How to find largest common subtrees in a multi tree - java

Recently, I encounter a algorithm problem: the tree is defined as
public class Node
{
int id;
private final List<Node> children;
Node(int id) {
this.id = id;
this.children = new ArrayList<>();
}
}
Two subtrees are in common if their structure is identical. The largest common subtrees maximizes the number of nodes in each individual subtrees. So how to find the maxmum common subtree(the id of each node does not matter, just the structure of the subtrees be the same). If there are separate groups of subtrees that are in common with the same maximal size, then we should should return the root nodes from all of the subtrees.
My idea is to serialize each subtree into unique string using BFS. After we get all strings, sort them, and compare which two are equal. So below is my code. My question is because the serialization each subtree cause much overhead, is there any other idea to solve this problem in a better time complexity.
public static List<Node> getLargestCommonSubtrees(Node root) {
HashMap<String, ArrayList<Node>> map = new HashMap<String, ArrayList<Node>>();
LinkedList<Node> queue = new LinkedList<Node>();
queue.add(root);
while (!queue.isEmpty()) {
Node cur = queue.pollFirst();
String sig = serialize(cur);
if (map.containsKey(sig)) {
ArrayList<Node> list = map.get(sig);
list.add(cur);
map.put(sig, list);
} else {
ArrayList<Node> list = new ArrayList<Node>();
list.add(cur);
map.put(sig, list);
}
for (int i = 0; i < cur.children.size(); i++) {
if (cur.children.get(i) != null) {
queue.add(cur.children.get(i));
}
}
}
int max = Integer.MIN_VALUE;
ArrayList<Node> ans = new ArrayList<Node>();
for (Entry<String, ArrayList<Node>> e : map.entrySet()) {
if (e.getKey().length() >= max) {
if (e.getKey().length() > max) {
ans.clear();
}
ans.addAll(e.getValue());
}
}
return ans;
}
private static String serialize(Node n) {
String signature = "";
LinkedList<Node> q = new LinkedList<Node>();
q.add(n);
if (n.children.size() == 0) {
signature = "0";
return signature;
}
Node curr = null;
while (!q.isEmpty()) {
curr = q.peek();
q.poll();
signature += String.valueOf(curr.children.size());
for (int i = 0; i < curr.children.size(); i++) {
q.offer(curr.children.get(i));
}
}
return signature;
}

JoJo, there might already exist an efficient algorithm out there for this or a similar problem. However, here is how I would do it.
import java.util.ArrayList;
import java.util.List;
public class Node
{
//signature = number of Node's children + signature of each child = total number of all nodes below this Node (including children and children's children...etc)
//
// for example, a tree would have it's signature as
// 13
// 1 5 4
// 0 1 2 1 1
// 0 0 0 0 0
//
private int signature;
private int id;
private final List<Node> children;
private Node parent;
public Node(int id, Node parent) {
this.id = id;
this.children = new ArrayList<Node>();
this.parent = parent;
}
//updates signature, should be called every time there is a change to Node.
private void updateSignature() {
signature = children.size();
for(Node childNode : children) {
signature += childNode.signature;
}
//tell parent to update it's signature
if(parent != null) {
parent.updateSignature();
}
}
//compares two trees to check if their structure is similar
private boolean hasSameStructureAs(Node otherNode) {
return otherNode != null && signature == otherNode.signature;
}
}

Related

Is depth between any two leaf node in binary tree greater than one

I've been working on this coding problem and have been able to successfully get the depth of each leaf node into a hash set. What I'm trying to do is determine if the difference in depth is of a leaf node is greater than one BEFORE that depth is added to the hash set. I don't want to put all of the leaf nodes in the hash set and use two for loops to check if there is a difference in depth greater than one. In my code below, the int variable count represents depth.
The problem is my code always returns true. Something is wrong with the code where is checks the difference in depths/count for each leaf node. Code is below. I'm trying to keep this method in O(n) time, and avoid O(n^2).
The depths of the four leaf nodes in this tree are : 3, 2, 2, 5
import java.util.*;
public class cakeEightWeekly {
static int count = 0;
public static class Node {
public int value;
public Node leftChild;
public Node rightChild;
public Node(int value) {
this.value = value;
}
public void setLeft(Node leftValue) {
this.leftChild = leftValue;
}
public void setRight(Node rightValue) {
this.rightChild = rightValue;
}
public Node getRight() {
return rightChild;
}
public Node getLeft() {
return leftChild;
}
}
public static boolean isBalanced(Node root) {
HashSet < Integer > hset = new HashSet < Integer > ();
if (root != null) {
count++;
isBalanced(root.getLeft());
isBalanced(root.getRight());
count--;
if (root.getLeft() == null && root.getRight() == null) {
if (!hset.isEmpty()) {
for (int x: hset) {
if ((x - count) < 0) {
int sum = count - x;
if (sum > 1) {
return false;
}
} else if ((x - count) > 1) {
return false;
}
}
hset.add(count);
} else {
hset.add(count);
}
}
}
return true;
}
public static void main(String[] args) {
Node One = new Node(1);
Node Two = new Node(2);
Node Three = new Node(3);
Node Four = new Node(4);
Node Five = new Node(5);
Node Six = new Node(6);
Node Seven = new Node(7);
Node Eight = new Node(8);
Node Nine = new Node(9);
Node Ten = new Node(10);
Node Eleven = new Node(11);
Five.setLeft(Three);
Five.setRight(Seven);
Three.setLeft(Two);
Three.setRight(Four);
Two.setLeft(One);
Seven.setLeft(Six);
Seven.setRight(Eight);
Eight.setRight(Nine);
Nine.setRight(Ten);
Ten.setRight(Eleven);
System.out.print(isBalanced(Five));
}
}

Find number of unique routes to specific node using Depth First Search

I have a directed graph with vertexes 123456. Using a depth first search, if I wanted to be able to find the number of unique routes from 1-4 (for example), how would I go about doing it? Here is my current DFS.
private final Map<Character, Node> mNodes;
private final List<Edge> mEdges;
private List<Node> mVisited = new ArrayList<>();
int weight;
int numberOfPaths;
public DepthFirstSearch(Graph graph){
mNodes = graph.getNodes();
mEdges = new ArrayList<>(graph.getEdges());
for(Node node : mNodes.values()){
node.setVisited(false);
}
}
public void depthFirstSearch(Node source){
source.setVisited(true);
List<Edge> neighbours = source.getNeighbouringEdges(mEdges);
for(Edge edge : neighbours){
System.out.println(edge.getFrom().getName()+"-"+edge.getTo().getName());
if(!edge.getTo().isVisited()){
mVisited.add(edge.getTo());
weight += edge.getWeight();
depthFirstSearch(edge.getTo());
}
}
}
Since cycles aren't allowed, you have actually a DAG (directed acyclid graph).
These are some questions related to this topic:
Number of paths between two nodes in a DAG
Topological sort to find the number of paths to t
Basically, the idea is get a topological sort of the DAG, then iterate the nodes starting from the destination node backwards to the source node, calculating how many paths are from that node.
Since the array haven't cycles and the nodes are topological sorted, when you visit a node, all nodes that can be reached from that node appears latter in the sort and are already visited. So, the count of paths from an node to the target is the sum of the counts of the nodes that are adjacent to it.
Models:
class Graph
{
private List<Node> nodes;
private List<Edge> edges;
public Graph() {
nodes = new ArrayList<>();
edges = new ArrayList<>();
}
public List<Node> getNodes() { return nodes; }
public List<Edge> getEdges() { return edges; }
public void addNode(Node node) { nodes.add(node); }
public void addEdge(Edge edge) {
edges.add(edge);
edge.getFrom().addEdge(edge);
edge.getTo().addEdge(edge);
}
}
class Node
{
private List<Edge> outgoings, incomings;
public Node() {
outgoings = new ArrayList<>();
incomings = new ArrayList<>();
}
public List<Edge> getOutgoings() { return outgoings; }
public List<Edge> getIncomings() { return incomings; }
public void addEdge(Edge edge) {
if (edge.getFrom() == this) outgoings.add(edge);
if (edge.getTo() == this) incomings.add(edge);
}
}
class Edge
{
private Node from, to;
public Edge(Node from, Node to) {
this.from = from;
this.to = to;
}
public Node getFrom() { return from; }
public Node getTo() { return to; }
}
Algorithm:
static int countPaths(Graph graph, Node source, Node target)
{
List<Node> nodes = topologicalSort(graph);
int[] counts = new int[nodes.size()];
int srcIndex = nodes.indexOf(source);
int tgtIndex = nodes.indexOf(target);
counts[tgtIndex] = 1;
for (int i = tgtIndex; i >= srcIndex; i--) {
for (Edge edge : nodes.get(i).getOutgoings())
counts[i] += counts[nodes.indexOf(edge.getTo())];
}
return counts[srcIndex];
}
static List<Node> topologicalSort(Graph g)
{
List<Node> result = new ArrayList<>();
Set<Node> visited = new HashSet<>();
Set<Node> expanded = new HashSet<>();
for (Node node: g.getNodes())
explore(node, g, result, visited, expanded);
return result;
}
static void explore(Node node, Graph g, List<Node> ordering, Set<Node> visited, Set<Node> expanded) {
if (visited.contains(node)) {
if (expanded.contains(node)) return;
throw new IllegalArgumentException("Graph contains a cycle.");
}
visited.add(node);
for (Edge edge: node.getIncomings())
explore(edge.getFrom(), g, ordering, visited, expanded);
ordering.add(node);
expanded.add(node);
}
Usage:
Graph g = new Graph();
Node a = new Node();
Node b = new Node();
Node c = new Node();
Node d = new Node();
Node e = new Node();
Edge ab = new Edge(a, b);
Edge bc = new Edge(b, c);
Edge cd = new Edge(c, d);
Edge ad = new Edge(a, d);
Edge ae = new Edge(a, e);
Edge ed = new Edge(e, d);
Edge be = new Edge(b, e);
Edge ec = new Edge(e, c);
g.addNode(a);
g.addNode(b);
g.addNode(c);
g.addNode(d);
g.addNode(e);
g.addEdge(ab);
g.addEdge(bc);
g.addEdge(cd);
g.addEdge(ad);
g.addEdge(ae);
g.addEdge(ed);
g.addEdge(be);
g.addEdge(ec);
int count = countPaths(g, a, d);
//count: 6
// Paths:
//1. A->B->C->D
//2. A->D
//3. A->E->D
//4. A->B->E->C->D
//5. A->B->E->D
//6. A->E->C->D
But, if you want to do it using a BFS, you can try doing a backtrack resetting the visited nodes:
static int countPaths(Graph graph, Node source, Node target)
{
Set<Node> visiteds = new HashSet<>();
return BFS(source, target, visiteds);
}
static int BFS(Node current, Node target, Set<Node> visiteds) {
if (current == target) return 1;
else
{
int count = 0;
visiteds.add(current);
for (Edge edge : current.getOutgoings())
if (!visiteds.contains(edge.getTo()))
count += BFS(edge.getTo(), target, visiteds);
visiteds.remove(current);
return count;
}
}
However, to increase the performance, you can implement some kind of memoization:
static int countPaths(Graph graph, Node source, Node target)
{
Set<Node> visiteds = new HashSet<>();
Map<Node, Integer> memoize = new HashMap<>();
for (Node node : graph.getNodes())
memoize.put(node, -1);
memoize.put(target, 1);
return BFS(source, visiteds, memoize);
}
static int BFS(Node current, Set<Node> visiteds, Map<Node, Integer> memoize) {
if (memoize.get(current) != -1) return memoize.get(current);
else
{
int count = 0;
visiteds.add(current);
for (Edge edge : current.getOutgoings())
if (!visiteds.contains(edge.getTo()))
count += BFS(edge.getTo(), visiteds, memoize);
visiteds.remove(current);
memoize.put(current, count);
return count;
}
}
(Assuming directed acyclic graph)
All you need to do is to run your DFS and count every discovered route which leads to the destination node.
The mistake in your code is that your setVisited() and isVisited() state is global. This means that whenever you encounter node C you mark it as visited and it stays marked so for the whole DFS run -- even for paths where it actually has not been visited yet.
An example DFS run (given simple graph A -> B, B -> C, A -> C):
(Step 1 -- path A) Visit A, mark A visited
(Step 1.1 -- path A -> B) Visit B, mark B visited
(Step 1.1.1 -- path A -> B -> C) Visit C, mark C visited
(Step 1.2 -- path A -> C) Here you skip this route as C is marked as visited from step 1.1.1 (which is wrong)
You need to trace visited nodes correctly by e.g.:
trust the caller that the input graph really is acyclic and do not trace visited nodes at all (as there is no way to visit a single node twice in an acyclic graph). You risk that your program enter infinite recursion for wrong input
use simpler/cheaper cycle detection. You can trace the depth of recursion and when it gets deeper than the total number of nodes in the graph raise an exception
reset the node visited state right after the visit (this is what #Arturo Menchaca suggests in his great answer)
keep a separate visited state for each route being processed
Example java code which traces visited nodes in a list (this way you can print the discovered routes):
package test.java.so;
import java.util.ArrayList;
import java.util.List;
import java.util.Map;
import java.util.TreeMap;
public class So37503760 {
public static class Graph {
private final Map<Character, Node> nodes = new TreeMap<Character, Node>();
public Node addNode(char c) {
Node existingNode = nodes.get(c);
if(existingNode!=null) {
return existingNode;
}
Node newNode = new Node(c);
nodes.put(c, newNode);
return newNode;
}
public void addEdge(char f, char t) {
addNode(f).addChild(addNode(t));
}
public Node getNode(char name) {
Node ret = nodes.get(name);
if(ret==null) {
throw new RuntimeException("No such node " + name);
}
return ret;
}
}
public static class Node {
private final char name;
private final ArrayList<Node> children = new ArrayList<Node>();
public Node(char c) {
this.name=c;
}
public void addChild(Node childNode) {
children.add(childNode);
}
public ArrayList<Node> getChildren() {
return children;
}
public char getName() {
return name;
}
}
public static void main(String[] args) {
Graph graph = new Graph();
graph.addEdge('A', 'B');
graph.addEdge('A', 'C');
graph.addEdge('B', 'C');
graph.addEdge('C', 'D');
graph.addEdge('C', 'E');
graph.addEdge('D', 'E');
int numberOfPaths = depthFirstSearch(graph, 'A', 'E');
System.out.println("Found " + numberOfPaths + " paths");
}
public static int depthFirstSearch(Graph graph, char startNode, char destinationNode){
return depthFirstSearch(graph, graph.getNode(startNode), graph.getNode(destinationNode), new ArrayList<Node>());
}
public static int depthFirstSearch(Graph graph, Node startNode, Node destinationNode, List<Node> currentPath){
if(currentPath.contains(startNode)) {
currentPath.add(startNode);
throw new RuntimeException("Cycle detected: " + pathToString(currentPath));
}
currentPath.add(startNode);
try {
// System.out.println("Progress: " + pathToString(currentPath));
if(startNode==destinationNode) {
System.out.println("Found path: " + pathToString(currentPath));
return 1;
}
int ret=0;
for(Node nextNode : startNode.getChildren()){
ret += depthFirstSearch(graph, nextNode, destinationNode, currentPath);
}
return ret;
} finally {
currentPath.remove(currentPath.size()-1);
}
}
private static String pathToString(List<Node> path) {
StringBuilder b = new StringBuilder();
boolean printArrow=false;
for(Node n : path) {
if(printArrow) {
b.append(" -> ");
}
b.append(n.getName());
printArrow=true;
}
return b.toString();
}
}
It really depends on the edges of your graph. If all of your vertices are connected to one another it would be very simple because you'd get the same number of paths every time (1->4, 1->2->4, 1->3->4, 1->5->4,...,1->6->5->3->2->4 [going with the paths from 1 to 4 example). It would look very similar given any n->m path (given the fact that you want no cycles), and there would be the same number of paths each time.
However, if there are any vertices that aren't connected to other vertices, that's where it would get interesting. You'd probably want to use a modified Djikstra's algorithm that would then give you the different answers (I'm kind of guessing you're looking for) for number of unique paths.

Finding maximum depth of a tree

I know how to find the depth of a binary tree. But I cannot generalize it to work for any tree.
Can someone please outline a pseudo code for finding the depth of a tree (not necessarily a binary tree).
int findDepthOfTree(tree):
int deepest = 0;
for (child of root node)
deepest = max(deepest, findDepthOfTree(child))
return deepest + 1
Java implementation to find depth of a k-ary tree:
static int findDepth(Node root) {
int deepest = 0;
if (root.children != null) {
for (Node child : root.children) {
deepest = Math.max(deepest, findDepth(child));
}
}
return deepest+1;
}
This assumes the following Node class is implemented to hava a data element as well as a reference to the list of nodes representing its children. Would be something like this:
class Node {
int data;
List<Node> children;
public Node (int data, List<Node> children) {
this.data = data;
this.children = children;
}
public Node (int data) {
this.data = data;
this.children = null;
}
}
public static int GetMaxDepth(MyTree node)
{
List<int> result = new List<int>();
foreach (var childNode in node.Items)
{
result.Add(GetMaxDepth(childNode));
}
return (result.Any() ? result.Max(n => n) : 0) + 1;
}
Recursive StreamAPI solution: O(n)
int calculateMaxDepth(Node node) {
if (node == null)
return 0;
var localDepth = node.children
.stream()
.map(NodeService::calculateMaxDepth)
.max(Comparator.naturalOrder())
.orElse(0); // if root has no children -> return 0
return ++localDepth;
}
Iterative Queue solution: O(n)
int calculateMaxDepth(Node rootNode) {
if (rootNode == null) return 0;
int height = 0;
// level representing queue
Queue<Node> nodesQueue = new LinkedList<>();
nodesQueue.add(rootNode);
while (true) {
// amount of nodes on level
int nodesCount = nodesQueue.size();
if (nodesCount == 0) return height;
++height;
// deque all nodes of current level and
// enqueue all nodes of next level
while (nodesCount > 0) {
var currentLevelNode = nodesQueue.remove();
var validChildrenNodes = currentLevelNode.children
.parallelStream()
.filter(Objects::nonNull)
.collect(Collectors.toList());
nodesQueue.addAll(validChildrenNodes);
--nodesCount;
}
}
}
For additional info you can visit:
https://www.geeksforgeeks.org/write-a-c-program-to-find-the-maximum-depth-or-height-of-a-tree/
https://www.geeksforgeeks.org/iterative-method-to-find-height-of-binary-tree/

Lowest Common Ancestor of a Binary Tree

This is a popular interview question and the only article I can find on the topic is one from TopCoder. Unfortunately for me, it looks overly complicated from an interview answer's perspective.
Isn't there a simpler way of doing this other than plotting the path to both nodes and deducing the ancestor? (This is a popular answer, but there's a variation of the interview question asking for a constant space answer).
A simplistic (but much less involved version) could simply be (.NET guy here Java a bit rusty, so please excuse the syntax, but I think you won't have to adjust too much). This is what I threw together.
class Program
{
static void Main(string[] args)
{
Node node1 = new Node { Number = 1 };
Node node2 = new Node { Number = 2, Parent = node1 };
Node node3 = new Node { Number = 3, Parent = node1 };
Node node4 = new Node { Number = 4, Parent = node1 };
Node node5 = new Node { Number = 5, Parent = node3 };
Node node6 = new Node { Number = 6, Parent = node3 };
Node node7 = new Node { Number = 7, Parent = node3 };
Node node8 = new Node { Number = 8, Parent = node6 };
Node node9 = new Node { Number = 9, Parent = node6 };
Node node10 = new Node { Number = 10, Parent = node7 };
Node node11 = new Node { Number = 11, Parent = node7 };
Node node12 = new Node { Number = 12, Parent = node10 };
Node node13 = new Node { Number = 13, Parent = node10 };
Node commonAncestor = FindLowestCommonAncestor(node9, node12);
Console.WriteLine(commonAncestor.Number);
Console.ReadLine();
}
public class Node
{
public int Number { get; set; }
public Node Parent { get; set; }
public int CalculateNodeHeight()
{
return CalculateNodeHeight(this);
}
private int CalculateNodeHeight(Node node)
{
if (node.Parent == null)
{
return 1;
}
return CalculateNodeHeight(node.Parent) + 1;
}
}
public static Node FindLowestCommonAncestor(Node node1, Node node2)
{
int nodeLevel1 = node1.CalculateNodeHeight();
int nodeLevel2 = node2.CalculateNodeHeight();
while (nodeLevel1 > 0 && nodeLevel2 > 0)
{
if (nodeLevel1 > nodeLevel2)
{
node1 = node1.Parent;
nodeLevel1--;
}
else if (nodeLevel2 > nodeLevel1)
{
node2 = node2.Parent;
nodeLevel2--;
}
else
{
if (node1 == node2)
{
return node1;
}
node1 = node1.Parent;
node2 = node2.Parent;
nodeLevel1--;
nodeLevel2--;
}
}
return null;
}
}
Constant space answer: (although not necessarily efficient).
Have a function findItemInPath(int index, int searchId, Node root)
then iterate from 0 .. depth of tree, finding the 0-th item, 1-th item etc. in both search paths.
When you find i such that the function returns the same result for both, but not for i+1,
then the i-th item in the path is the lowest common ancestor.
The main reason why the article's solutions are more complicated is that it is dealing with a two-stage problem- preprocessing and then queries- while from your question it sounds like you're only doing one query so preprocessing doesn't make sense. It's also dealing with arbitrary trees rather than binary trees.
The best answer will certainly depend on details about the tree. For many kinds of trees, the time complexity is going to be O(h) where h is the tree's height. If you've got pointers to parent nodes, then the easy "constant-space" answer is, as in Mirko's solution, to find both nodes' height and compare ancestors of the same height. Note that this works for any tree with parent links, binary or no. We can improve on Mirko's solution by making the height function iterative and by separating the "get to the same depth" loops from the main loop:
int height(Node n){
int h=-1;
while(n!=null){h++;n=n.parent;}
return h;
}
Node LCA(Node n1, Node n2){
int discrepancy=height(n1)-height(n2);
while(discrepancy>0) {n1=n1.parent;discrepancy--;}
while(discrepancy<0) {n2=n2.parent;discrepancy++;}
while(n1!=n2){n1=n1.parent();n2=n2.parent();}
return n1;
}
The quotation marks around "constant-space" are because in general we need O(log(h)) space to store the heights and the difference between them (say, 3 BigIntegers). But if you're dealing with trees with heights too large to stuff in a long, you likely have other problems to worry about that are more pressing than storing a couple nodes' heights.
If you have a BST, then you can easily take a common ancestor (usu. starting with root) and check its children to see whether either of them is a common ancestor:
Node LCA(Node n1, Node n2, Node CA){
while(true){
if(n1.val<CA.val & n2.val<CA.val) CA=CA.left;
else if (n1.val>CA.val & n2.val>CA.val) CA=CA.right;
else return CA;
}
}
As Philip JF mentioned, this same idea can be used in any tree for a constant-space algorithm, but for a general tree doing it this way will be really slow since figuring out repeatedly whether CA.left or CA.right is a common ancestor will repeat a lot of work, so you'd normally prefer to use more space to save some time. The main way to make that tradeoff would be basically the algorithm you've mentioned (storing the path from root).
It matters what kind of tree you are using. You can always tell if a node is the ancestor of another node in constant space, and the top node is always a common ancestor, so getting the Lowest Common Ancestor in constant space just requires iterating your way down. On a binary search tree this is pretty easy to do fast, but it will work on any tree.
Many different trade offs are relevant for this problem, and the type of tree matters. The problem tends is much easier if you have pointers to parent nodes, and not just to children (Mirko's code uses this)
See also:
http://en.wikipedia.org/wiki/Lowest_common_ancestor
The obvious solution, that uses log(n) space, (n is the number of nodes) is the algorithm you mentioned. Here's an implementation. In the worst case it takes O(n) time (imagine that one of the node you are searching common ancestor for includes the last node).
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace ConsoleApplication2
{
class Node
{
private static int counter = 0;
private Node left = null;
private Node right = null;
public int id = counter++;
static Node constructTreeAux(int depth)
{
if (depth == 0)
return null;
Node newNode = new Node();
newNode.left = constructTree(depth - 1);
newNode.right = constructTree(depth - 1);
return newNode;
}
public static Node constructTree(int depth)
{
if (depth == 0)
return null;
Node root = new Node();
root.left = constructTreeAux(depth - 1);
root.right = constructTreeAux(depth - 1);
return root;
}
private List<Node> findPathAux(List<Node> pathSoFar, int searchId)
{
if (this.id == searchId)
{
if (pathSoFar == null)
pathSoFar = new List<Node>();
pathSoFar.Add(this);
return pathSoFar;
}
if (left != null)
{
List<Node> result = left.findPathAux(null, searchId);
if (result != null)
{
result.Add(this);
return result;
}
}
if (right != null)
{
List<Node> result = right.findPathAux(null, searchId);
if (result != null)
{
result.Add(this);
return result;
}
}
return null;
}
public static void printPath(List<Node> path)
{
if (path == null)
{
Console.Out.WriteLine(" empty path ");
return;
}
Console.Out.Write("[");
for (int i = 0; i < path.Count; i++)
Console.Out.Write(path[i] + " ");
Console.Out.WriteLine("]");
}
public override string ToString()
{
return id.ToString();
}
/// <summary>
/// Returns null if no common ancestor, the lowest common ancestor otherwise.
/// </summary>
public Node findCommonAncestor(int id1, int id2)
{
List<Node> path1 = findPathAux(null, id1);
if (path1 == null)
return null;
path1 = path1.Reverse<Node>().ToList<Node>();
List<Node> path2 = findPathAux(null, id2);
if (path2 == null)
return null;
path2 = path2.Reverse<Node>().ToList<Node>();
Node commonAncestor = this;
int n = path1.Count < path2.Count? path1.Count : path2.Count;
printPath(path1);
printPath(path2);
for (int i = 0; i < n; i++)
{
if (path1[i].id == path2[i].id)
commonAncestor = path1[i];
else
return commonAncestor;
}
return commonAncestor;
}
private void printTreeAux(int depth)
{
for (int i = 0; i < depth; i++)
Console.Write(" ");
Console.WriteLine(id);
if (left != null)
left.printTreeAux(depth + 1);
if (right != null)
right.printTreeAux(depth + 1);
}
public void printTree()
{
printTreeAux(0);
}
public static void testAux(out Node root, out Node commonAncestor, out int id1, out int id2)
{
Random gen = new Random();
int startid = counter;
root = constructTree(5);
int endid = counter;
int offset = gen.Next(endid - startid);
id1 = startid + offset;
offset = gen.Next(endid - startid);
id2 = startid + offset;
commonAncestor = root.findCommonAncestor(id1, id2);
}
public static void test1()
{
Node root = null, commonAncestor = null;
int id1 = 0, id2 = 0;
testAux(out root, out commonAncestor, out id1, out id2);
root.printTree();
commonAncestor = root.findCommonAncestor(id1, id2);
if (commonAncestor == null)
Console.WriteLine("Couldn't find common ancestor for " + id1 + " and " + id2);
else
Console.WriteLine("Common ancestor for " + id1 + " and " + id2 + " is " + commonAncestor.id);
}
}
}
The bottom up approach described here is an O(n) time, O(1) space approach:
http://www.leetcode.com/2011/07/lowest-common-ancestor-of-a-binary-tree-part-i.html
Node *LCA(Node *root, Node *p, Node *q) {
if (!root) return NULL;
if (root == p || root == q) return root;
Node *L = LCA(root->left, p, q);
Node *R = LCA(root->right, p, q);
if (L && R) return root; // if p and q are on both sides
return L ? L : R; // either one of p,q is on one side OR p,q is not in L&R subtrees
}

Java Printing a Binary Tree using Level-Order in a Specific Format

Okay, I have read through all the other related questions and cannot find one that helps with java. I get the general idea from deciphering what i can in other languages; but i am yet to figure it out.
Problem: I would like to level sort (which i have working using recursion) and print it out in the general shape of a tree.
So say i have this:
1
/ \
2 3
/ / \
4 5 6
My code prints out the level order like this:
1 2 3 4 5 6
I want to print it out like this:
1
2 3
4 5 6
Now before you give me a moral speech about doing my work... I have already finished my AP Comp Sci project and got curious about this when my teacher mentioned the Breadth First Search thing.
I don't know if it will help, but here is my code so far:
/**
* Calls the levelOrder helper method and prints out in levelOrder.
*/
public void levelOrder()
{
q = new QueueList();
treeHeight = height();
levelOrder(myRoot, q, myLevel);
}
/**
* Helper method that uses recursion to print out the tree in
* levelOrder
*/
private void levelOrder(TreeNode root, QueueList q, int curLev)
{
System.out.print(curLev);
if(root == null)
{
return;
}
if(q.isEmpty())
{
System.out.println(root.getValue());
}
else
{
System.out.print((String)q.dequeue()+", ");
}
if(root.getLeft() != null)
{
q.enqueue(root.getLeft().getValue());
System.out.println();
}
if(root.getRight() != null)
{
q.enqueue(root.getRight().getValue());
System.out.println();
curLev++;
}
levelOrder(root.getLeft(),q, curLev);
levelOrder(root.getRight(),q, curLev);
}
From what i can figure out, i will need to use the total height of the tree, and use a level counter... Only problem is my level counter keeps counting when my levelOrder uses recursion to go back through the tree.
Sorry if this is to much, but some tips would be nice. :)
Here is the code, this question was asked to me in one of the interviews...
public void printTree(TreeNode tmpRoot) {
Queue<TreeNode> currentLevel = new LinkedList<TreeNode>();
Queue<TreeNode> nextLevel = new LinkedList<TreeNode>();
currentLevel.add(tmpRoot);
while (!currentLevel.isEmpty()) {
Iterator<TreeNode> iter = currentLevel.iterator();
while (iter.hasNext()) {
TreeNode currentNode = iter.next();
if (currentNode.left != null) {
nextLevel.add(currentNode.left);
}
if (currentNode.right != null) {
nextLevel.add(currentNode.right);
}
System.out.print(currentNode.value + " ");
}
System.out.println();
currentLevel = nextLevel;
nextLevel = new LinkedList<TreeNode>();
}
}
This is the easiest solution
public void byLevel(Node root){
Queue<Node> level = new LinkedList<>();
level.add(root);
while(!level.isEmpty()){
Node node = level.poll();
System.out.print(node.item + " ");
if(node.leftChild!= null)
level.add(node.leftChild);
if(node.rightChild!= null)
level.add(node.rightChild);
}
}
https://github.com/camluca/Samples/blob/master/Tree.java
in my github you can find other helpful functions in the class Tree like:
Displaying the tree
****......................................................****
42
25 65
12 37 43 87
9 13 30 -- -- -- -- 99
****......................................................****
Inorder traversal
9 12 13 25 30 37 42 43 65 87 99
Preorder traversal
42 25 12 9 13 37 30 65 43 87 99
Postorder traversal
9 13 12 30 37 25 43 99 87 65 42
By Level
42 25 65 12 37 43 87 9 13 30 99
Here is how I would do it:
levelOrder(List<TreeNode> n) {
List<TreeNode> next = new List<TreeNode>();
foreach(TreeNode t : n) {
print(t);
next.Add(t.left);
next.Add(t.right);
}
println();
levelOrder(next);
}
(Was originally going to be real code - got bored partway through, so it's psueodocodey)
Just thought of sharing Anon's suggestion in real java code and fixing a couple of KEY issues (like there is not an end condition for the recursion so it never stops adding to the stack, and not checking for null in the received array gets you a null pointer exception).
Also there is no exception as Eric Hauser suggests, because it is not modifying the collection its looping through, it's modifying a new one.
Here it goes:
public void levelOrder(List<TreeNode> n) {
List<TreeNode> next = new ArrayList<TreeNode>();
for (TreeNode t : n) {
if (t != null) {
System.out.print(t.getValue());
next.add(t.getLeftChild());
next.add(t.getRightChild());
}
}
System.out.println();
if(next.size() > 0)levelOrder(next);
}
Below method returns ArrayList of ArrayList containing all nodes level by level:-
public ArrayList<ArrayList<Integer>> levelOrder(TreeNode root) {
ArrayList<ArrayList<Integer>> result = new ArrayList<ArrayList<Integer>>();
if(root == null) return result;
Queue q1 = new LinkedList();
Queue q2 = new LinkedList();
ArrayList<Integer> list = new ArrayList<Integer>();
q1.add(root);
while(!q1.isEmpty() || !q2.isEmpty()){
while(!q1.isEmpty()){
TreeNode temp = (TreeNode)q1.poll();
list.add(temp.val);
if(temp.left != null) q2.add(temp.left);
if(temp.right != null) q2.add(temp.right);
}
if(list.size() > 0)result.add(new ArrayList<Integer>(list));
list.clear();
while(!q2.isEmpty()){
TreeNode temp = (TreeNode)q2.poll();
list.add(temp.val);
if(temp.left != null) q1.add(temp.left);
if(temp.right != null) q1.add(temp.right);
}
if(list.size() > 0)result.add(new ArrayList<Integer>(list));
list.clear();
}
return result;
}
The answer is close....the only issue I could see with it is that if a tree doesn't have a node in a particular position, you would set that pointer to null. What happens when you try to put a null pointer into the list?
Here is something I did for a recent assignment. It works flawlessly. You can use it starting from any root.
//Prints the tree in level order
public void printTree(){
printTree(root);
}
public void printTree(TreeNode tmpRoot){
//If the first node isn't null....continue on
if(tmpRoot != null){
Queue<TreeNode> currentLevel = new LinkedList<TreeNode>(); //Queue that holds the nodes on the current level
Queue<TreeNode> nextLevel = new LinkedList<TreeNode>(); //Queue the stores the nodes for the next level
int treeHeight = height(tmpRoot); //Stores the height of the current tree
int levelTotal = 0; //keeps track of the total levels printed so we don't pass the height and print a billion "null"s
//put the root on the currnt level's queue
currentLevel.add(tmpRoot);
//while there is still another level to print and we haven't gone past the tree's height
while(!currentLevel.isEmpty()&& (levelTotal< treeHeight)){
//Print the next node on the level, add its childen to the next level's queue, and dequeue the node...do this until the current level has been printed
while(!currentLevel.isEmpty()){
//Print the current value
System.out.print(currentLevel.peek().getValue()+" ");
//If there is a left pointer, put the node on the nextLevel's stack. If there is no ponter, add a node with a null value to the next level's stack
tmpRoot = currentLevel.peek().getLeft();
if(tmpRoot != null)
nextLevel.add(tmpRoot);
else
nextLevel.add(new TreeNode(null));
//If there is a right pointer, put the node on the nextLevel's stack. If there is no ponter, add a node with a null value to the next level's stack
tmpRoot = currentLevel.remove().getRight();
if(tmpRoot != null)
nextLevel.add(tmpRoot);
else
nextLevel.add(new TreeNode(null));
}//end while(!currentLevel.isEmpty())
//populate the currentLevel queue with items from the next level
while(!nextLevel.isEmpty()){
currentLevel.add(nextLevel.remove());
}
//Print a blank line to show height
System.out.println("");
//flag that we are working on the next level
levelTotal++;
}//end while(!currentLevel.isEmpty())
}//end if(tmpRoot != null)
}//end method printTree
public int height(){
return height(getRoot());
}
public int height(TreeNode tmpRoot){
if (tmpRoot == null)
return 0;
int leftHeight = height(tmpRoot.getLeft());
int rightHeight = height(tmpRoot.getRight());
if(leftHeight >= rightHeight)
return leftHeight + 1;
else
return rightHeight + 1;
}
I really like the simplicity of Anon's code; its elegant. But, sometimes elegant code doesn't always translate into code that is intuitively easy to grasp. So, here's my attempt to show a similar approach that requires Log(n) more space, but should read more naturally to those who are most familiar with depth first search (going down the length of a tree)
The following snippet of code sets nodes belonging to a particular level in a list, and arranges that list in a list that holds all the levels of the tree. Hence the List<List<BinaryNode<T>>> that you will see below. The rest should be fairly self explanatory.
public static final <T extends Comparable<T>> void printTreeInLevelOrder(
BinaryTree<T> tree) {
BinaryNode<T> root = tree.getRoot();
List<List<BinaryNode<T>>> levels = new ArrayList<List<BinaryNode<T>>>();
addNodesToLevels(root, levels, 0);
for(List<BinaryNode<T>> level: levels){
for(BinaryNode<T> node: level){
System.out.print(node+ " ");
}
System.out.println();
}
}
private static final <T extends Comparable<T>> void addNodesToLevels(
BinaryNode<T> node, List<List<BinaryNode<T>>> levels, int level) {
if(null == node){
return;
}
List<BinaryNode<T>> levelNodes;
if(levels.size() == level){
levelNodes = new ArrayList<BinaryNode<T>>();
levels.add(level, levelNodes);
}
else{
levelNodes = levels.get(level);
}
levelNodes.add(node);
addNodesToLevels(node.getLeftChild(), levels, level+1);
addNodesToLevels(node.getRightChild(), levels, level+1);
}
Following implementation uses 2 queues. Using ListBlokcingQueue here but any queue would work.
import java.util.concurrent.*;
public class Test5 {
public class Tree {
private String value;
private Tree left;
private Tree right;
public Tree(String value) {
this.value = value;
}
public void setLeft(Tree t) {
this.left = t;
}
public void setRight(Tree t) {
this.right = t;
}
public Tree getLeft() {
return this.left;
}
public Tree getRight() {
return this.right;
}
public String getValue() {
return this.value;
}
}
Tree tree = null;
public void setTree(Tree t) {
this.tree = t;
}
public void printTree() {
LinkedBlockingQueue<Tree> q = new LinkedBlockingQueue<Tree>();
q.add(this.tree);
while (true) {
LinkedBlockingQueue<Tree> subQueue = new LinkedBlockingQueue<Tree>();
while (!q.isEmpty()) {
Tree aTree = q.remove();
System.out.print(aTree.getValue() + ", ");
if (aTree.getLeft() != null) {
subQueue.add(aTree.getLeft());
}
if (aTree.getRight() != null) {
subQueue.add(aTree.getRight());
}
}
System.out.println("");
if (subQueue.isEmpty()) {
return;
} else {
q = subQueue;
}
}
}
public void testPrint() {
Tree a = new Tree("A");
a.setLeft(new Tree("B"));
a.setRight(new Tree("C"));
a.getLeft().setLeft(new Tree("D"));
a.getLeft().setRight(new Tree("E"));
a.getRight().setLeft(new Tree("F"));
a.getRight().setRight(new Tree("G"));
setTree(a);
printTree();
}
public static void main(String args[]) {
Test5 test5 = new Test5();
test5.testPrint();
}
}
public class PrintATreeLevelByLevel {
public static class Node{
int data;
public Node left;
public Node right;
public Node(int data){
this.data = data;
this.left = null;
this.right = null;
}
}
public void printATreeLevelByLevel(Node n){
Queue<Node> queue = new LinkedList<Node>();
queue.add(n);
int node = 1; //because at root
int child = 0; //initialize it with 0
while(queue.size() != 0){
Node n1 = queue.remove();
node--;
System.err.print(n1.data +" ");
if(n1.left !=null){
queue.add(n1.left);
child ++;
}
if(n1.right != null){
queue.add(n1.right);
child ++;
}
if( node == 0){
System.err.println();
node = child ;
child = 0;
}
}
}
public static void main(String[]args){
PrintATreeLevelByLevel obj = new PrintATreeLevelByLevel();
Node node1 = new Node(1);
Node node2 = new Node(2);
Node node3 = new Node(3);
Node node4 = new Node(4);
Node node5 = new Node(5);
Node node6 = new Node(6);
Node node7 = new Node(7);
Node node8 = new Node(8);
node4.left = node2;
node4.right = node6;
node2.left = node1;
// node2.right = node3;
node6.left = node5;
node6.right = node7;
node1.left = node8;
obj.printATreeLevelByLevel(node4);
}
}
Try this, using 2 Queues to keep track of the levels.
public static void printByLevel(Node root){
LinkedList<Node> curLevel = new LinkedList<Node>();
LinkedList<Node> nextLevel = curLevel;
StringBuilder sb = new StringBuilder();
curLevel.add(root);
sb.append(root.data + "\n");
while(nextLevel.size() > 0){
nextLevel = new LinkedList<Node>();
for (int i = 0; i < curLevel.size(); i++){
Node cur = curLevel.get(i);
if (cur.left != null) {
nextLevel.add(cur.left);
sb.append(cur.left.data + " ");
}
if (cur.right != null) {
nextLevel.add(cur.right);
sb.append(cur.right.data + " ");
}
}
if (nextLevel.size() > 0) {
sb.append("\n");
curLevel = nextLevel;
}
}
System.out.println(sb.toString());
}
A - Solution
I've written direct solution here. If you want the detailed answer, demo code and explanation, you can skip and check the rest headings of the answer;
public static <T> void printLevelOrder(TreeNode<T> root) {
System.out.println("Tree;");
System.out.println("*****");
// null check
if(root == null) {
System.out.printf(" Empty\n");
return;
}
MyQueue<TreeNode<T>> queue = new MyQueue<>();
queue.enqueue(root);
while(!queue.isEmpty()) {
handleLevel(queue);
}
}
// process each level
private static <T> void handleLevel(MyQueue<TreeNode<T>> queue) {
int size = queue.size();
for(int i = 0; i < size; i++) {
TreeNode<T> temp = queue.dequeue();
System.out.printf("%s ", temp.data);
queue.enqueue(temp.left);
queue.enqueue(temp.right);
}
System.out.printf("\n");
}
B - Explanation
In order to print a tree in level-order, you should process each level using a simple queue implementation. In my demo, I've written a very minimalist simple queue class called as MyQueue.
Public method printLevelOrder will take the TreeNode<T> object instance root as a parameter which stands for the root of the tree. The private method handleLevel takes the MyQueue instance as a parameter.
On each level, handleLevel method dequeues the queue as much as the size of the queue. The level restriction is controlled as this process is executed only with the size of the queue which exactly equals to the elements of that level then puts a new line character to the output.
C - TreeNode class
public class TreeNode<T> {
T data;
TreeNode<T> left;
TreeNode<T> right;
public TreeNode(T data) {
this.data = data;;
}
}
D - MyQueue class : A simple Queue Implementation
public class MyQueue<T> {
private static class Node<T> {
T data;
Node next;
public Node(T data) {
this(data, null);
}
public Node(T data, Node<T> next) {
this.data = data;
this.next = next;
}
}
private Node head;
private Node tail;
private int size;
public MyQueue() {
head = null;
tail = null;
}
public int size() {
return size;
}
public void enqueue(T data) {
if(data == null)
return;
if(head == null)
head = tail = new Node(data);
else {
tail.next = new Node(data);
tail = tail.next;
}
size++;
}
public T dequeue() {
if(tail != null) {
T temp = (T) head.data;
head = head.next;
size--;
return temp;
}
return null;
}
public boolean isEmpty() {
return size == 0;
}
public void printQueue() {
System.out.println("Queue: ");
if(head == null)
return;
else {
Node<T> temp = head;
while(temp != null) {
System.out.printf("%s ", temp.data);
temp = temp.next;
}
}
System.out.printf("%n");
}
}
E - DEMO : Printing Tree in Level-Order
public class LevelOrderPrintDemo {
public static void main(String[] args) {
// root level
TreeNode<Integer> root = new TreeNode<>(1);
// level 1
root.left = new TreeNode<>(2);
root.right = new TreeNode<>(3);
// level 2
root.left.left = new TreeNode<>(4);
root.right.left = new TreeNode<>(5);
root.right.right = new TreeNode<>(6);
/*
* 1 root
* / \
* 2 3 level-1
* / / \
* 4 5 6 level-2
*/
printLevelOrder(root);
}
public static <T> void printLevelOrder(TreeNode<T> root) {
System.out.println("Tree;");
System.out.println("*****");
// null check
if(root == null) {
System.out.printf(" Empty\n");
return;
}
MyQueue<TreeNode<T>> queue = new MyQueue<>();
queue.enqueue(root);
while(!queue.isEmpty()) {
handleLevel(queue);
}
}
// process each level
private static <T> void handleLevel(MyQueue<TreeNode<T>> queue) {
int size = queue.size();
for(int i = 0; i < size; i++) {
TreeNode<T> temp = queue.dequeue();
System.out.printf("%s ", temp.data);
queue.enqueue(temp.left);
queue.enqueue(temp.right);
}
System.out.printf("\n");
}
}
F - Sample Input
1 // root
/ \
2 3 // level-1
/ / \
4 5 6 // level-2
G - Sample Output
Tree;
*****
1
2 3
4 5 6
public void printAllLevels(BNode node, int h){
int i;
for(i=1;i<=h;i++){
printLevel(node,i);
System.out.println();
}
}
public void printLevel(BNode node, int level){
if (node==null)
return;
if (level==1)
System.out.print(node.value + " ");
else if (level>1){
printLevel(node.left, level-1);
printLevel(node.right, level-1);
}
}
public int height(BNode node) {
if (node == null) {
return 0;
} else {
return 1 + Math.max(height(node.left),
height(node.right));
}
}
First of all, I do not like to take credit for this solution. It's a modification of somebody's function and I tailored it to provide the solution.
I am using 3 functions here.
First I calculate the height of the tree.
I then have a function to print a particular level of the tree.
Using the height of the tree and the function to print the level of a tree, I traverse the tree and iterate and print all levels of the tree using my third function.
I hope this helps.
EDIT: The time complexity on this solution for printing all node in level order traversal will not be O(n). The reason being, each time you go down a level, you will visit the same nodes again and again.
If you are looking for a O(n) solution, i think using Queues would be a better option.
I think we can achieve this by using one queue itself. This is a java implementation using one queue only. Based on BFS...
public void BFSPrint()
{
Queue<Node> q = new LinkedList<Node>();
q.offer(root);
BFSPrint(q);
}
private void BFSPrint(Queue<Node> q)
{
if(q.isEmpty())
return;
int qLen = q.size(),i=0;
/*limiting it to q size when it is passed,
this will make it print in next lines. if we use iterator instead,
we will again have same output as question, because iterator
will end only q empties*/
while(i<qLen)
{
Node current = q.remove();
System.out.print(current.data+" ");
if(current.left!=null)
q.offer(current.left);
if(current.right!=null)
q.offer(current.right);
i++;
}
System.out.println();
BFSPrint(q);
}
the top solutions only print the children of each node together. This is wrong according to the description.
What we need is all the nodes of the same level together in the same line.
1) Apply BFS
2) Store heights of nodes to a map that will hold level - list of nodes.
3) Iterate over the map and print out the results.
See Java code below:
public void printByLevel(Node root){
Queue<Node> q = new LinkedBlockingQueue<Node>();
root.visited = true;
root.height=1;
q.add(root);
//Node height - list of nodes with same level
Map<Integer, List<Node>> buckets = new HashMap<Integer, List<Node>>();
addToBuckets(buckets, root);
while (!q.isEmpty()){
Node r = q.poll();
if (r.adjacent!=null)
for (Node n : r.adjacent){
if (!n.visited){
n.height = r.height+1; //adjust new height
addToBuckets(buckets, n);
n.visited = true;
q.add(n);
}
}
}
//iterate over buckets and print each list
printMap(buckets);
}
//helper method that adds to Buckets list
private void addToBuckets(Map<Integer, List<Node>> buckets, Node n){
List<Node> currlist = buckets.get(n.height);
if (currlist==null)
{
List<Node> list = new ArrayList<Node>();
list.add(n);
buckets.put(n.height, list);
}
else{
currlist.add(n);
}
}
//prints the Map
private void printMap(Map<Integer, List<Node>> buckets){
for (Entry<Integer, List<Node>> e : buckets.entrySet()){
for (Node n : e.getValue()){
System.out.print(n.value + " ");
}
System.out.println();
}
Simplest way to do this without using any level information implicitly assumed to be in each Node. Just append a 'null' node after each level. check for this null node to know when to print a new line:
public class BST{
private Node<T> head;
BST(){}
public void setHead(Node<T> val){head = val;}
public static void printBinaryTreebyLevels(Node<T> head){
if(head == null) return;
Queue<Node<T>> q = new LinkedList<>();//assuming you have type inference (JDK 7)
q.add(head);
q.add(null);
while(q.size() > 0){
Node n = q.poll();
if(n == null){
System.out.println();
q.add(null);
n = q.poll();
}
System.out.print(n.value+" ");
if(n.left != null) q.add(n.left);
if(n.right != null) q.add(n.right);
}
}
public static void main(String[] args){
BST b = new BST();
c = buildListedList().getHead();//assume we have access to this for the sake of the example
b.setHead(c);
printBinaryTreeByLevels();
return;
}
}
class Node<T extends Number>{
public Node left, right;
public T value;
Node(T val){value = val;}
}
This works for me. Pass an array list with rootnode when calling printLevel.
void printLevel(ArrayList<Node> n){
ArrayList<Node> next = new ArrayList<Node>();
for (Node t: n) {
System.out.print(t.value+" ");
if (t.left!= null)
next.add(t.left);
if (t.right!=null)
next.add(t.right);
}
System.out.println();
if (next.size()!=0)
printLevel(next);
}
Print Binary Tree in level order with a single Queue:
public void printBFSWithQueue() {
java.util.LinkedList<Node> ll = new LinkedList<>();
ll.addLast(root);
ll.addLast(null);
Node in = null;
StringBuilder sb = new StringBuilder();
while(!ll.isEmpty()) {
if(ll.peekFirst() == null) {
if(ll.size() == 1) {
break;
}
ll.removeFirst();
System.out.println(sb);
sb = new StringBuilder();
ll.addLast(null);
continue;
}
in = ll.pollFirst();
sb.append(in.v).append(" ");
if(in.left != null) {
ll.addLast(in.left);
}
if(in.right != null) {
ll.addLast(in.right);
}
}
}
void printTreePerLevel(Node root)
{
Queue<Node> q= new LinkedList<Node>();
q.add(root);
int currentlevel=1;
int nextlevel=0;
List<Integer> values= new ArrayList<Integer>();
while(!q.isEmpty())
{
Node node = q.remove();
currentlevel--;
values.add(node.value);
if(node.left != null)
{
q.add(node.left);
nextlevel++;
}
if(node.right != null)
{
q.add(node.right);
nextlevel++;
}
if(currentlevel==0)
{
for(Integer i:values)
{
System.out.print(i + ",");
}
System.out.println();
values.clear();
currentlevel=nextlevel;
nextlevel=0;
}
}
}
Python implementation
# Function to print level order traversal of tree
def printLevelOrder(root):
h = height(root)
for i in range(1, h+1):
printGivenLevel(root, i)
# Print nodes at a given level
def printGivenLevel(root , level):
if root is None:
return
if level == 1:
print "%d" %(root.data),
elif level > 1 :
printGivenLevel(root.left , level-1)
printGivenLevel(root.right , level-1)
""" Compute the height of a tree--the number of nodes
along the longest path from the root node down to
the farthest leaf node
"""
def height(node):
if node is None:
return 0
else :
# Compute the height of each subtree
lheight = height(node.left)
rheight = height(node.right)
#Use the larger one
if lheight > rheight :
return lheight+1
else:
return rheight+1
Queue<Node> queue = new LinkedList<>();
queue.add(root);
Node leftMost = null;
while (!queue.isEmpty()) {
Node node = queue.poll();
if (leftMost == node) {
System.out.println();
leftMost = null;
}
System.out.print(node.getData() + " ");
Node left = node.getLeft();
if (left != null) {
queue.add(left);
if (leftMost == null) {
leftMost = left;
}
}
Node right = node.getRight();
if (right != null) {
queue.add(right);
if (leftMost == null) {
leftMost = right;
}
}
}
To solve this type of question which require in-level or same-level traversal approach, one immediately can use Breath First Search or in short BFS. To implement the BFS one can use Queue. In Queue each item comes in order of insertion, so for example if a node has two children, we can insert its children into queue one after another, thus make them in order inserted. When in return polling from queue, we traverse over children as it like we go in same-level of tree. Hense I am going to use a simple implementation of an in-order traversal approach.
I build up my Tree and pass the root which points to the root.
inorderTraversal takes root and do a while-loop that peeks one node first, and fetches children and insert them back into queue. Note that nodes one by one get inserted into queue, as you see, once you fetch the children nodes, you append it to the StringBuilder to construct the final output.
In levelOrderTraversal method though, I want to print the tree in level order. So I need to do the above approach, but instead I don't poll from queue and insert its children back to queue. Because I intent to insert "next-line-character" in a loop, and if I insert the children to queue, this loop would continue inserting a new line for each node, instead I need to check do it only for a level. That's why I used a for-loop to check how many items I have in my queue.
I simply don't poll anything from queue, because I only want to know if there are any level exists.
This separation of method helps me to still keep using BFS data and when required I can print them in-order or level-order , based-on requirements of the application.
public class LevelOrderTraversal {
public static void main(String[] args) throws InterruptedException {
BinaryTreeNode node1 = new BinaryTreeNode(100);
BinaryTreeNode node2 = new BinaryTreeNode(50);
BinaryTreeNode node3 = new BinaryTreeNode(200);
node1.left = node2;
node1.right = node3;
BinaryTreeNode node4 = new BinaryTreeNode(25);
BinaryTreeNode node5 = new BinaryTreeNode(75);
node2.left = node4;
node2.right = node5;
BinaryTreeNode node6 = new BinaryTreeNode(350);
node3.right = node6;
String levelOrderTraversal = levelOrderTraversal(node1);
System.out.println(levelOrderTraversal);
String inorderTraversal = inorderTraversal(node1);
System.out.println(inorderTraversal);
}
private static String inorderTraversal(BinaryTreeNode root) {
Queue<BinaryTreeNode> queue = new LinkedList<>();
StringBuilder sb = new StringBuilder();
queue.offer(root);
BinaryTreeNode node;
while ((node = queue.poll()) != null) {
sb.append(node.data).append(",");
if (node.left != null) {
queue.offer(node.left);
}
if (node.right != null) {
queue.offer(node.right);
}
}
return sb.toString();
}
public static String levelOrderTraversal(BinaryTreeNode root) {
Queue<BinaryTreeNode> queue = new LinkedList<>();
queue.offer(root);
StringBuilder stringBuilder = new StringBuilder();
while (!queue.isEmpty()) {
handleLevelPrinting(stringBuilder, queue);
}
return stringBuilder.toString();
}
private static void handleLevelPrinting(StringBuilder sb, Queue<BinaryTreeNode> queue) {
for (int i = 0; i < queue.size(); i++) {
BinaryTreeNode node = queue.poll();
if (node != null) {
sb.append(node.data).append("\t");
queue.offer(node.left);
queue.offer(node.right);
}
}
sb.append("\n");
}
private static class BinaryTreeNode {
int data;
BinaryTreeNode right;
BinaryTreeNode left;
public BinaryTreeNode(int data) {
this.data = data;
}
}
}
Wow. So many answers. For what it is worth, my solution goes like this:
We know the normal way to level order traversal: for each node, first the node is visited and then it’s child nodes are put in a FIFO queue. What we need to do is keep track of each level, so that all the nodes at that level are printed in one line, without a new line.
So I naturally thought of it as miaintaining a queue of queues. The main queue contains internal queues for each level. Each internal queue contains all the nodes in one level in FIFO order. When we dequeue an internal queue, we iterate through it, adding all its children to a new queue, and adding this queue to the main queue.
public static void printByLevel(Node root) {
Queue<Node> firstQ = new LinkedList<>();
firstQ.add(root);
Queue<Queue<Node>> mainQ = new LinkedList<>();
mainQ.add(firstQ);
while (!mainQ.isEmpty()) {
Queue<Node> levelQ = mainQ.remove();
Queue<Node> nextLevelQ = new LinkedList<>();
for (Node x : levelQ) {
System.out.print(x.key + " ");
if (x.left != null) nextLevelQ.add(x.left);
if (x.right != null) nextLevelQ.add(x.right);
}
if (!nextLevelQ.isEmpty()) mainQ.add(nextLevelQ);
System.out.println();
}
}
public void printAtLevel(int i){
printAtLevel(root,i);
}
private void printAtLevel(BTNode<T> n,int i){
if(n != null){
sop(n.data);
} else {
printAtLevel(n.left,i-1);
printAtLevel(n.right,i-1);
}
}
private void printAtLevel(BTNode<T> n,int i){
if(n != null){
sop(n.data);
printAtLevel(n.left,i-1);
printAtLevel(n.right,i-1);
}
}

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