    	// Inorder
    	if (inorder(root, order, 0) != n) {
    		pr.println("Error");
    	}
    	
    	pr.println("Inorder");
    	pr.printArray(order);
    	
    	// Postorder
    	if (postorder(root, order, 0) != n) {
    		pr.println("Error");
    	}
    	
    	pr.println("Postorder");
    	pr.printArray(order);
    	
    	pr.close();
        sc.close();
	}

	private static int preorder(int id, int[] order, int k) {
		order[k] = id;
		k++;
		
		if (nodes[id].l_child != -1) {
			k = preorder(nodes[id].l_child, order, k);
		}
		
		if (nodes[id].r_child != -1) {
			k = preorder(nodes[id].r_child, order, k);
		}

		return k;
		
	}
	
	private static int inorder(int id, int[] order, int k) {
		if (nodes[id].l_child != -1) {
			k = inorder(nodes[id].l_child, order, k);
		}
		
		order[k] = id;
		k++;
		
		if (nodes[id].r_child != -1) {
			k = inorder(nodes[id].r_child, order, k);
		}

		return k;
		
	}
	
	private static int postorder(int id, int[] order, int k) {
		if (nodes[id].l_child != -1) {
			k = postorder(nodes[id].l_child, order, k);
		}
		
		if (nodes[id].r_child != -1) {
			k = postorder(nodes[id].r_child, order, k);
		}

		order[k] = id;
		k++;
		
		return k;
		
	}
	
	private static void setParent(int id) {
		nodes[id].degree = 0;
		if (nodes[id].l_child != -1) {
			nodes[nodes[id].l_child].parent = id;
			nodes[id].degree++;
		}
		if (nodes[id].r_child != -1) {
			nodes[nodes[id].r_child].parent = id;
			nodes[id].degree++;
		}
	}
	
	private static int seekRoot() {
    	for (int i = 0; i < nodes.length; i++) {
    		if (nodes[i].parent == -1){
    			return i;
    		}
    	}
    	
    	return -1;
	}
	
//	private static void setDepth(int id, int depth) {
//		if (nodes[id].parent == -1) {
//			nodes[id].type = NodeType.ROOT;
//		} else {
//			if (nodes[id].degree == 0) {
//				nodes[id].type = NodeType.LEAF;
//				nodes[id].height = 0;
//			} else {
//				nodes[id].type = NodeType.INTERNAL_NODE;
//				nodes[id].height = -1;
//			}
//		}
//		nodes[id].depth = depth;
//
//		if (nodes[id].degree == 2) {
//			nodes[nodes[id].l_child].sibling = nodes[id].r_child;
//			nodes[nodes[id].r_child].sibling = nodes[id].l_child;
//		}
//		
//		if (nodes[id].l_child != -1) {
//			setDepth(nodes[id].l_child, depth + 1);
//		}
//		if (nodes[id].r_child != -1) {
//			setDepth(nodes[id].r_child, depth + 1);
//		}
//
//		return;
//	}
		
//	private static void setHeight(int id) {
//		if (nodes[id].height != 0) {
//			return;
//		} else {
//			for (int j = nodes[id].parent, h = 0; j != -1; j = nodes[j].parent, h++) {
//				if (nodes[j].height < h + 1) {
//					nodes[j].height = h + 1;
//				}
//			}
//		}
//	}

	private static enum NodeType {
		ROOT, INTERNAL_NODE, LEAF;
	}
	
	private static class Node {
		public int id;
		public int parent;
		public int l_child;
		public int r_child;
		public int sibling;
		public int depth;
		public int height;
		public int degree;
		public NodeType type;
	
		public Node(int id, int l_child, int r_child) {
			this.id = id;
			this.l_child = l_child;
			this.r_child = r_child;
			this.sibling = -1;
			this.parent = -1;
		}
		
		@Override
		public String toString() {
			StringBuffer str = new StringBuffer();

			str.append("node ");
			str.append(id);
			str.append(": parent = ");
			str.append(parent);
			str.append(", sibling = ");
			str.append(sibling);
			str.append(", degree = ");
			str.append(degree);
			str.append(", depth = ");
			str.append(depth);
			str.append(", height = ");
			str.append(height);
			str.append(", ");
			String type;
			switch (nodes[id].type) {
			case INTERNAL_NODE:
				type = "internal node";
				break;
			case LEAF:
				type = "leaf";
				break;
			case ROOT:
				type = "root";
				break;
			default:
				type = null;
			}
			str.append(type);
			
			return str.toString();
		}
	}


	private static class Scanner {
		InputStreamReader isr;
		BufferedReader br;
		StreamTokenizer st;
		
		Scanner (InputStream in) {
			isr = new InputStreamReader(in);
			br = new BufferedReader(isr);
			st = new StreamTokenizer(br);
		}
		
		String next() throws RuntimeException  {
			try {
				if (st.nextToken() != StreamTokenizer.TT_WORD) {
				}
			} catch (IOException e) {
				throw new IllegalStateException();
			}
			
			return st.sval;
		}
		
		int nextInt() throws RuntimeException {
			try {
				if (st.nextToken() != StreamTokenizer.TT_NUMBER) {
					throw new InputMismatchException();
				}
			} catch (IOException e) {
				throw new IllegalStateException();
			}
			
			return (int)st.nval;
		}

		void close() {
		}
	}
	
	private static class Printer {
		PrintStream out;
		StringBuffer strbuf;
		int bufSize;
		final String CR;

		Printer(PrintStream out) {
			this.out = out;
			strbuf = new StringBuffer();
			bufSize = 64 * 1024;
			CR = System.getProperty("line.separator");
		}

		void println(String str) {
			strbuf.append(str);
			strbuf.append(CR);
			checkStringBuffer();
		}

		void print(String str) {
			strbuf.append(str);
			checkStringBuffer();
		}

		void println(int n) {
			strbuf.append(n);
			strbuf.append(CR);
			checkStringBuffer();
		}

		void print(int n) {
			strbuf.append(n);
			checkStringBuffer();
		}

		void print(char c) {
			strbuf.append(c);
			checkStringBuffer();
		}

		void printArray(int[] array) {
			for (int i = 0; i < array.length; i++) {
				checkStringBuffer();
				strbuf.append(array[i]);
				strbuf.append(" ");
			}
			strbuf.delete(strbuf.length() - 1, strbuf.length());
			strbuf.append(CR);
		}

		void close() {
			flashStringBuffer();
		}
		
		private void flashStringBuffer() {
			if (strbuf.length() > 0) {
				out.print(strbuf);
				strbuf.setLength(0);
			}
		}
		
		private void checkStringBuffer() {
			if (strbuf.length() > bufSize) {
				out.print(strbuf);
				strbuf.setLength(0);
			}
		}
	}
}