I found an implementation of the Morris tree traversal,
It works fine,,, but having a bit of a problem trying
to traverse the tree in reverse order.. -
void MorrisTraversal(struct Node *root)
{
struct Node *p,*pre;
if(root==0) { return; }
for(p=root;p!=0;)
{
if(p->Left==0) { printf(" %d ",p->Data); p=p->Right; continue; }
for(pre=p->Left;pre->Right!=0 && pre->Right!=p;pre=pre->Right) { }
if(pre->Right==0)
{ pre->Right=p; p=p->Left; continue; }
else
{ pre->Right=0; printf(" %d ",p->Data); p=p->Right; continue; }
}
}
By reverse order, I'm assuming you mean reverse inorder traversal. You have at least two options:
You could modify the code and swap all the ->Right pointer references with ->Left ones.
You could replace the two printf statements with pushes onto a stack. Once the algorithm completes, you would then pop off the data from the stack to print them. This however defeats the whole purpose of the Morris traversal algorithm, which was to be stackless.
This related SO thread might help you understanding.
I hope this helps.
Here is one sample in Java. Click Here for one more sample using iteration instead of recursion.
public int depthOfTree(TreeNode node){
if(node == null){
return 0;
}
int leftDepth = depthOfTree(node.left);
int rightDepth = depthOfTree(node.right);
if(leftDepth > rightDepth){
return leftDepth+1;
} else {
return rightDepth+1;
}
}
//Reverse Level with recursion
public void reverseLevelOrder(TreeNode node){
int depth = depthOfTree(node);
for(int i=depth;i>0;i--){
printTree(node,i);
}
}
public void printTree(TreeNode node, int level){
if(node == null){
return;
}
if(level == 1){
System.out.print(node.data+" ,");
} else if(level>1){
printTree(node.left, level-1);
printTree(node.right, level-1);
}
}
Related
I am very new to binary tree and recursion. My program is to find the height of the tree but I am a bit confused as to why my program doesn't work.
struct Node {
int value;
Node *left;
Node *right;
}
int heightOfTree(Node node){
if(node ==NULL)
{
return 0;
}
else
{
int lheight=heightOfTree(node->left);
int rheight = heightOfTree(node->right);
if(lheight>rheight)
{
return lheight;
}
else
{
return rheight;
}
}
}
I followed a pseudocode online so I implemented it myself because I don't want to just copy and paste. I tried to insert a lot of nodes but When I run my program I always get 0 height? Thank you
return lheight + 1;
and
return rheight + 1;
You need to increment the height at each level.
The right pointer can be made to point to the right sibling by performing a level order traversal and changing accordingly. However, i don't know the procedure to do this simultaneously. Any suggestions?
Just do a BFS and remember the level and parent. The following a c++ code for that
void BSTRightSibling(BSTNode *root)
{
queue<BSTNode*> q;
map<BSTNode*, BSTNode*> m;
BSTNode* levelNode = root;
q.push(root);
while(! q.empty()) {
BSTNode* n = q.front();
if (n->left) {
q.push(n->left);
m[n->left] = n;
if (n == levelNode) {
levelNode = n->left;
}
}
if (n->right) {
q.push(n.right);
m[n->right] = n;
if (n == levelNode) {
levelNode = n->right;
}
}
q.pop();
if ((!q.empty()) && (n != levelNode)) {
n->right = q.front();
} else {
n->right = NULL;
}
n->left = m[n];
}
}
In tournament problem you can use a gray-code to decide when its a left or right node. Another method is also if the value is less or equal then the parent value then its a right node.
I need to implement a non-recursive function to determine if a binary tree is balanced or not.
Anyone?
Thanks!!!
Assuming that by "balanced", you mean "height-balanced" in the AVL-tree sense, and you can store arbitrary information for each node,
For each node in post-order,
if either child doesn't exist, assume its respective height is 0.
if the height of both children differs by more than one, the tree is not balanced.
otherwise, this node's height is the larger of both children's heights.
If this point is reached, the tree is balanced.
One way to perform post-order traversal:
start at the root
loop
if this node's left child exists and does not have its height computed, visit its left child next.
else if this node's right child exists and does not have its height computed, visit its right child next.
else
compute this node's height, possibly returning early
if this node is not the root, visit its parent next.
If this point is reached, the tree is balanced.
Try this,
public class BalancedBinaryTree {
public static class TreeNode {
int val;
TreeNode left;
TreeNode right;
TreeNode() {}
TreeNode(int val) { this.val = val; }
TreeNode(int val, TreeNode left, TreeNode right) {
this.val = val;
this.left = left;
this.right = right;
}
}
public boolean isBalanced(TreeNode root) {
if (root==null) {
return true;
}
Stack<TreeNode> stack = new Stack<>();
Map<TreeNode, Integer> map = new HashMap<>();
stack.push(root);
while(!stack.isEmpty()) {
TreeNode node = stack.pop();
if ((node.left==null || (node.left!=null && map.containsKey(node.left))) && (node.right==null || (node.right!=null && map.containsKey(node.right)))) {
int right = (node.right==null) ? 0 : map.get(node.right);
int left = (node.left==null) ? 0 : map.get(node.left);
if (Math.abs(right-left)>1) {
return false;
} else {
map.put(node, Math.max(right, left)+1);
}
} else {
if (node.left!=null && !map.containsKey(node.left)) {
stack.push(node);
stack.push(node.left);
} else {
stack.push(node);
stack.push(node.right);
}
}
}
return true;
}
public static void main(String[] args) {
BalancedBinaryTree b = new BalancedBinaryTree();
boolean v = b.isBalanced(new TreeNode(3, new TreeNode(9), new TreeNode(20, new TreeNode(15), new TreeNode(7))));
System.out.println(v);
v = b.isBalanced(new TreeNode(1, new TreeNode(2, new TreeNode(3, new TreeNode(4), new TreeNode(4)), new TreeNode(3)), new TreeNode(2)));
System.out.println(v);
v = b.isBalanced(new TreeNode(1, new TreeNode(2, new TreeNode(4, new TreeNode(8), null), new TreeNode(5)), new TreeNode(3, new TreeNode(6), null)));
System.out.println(v);
}
}
Here is a c++ code that works, inspired by the postorder traversal. The code is not commented because i do not think a simple comment is enough to explain the whole algorithm. You can execute this code manually with the example below and then you will understand everything.
bool IsBalance(const Node *head)
{
std::stack<const Node *> s;
std::stack<int> sV;
const Node *curr = head, *lastVisit = nullptr;
int deep = 0;
while (curr || !s.empty())
{
while (curr)
{
s.push(curr);
sV.push(-1);
curr = curr->m_pLeft;
}
curr = s.top();
if (sV.top() == -1)
{
sV.top() = deep;
}
if (!curr->m_pRight || curr->m_pRight == lastVisit)
{
if (!curr->m_pRight)
{
deep = 0;
}
if (std::abs(sV.top() - deep) > 1)
{
return false;
}
deep = std::max(sV.top(), deep) + 1;
lastVisit = curr;
s.pop();
sV.pop();
curr = nullptr;
}
else
{
deep = 0;
curr = curr->m_pRight;
}
}
return true;
}
examples:
(1) 21,10,3,1,#,#,5,#,6,#,#,15,12,#,#,18,16,#,#,20,#,#,35,30,22,#,#,#,40,36,#,#,42,#,45,#,#
(2) 1,2,#,4,#,5,#,#,3,6,8,#,#,#,7,#,#
(3) 3,1,#,2,#,#,#
Where nodes are arranged by PreOrder, separated by commas, and # indicates an empty node.
Find the height of left subtree and right subtree for a node of the tree, using Level order traversal and check if that node is balanced.
Repeat this for every node of the tree. For traversing all the nodes we can use level order traversal to avoid recursion.
int height(TreeNode* root){
if(!root){
return 0;
}
queue<TreeNode*> q;
q.push(root);
int count=0;
while(!q.empty()){
int size=q.size();
for(int i=0;i<size;++i){
TreeNode* temp=q.front();
q.pop();
if(temp->left){
q.push(temp->left);
}
if(temp->right){
q.push(temp->right);
}
}
count++;
}
return count;
}
bool checkEveryNode(TreeNode* root){
if(!root){
return true;
}
queue<TreeNode*> q;
q.push(root);
while(!q.empty()){
int count=q.size();
for(int i=0;i<count;++i){
TreeNode* temp=q.front();
q.pop();
int left=height(temp->left);
int right=height(temp->right);
if(abs(left-right)>1){
return false;
}
if(temp->left){
q.push(temp->left);
}
if(temp->right){
q.push(temp->right);
}
}
}
return true;
}
bool isBalanced(TreeNode* root) {
return checkEveryNode(root);
}
Time complexity of this approach is O(n^2), as we need to traverse all the descendant nodes for finding the height of a node(N) and we need to do this for all the nodes(N)
I was reading through Introduction to algorithms i came across this problem about In-order Traversal of binary search tree without using a stack or recursion. Hint says to assume that testing of pointers for equality is a legitimate operation.I'm stuck finding the solution to this problem. Please give me some direction. I'm not looking for the code. Just give me the right direction.
Exact duplicate here
No stack nor recursion means you have to use pointers. Not giving you code nor the exact answer, since you asked not to :)
Think about how to explore the tree without using recursion: what would you need to do? What pointer(s) do you need to keep? Can a tree node have a pointer to the parent?
Hope it helps.
We need a Threaded Binary Tree to do in-order Traversal without recursion / stack.
Wiki says 'A binary tree is threaded by making all right child pointers that would normally be null point to the inorder successor of the node, and all left child pointers that would normally be null point to the inorder predecessor of the node'
So you are given a normal Binary Tree , Convert it into a Threaded Binary Tree which can be done using Morris Traversal.
What you are going to do in Morris Traversal is to connect each node with its in-order successor. So while visiting a node ,Search for its in-order predecessor and let it be Pred.
then make Pred->right=Current node and we have to revert back the changes too. You can better refer this http://www.geeksforgeeks.org/archives/6358 for a great explanation.
Hello Parminder i have implemented your question in java.Please check it once
class InorderWithoutRecursion {
public static void morrisTraversal(TreeNode root) {
TreeNode current,pre;
if(root == null)
return;
current = root;
while(current != null){
if(current.left == null){
System.out.println(current.data);
current = current.right;
}
else {
/* Find the inorder predecessor of current */
pre = current.left;
while(pre.right != null && pre.right != current)
pre = pre.right;
/* Make current as right child of its inorder predecessor */
if(pre.right == null){
pre.right = current;
current = current.left;
}
/* Revert the changes made in if part to restore the original
tree i.e., fix the right child of predecssor */
else {
pre.right = null;
System.out.println(current.data);
current = current.right;
}
}
}
}
public static void main(String[] args) {
int[] nodes_flattened = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
TreeNode root = TreeNode.createMinimalBST(nodes_flattened);
morrisTraversal(root);
}
}
For TreeNode class below code will help you..
public class TreeNode {
public int data;
public TreeNode left;
public TreeNode right;
public TreeNode parent;
public TreeNode(int d) {
data = d;
}
public void setLeftChild(TreeNode left) {
this.left = left;
if (left != null) {
left.parent = this;
}
}
public void setRightChild(TreeNode right) {
this.right = right;
if (right != null) {
right.parent = this;
}
}
public void insertInOrder(int d) {
if (d <= data) {
if (left == null) {
setLeftChild(new TreeNode(d));
} else {
left.insertInOrder(d);
}
} else {
if (right == null) {
setRightChild(new TreeNode(d));
} else {
right.insertInOrder(d);
}
}
}
public boolean isBST() {
if (left != null) {
if (data < left.data || !left.isBST()) {
return false;
}
}
if (right != null) {
if (data >= right.data || !right.isBST()) {
return false;
}
}
return true;
}
public int height() {
int leftHeight = left != null ? left.height() : 0;
int rightHeight = right != null ? right.height() : 0;
return 1 + Math.max(leftHeight, rightHeight);
}
public TreeNode find(int d) {
if (d == data) {
return this;
} else if (d <= data) {
return left != null ? left.find(d) : null;
} else if (d > data) {
return right != null ? right.find(d) : null;
}
return null;
}
private static TreeNode createMinimalBST(int arr[], int start, int end){
if (end < start) {
return null;
}
int mid = (start + end) / 2;
TreeNode n = new TreeNode(arr[mid]);
n.setLeftChild(createMinimalBST(arr, start, mid - 1));
n.setRightChild(createMinimalBST(arr, mid + 1, end));
return n;
}
public static TreeNode createMinimalBST(int array[]) {
return createMinimalBST(array, 0, array.length - 1);
}
}
This is an Amazon interview question. Can any one give an algorithm to do this?
There is a binary tree with the following properties:
All of its inner node have the value 'N', and all the leaves have the value 'L'.
Every node either has two children or has no child.
Given its preorder, construct the tree and return the root node.
Since it is guaranteed that each internal node has exactly 2 children, we can simply build the tree recursively using that.
We call our function with the input provided, and it examines the first character it got. If it is a leaf node, it just returns a leaf. If it is an internal node, it just calls itself for the left and right subtrees and returns the tree formed using the node as root and the left and right subtrees as its left and right children.
Code follows (in Python). Note, I am using tuples to represent node, so the tree is a tuple of tuples.
#! /usr/bin/env python
from collections import deque
def build_tree(pre_order):
root=pre_order.popleft()
if root=='L':
return root
else:
return (root,build_tree(pre_order),build_tree(pre_order))
if __name__=='__main__':
print build_tree(deque("NNLLL"))
Edit: Code in Java
import java.util.*;
class Preorder{
public static Node buildTree(List<Character> preorder){
char token=preorder.remove(0);
if (token=='L'){
return new Node(token,null,null);
}
else{
return new Node(token,buildTree(preorder),buildTree(preorder));
}
}
public static void main(String args[]){
List<Character> tokens=new LinkedList<Character>();
String input="NNLLL";
for(int i=0;i<input.length();i++) tokens.add(input.charAt(i));
System.out.println(buildTree(tokens));
}
}
class Node{
char value;
Node left,right;
public Node(char value, Node left, Node right){
this.value=value;
this.left=left;
this.right=right;
}
public String toString(){
if (left==null && right==null){
return "("+value+")";
}
else{
return "("+value+", "+left+", "+right+")";
}
}
}
I can think of a recursive algorithm.
head = new node.
remove first character in preorderString
Invoke f(head, preorderString)
Recursive function f(node, s)
- remove first char from s, if L then attach to node as leaf.
else create a nodeLeft, attach to node, invoke f(nodeLeft, s)
- remove first char from s, if L then attach to node as leaf.
else create a nodeRight, attach to node, invoke f(nodeRight, s)
I think the key point is to realize that there are three possibilities for the adjacent nodes: NN, NL?, L? (``?'' means either N or L)
NN: the second N is the left child of the first N, but we don't know what the right child of the first N is
NL?: the second N is the left child of the first N, and the right child of the first N is ?
L?: ? is the right child of STACK top
A STACK is used because when we read a node in a preorder sequence, we don't know where its right child is (we do know where its left child is, as long as it has one). A STACK stores this node so that when its right child appears we can pop it up and finish its right link.
NODE * preorder2tree(void)
{
NODE * head = next_node();
NODE * p = head;
NODE * q;
while (1) {
q = next_node();
if (!q)
break;
/* possibilities of adjacent nodes:
* NN, NL?, L?
*/
if (p->val == 'N') {
p->L = q;
if (q->val == 'N') { /* NN */
push(p);
p = q;
} else { /* NL? */
q = next_node();
p->R = q;
p = q;
}
} else { /* L? */
p = pop();
p->R = q;
p = q;
}
}
return head;
}
The code above was tested using some simple cases. Hopefully it's correct.
Here is the java program::
import java.util.*;
class preorder_given_NNNLL
{
static Stack<node> stk = new Stack<node>();
static node root=null;
static class node
{
char value;
node left;
node right;
public node(char value)
{
this.value=value;
this.left=null;
this.right=null;
}
}
public static node stkoper()
{
node posr=null,posn=null,posl=null;
posr=stk.pop();
if(stk.empty())
{
stk.push(posr);
return null;
}
else
posl=stk.pop();
if(stk.empty())
{
stk.push(posl);
stk.push(posr);
return null;
}
else
{
posn=stk.pop();
}
if( posn.value == 'N' && posl.value == 'L' && posr.value == 'L')
{
root = buildtree(posn, posl, posr);
if(stk.empty())
{
return root;
}
else
{
stk.push(root);
root=stkoper();
}
}
else
{
stk.push(posn);
stk.push(posl);
stk.push(posr);
}
return root;
}
public static node buildtree(node posn,node posl,node posr)
{
posn.left=posl;
posn.right=posr;
posn.value='L';
return posn;
}
public static void inorder(node root)
{
if(root!=null)
{
inorder(root.left);
if((root.left == null) && (root.right == null))
System.out.println("L");
else
System.out.println("N");
inorder(root.right);
}
}
public static void main(String args[]){
String input="NNNLLLNLL";
char[] pre = input.toCharArray();
for (int i = 0; i < pre.length; i++)
{
node temp = new node(pre[i]);
stk.push(temp);
root=stkoper();
}
inorder(root);
}
}
The construct function does the actual tree construction. The code snippet is the solution for the GeeksforGeeks question that you mentioned as above.
struct Node*construct(int &index, Node*root, int pre[], int n, char preLN[])
{
Node*nodeptr;
if(index==n)
{
return NULL;
}
if(root==NULL)
{
nodeptr = newNode(pre[index]);
}
if(preLN[index]=='N')
{
index = index+1;
nodeptr->left = construct(index, nodeptr->left, pre,n,preLN);
index = index+1;
nodeptr->right = construct(index, nodeptr->right,pre,n,preLN);
return nodeptr;
}
return nodeptr;
}
struct Node *constructTree(int n, int pre[], char preLN[])
{
int index =0;
Node*root = construct(index,NULL,pre,n,preLN);
return root;
}
Points to Note:
Index has been declared a reference variable so that on returning back to the parent node, the function starts constructing the tree from the overall most recent value of index and not the value of index as possessed by the function when initially executing the call.
Different values of index for right and left subtrees since preorder traversal follows Root, Left ,Right sequence of nodes.
Hope it Helps.