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: Accepted)

import java.io.DataInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;


public class Main {
	
	public static void main(String[] args) throws IOException, InstantiationException, IllegalAccessException {
		new Main().exec();
	}
	
	public void exec() throws IOException, InstantiationException, IllegalAccessException {
		InputUtil in = new InputUtil();
		PrintWriter out = new PrintWriter(System.out);
		int n = in.nextInt();
		BinaryTree bt = new BinaryTree(n);
		
		for(int i=0; i<n; i++){
			int id = in.nextInt();
			int leftId = in.nextInt();
			int rightId = in.nextInt();
			bt.setNode(id, leftId, rightId);
		}
		int[] nodeBuf = new int[n];
		bt.preOrder(nodeBuf,0,bt.getRootId());
		out.println("Preorder");
		out.print(" ");
		output(out,nodeBuf,0,n," ");

		bt.inOrder(nodeBuf,0,bt.getRootId());
		out.println("Inorder");
		out.print(" ");
		output(out,nodeBuf,0,n," ");

		bt.postOrder(nodeBuf,0,bt.getRootId());
		out.println("Postorder");
		out.print(" ");
		output(out,nodeBuf,0,n," ");

		out.flush();
	}
	
	public void output(PrintWriter out, int[] a, int off, int len, String delim) {
		out.print(a[off]);
		for(int i=off+1; i<len; i++){
			out.print(delim);
			out.print(a[i]);
		}
		out.println("");
		out.flush();
	}
}


class BinaryTree {
	
	private int[] left;
	private int[] right;
	private int[] parent;
	private int[] sibling;
	private int[] degree;
	private int[] depth;
	private int[] height;
	private int maxNodes;
	
	public BinaryTree(int maxNodes) {
		this.maxNodes=maxNodes;
		left = new int[maxNodes];
		right = new int[maxNodes];
		parent = new int[maxNodes];
		
		sibling = new int[maxNodes];
		degree = new int[maxNodes];
		depth = new int[maxNodes];
		height = new int[maxNodes];
		
		
		Arrays.fill(left, -1);
		Arrays.fill(right, -1);
		Arrays.fill(parent, -1);
		Arrays.fill(sibling, -1);
	}
	
	public void setNode(int id, int leftId, int rightId) {
		left[id] = leftId;
		if(leftId != -1) {
			parent[leftId] = id;
			sibling[leftId] = rightId;
		}
		right[id] = rightId;
		if(rightId != -1) {
			parent[rightId] = id;
			sibling[rightId] = leftId;
		}
	}
	
	public int getRootId() {
		int rootId = 0;
		while(parent[rootId] != -1)
			rootId = parent[rootId];
		return rootId;
	}
	
	public void refresh() throws InstantiationException, IllegalAccessException {
		refresh(getRootId(),0);
	}
	
	private int refresh(int id, int d) throws InstantiationException, IllegalAccessException {
		depth[id] = d;
		if(left[id] != -1) {
			degree[id] ++;
			height[id] = refresh(left[id], d+1);
		}
		if(right[id] != -1) {
			degree[id] ++;
			height[id] = Math.max(height[id], refresh(right[id], d+1));
		}
		return height[id]+1;
	}
	
	public int preOrder(int[] nodeIdList, int nodePtr, int id) {
		if(id == -1) return nodePtr;
		nodeIdList[nodePtr++] = id;
		nodePtr = preOrder(nodeIdList,nodePtr,left[id]);
		nodePtr = preOrder(nodeIdList,nodePtr,right[id]);
		return nodePtr;
	}
	
	public int inOrder(int[] nodeIdList, int nodePtr, int id) {
		if(id == -1) return nodePtr;
		nodePtr = inOrder(nodeIdList,nodePtr,left[id]);
		nodeIdList[nodePtr++] = id;
		nodePtr = inOrder(nodeIdList,nodePtr,right[id]);
		return nodePtr;
	}
	
	public int postOrder(int[] nodeIdList, int nodePtr, int id) {
		if(id == -1) return nodePtr;
		nodePtr = postOrder(nodeIdList,nodePtr,left[id]);
		nodePtr = postOrder(nodeIdList,nodePtr,right[id]);
		nodeIdList[nodePtr++] = id;
		return nodePtr;
	}

	
	public String toString() {
		StringBuilder sb = new StringBuilder();
		for(int i=0; i<maxNodes; i++) {
			sb.append("node ").append(i)
				.append(": parent = ").append(parent[i])
				.append(", sibling = ").append(sibling[i])
				.append(", degree = ").append(degree[i])
				.append(", depth = ").append(depth[i])
				.append(", height = ").append(height[i])
				.append(", ");

			if(parent[i] == -1)
				sb.append("root");
			else if(left[i] == -1 && right[i] == -1)
				sb.append("leaf");
			else 
				sb.append("internal node");
			
			sb.append(System.lineSeparator());
		}
		return sb.toString();
	}
}


class InputUtil {
	//Static Fields
	private static final int BUFSIZ = 100000;
	
	//Fields
	protected InputStream in;
	private byte[] buf = null;
	private int ptr = 0;
	private int max = -1;
	private DataInputStream dis = null;
	//Constructors
	public InputUtil() {this(System.in,BUFSIZ);}
	public InputUtil(InputStream in, int bufsiz) {
		initBuf(bufsiz);
		initIn(in);
	}
	
	//Methods
	//Initializer
	protected void initIn(InputStream in) {dis = new DataInputStream(this.in = in);}
	protected void initBuf(int bufsiz) {buf = new byte[bufsiz];}
	
	//buffer operation
	private void next() throws IOException {ptr++; readBuf();}
	private void readBuf() throws IOException {
		if(ptr >= max && dis.available()>0) {
			if(max>0) Arrays.fill(buf,0,max,(byte)0);
			max = dis.read(buf);
			ptr = 0;
		}
	}
	
	//Number Input Reader/Parser
	private boolean isNum(byte b) {return '0' <= b && b <= '9'; }
	private boolean isMinus(byte b) {return b=='-'; }

	private int _nextInt() throws IOException {
		int sign = 1;
		int res = 0;
		byte c;
		while (!isNum(c=buf[ptr]) && !isMinus(c)) 
			next();
		if (isMinus(buf[ptr])) {
			sign = -1;
			next();
		}
		while (isNum(c=buf[ptr])) {
			res *= 10;
			res += c - '0' ;
			next();
		}
		next();
		return sign * res;
	}
	
	public int nextInt() throws IOException {
		readBuf();
		return _nextInt();
	}

	public int[] nextInt(int[] result) throws IOException {
		readBuf();
		for(int i=0; i<result.length; i++) {
			result[i] = _nextInt();
		}
		return result;
	}
	
	//Close 
	public void close() throws IOException {
		if(!this.in.equals(System.in)) 
			this.in.close();
	}

}