Depth of Huffman nodes - java

I'm new in Java. I'm trying to obtain the average depth tree depth. I already have the number of nodes. I just need each node's depth. I have a method to obtain the height of the tree. I'm thinking if I could use this method and reverse it to obtain the depth of every node. But I don't know how to specify the node in the method.
Do you guys have any advice for specifying the nodes one by one in the method?
Right now my method take a tree type as parameter
PS: English is not my native language. Sorry for any confusion
import java.util.*;
public class HuffmanCode {
int numberOfNode = 1;
int height;
String fullcode = "";
String realcode = "";
// input is an array of frequencies, indexed by character code
public HuffmanTree createTree(int[] charFreqs) {
PriorityQueue<HuffmanTree> trees = new PriorityQueue<HuffmanTree>();
// initially, we have a forest of leaves
// one for each non-empty character
for (int x = 0; x < charFreqs.length; x++) {
if (charFreqs[x] > 0)
trees.offer(new HuffmanLeaf(charFreqs[x], (char) x));
}
/*
* Step 2 in Huffman coding While loop to remove 2 nodes with the
* highest priority(lowest probability)
*/
while (trees.size() > 1) {
// Poll the two nodes with least frequency
HuffmanTree a = trees.poll();
HuffmanTree b = trees.poll();
// put into new node and re-insert into queue
trees.offer(new HuffmanNode(a, b));
numberOfNode++;
}
return trees.poll();
}
public void printResults(HuffmanTree tree, StringBuffer prefix) {
if (tree instanceof HuffmanLeaf) {
HuffmanLeaf leaf = (HuffmanLeaf) tree;
// print out character, frequency, and code for this leaf (which is
// just the prefix)
System.out.println(leaf.value + "\t" + leaf.frequency + "\t" + prefix);
encodedInput(prefix);
for (int x = 0; x < leaf.frequency; x++) {
realcode = realcode + prefix;
}
} else if (tree instanceof HuffmanNode) {
HuffmanNode node = (HuffmanNode) tree;
numberOfNode++;
// move left
prefix.append('0');
printResults(node.left, prefix);
prefix.deleteCharAt(prefix.length() - 1);
// move right
prefix.append('1');
printResults(node.right, prefix);
prefix.deleteCharAt(prefix.length() - 1);
height = findHeight(node);
}
}
public void encodedInput(StringBuffer prefix) {
fullcode = fullcode + " , " + prefix;
}
public int findHeight(HuffmanTree tree) {
if (tree == null) {
return -1;
}
if (tree instanceof HuffmanLeaf) {
return 0;
} else if (tree instanceof HuffmanNode) {
int left = findHeight(((HuffmanNode) tree).left);
int right = findHeight(((HuffmanNode) tree).right);
if (left > right) {
return left + 1;
} else {
return right + 1;
}
} else {
return -1; // does not happen, you might want to raise exception.
}
}
public void printQueue(PriorityQueue<HuffmanTree> pq) {
while (pq.size() > 0) {
System.out.println(pq.poll());
}
}
}
Other class I have:
class HuffmanNode extends HuffmanTree {
public HuffmanTree left;
public HuffmanTree right;
public HuffmanNode(HuffmanTree left, HuffmanTree right) {
super(left.frequency + right.frequency);
this.left = left;
this.right = right;
}
}
class HuffmanLeaf extends HuffmanTree {
public char value; // the character this leaf represents
public HuffmanLeaf(int frequency, char value) {
super(frequency);
this.value = value;
}
}
public class HuffmanTree implements Comparable<HuffmanTree> {
public int frequency; // the frequency of this tree
public HuffmanTree(int frequency) {
this.frequency = frequency;
}
public int compareTo(HuffmanTree tree) {
return frequency - tree.frequency;
}
}

This code maybe help you. you can traverse from root and calculate sum of depth.
public int sum(HuffmanTree tree,int currentDepth) {
if (tree == null) {
return -1;
}
if (tree instanceof HuffmanLeaf) {
return currentDepth;
} else if (tree instanceof HuffmanNode) {
int left = sum(((HuffmanNode) tree).left , currentDepth+1);
int right = sum(((HuffmanNode) tree).right, currentDepth+1);
return left+right;
} else {
return -1; // does not happen, you might want to raise exception.
}
}

Related

Why am I getting an incorrect answer while trying to find the closest value in a BST given a target value?

There is only one difference between the correct answer and my answer, and that is, I am traversing the entire tree instead of comparing the target with the node value and eliminating one-half of the tree in each recursion. Please help me with the explanation. Thanks.
My code:
import java.util.*;
class Program {
public static int findClosestValueInBst(BST tree, int target) {
//int closest = Integer.MAX_VALUE;
// int val = 0;
int vl = findClosestValueInBst1(tree, target, tree.value);
return vl;
}
public static int findClosestValueInBst1(BST tree, int target, int val) {
// System.out.println((closest + " " + Math.abs(tree.value - target)));
//c = closest;
if(( Math.abs(target - tree.value)) < ( Math.abs(target - val))){
System.out.println(val);
val = tree.value;
}
if(tree.left != null){
return findClosestValueInBst1(tree.left, target, val);
}
if(tree.right != null){
return findClosestValueInBst1(tree.right, target, val);
}
return val;
}
static class BST {
public int value;
public BST left;
public BST right;
public BST(int value) {
this.value = value;
}
}
}
Question tree- Root =10,
Nodes-> [10,15,22,13,14,5,5,2,1],
Target: 12,
My output: 10,
Correct answer: 13,
import java.util.*;
class Program {
public static int findClosestValueInBst(BST tree, int target) {
//int closest = Integer.MAX_VALUE;
// int val = 0;
int vl = findClosestValueInBst1(tree, target, tree.value);
return vl;
}
public static int findClosestValueInBst1(BST tree, int target, int val) {
// System.out.println((closest + " " + Math.abs(tree.value - target)));
//c = closest;
if(( Math.abs(target - tree.value)) < ( Math.abs(target - val))){
System.out.println(val);
val = tree.value;
}
if( target < tree.value && tree.left != null){
return findClosestValueInBst1(tree.left, target, val);
} else
if(target > tree.value && tree.right != null){
return findClosestValueInBst1(tree.right, target, val);
} else
return val;
}
static class BST {
public int value;
public BST left;
public BST right;
public BST(int value) {
this.value = value;
}
}
}
The tree looks like this:
10
/\
5 15
/ /\
2 13 22
/ \
1 14
Your code is not actually traversing the whole tree. This code:
if(tree.left != null){
return findClosestValueInBst1(tree.left, target, val);
}
if(tree.right != null){
return findClosestValueInBst1(tree.right, target, val);
}
return val;
checks the left subtree if it exists (and ignores the right subtree). Otherwise, check the right subtree if it exists. Otherwise stop the recursion. This is because once you reach a return statement, the entire method stops there, and the lines after that do not get executed.
So your code always prefers the left subtree without taking into account what number the node actually stores. So right off the bat, you went to the wrong direction - you are looking for 13, and the current node is 10, a closer value is gotta be bigger than 10, i.e. in the right subtree.
An implementation that actually traverses the whole tree would be something like:
public static int findClosestValueInBst(BST tree, int target) { // no need for the val argument!
int leftClosest = tree.value;
int rightClosest = tree.value;
if(tree.left != null){
leftClosest = findClosestValueInBst1(tree.left, target);
}
if(tree.right != null){
rightClosest = findClosestValueInBst1(tree.right, target);
}
if (target - leftClosest < rightClosest - target) {
return leftClosest;
} else {
return rightClosest;
}
}
But why bother when you can do it more quickly? :)

given a definition of node, calculate the sum of the nodes in binary tree

class Node{
int value;
List<Node> childNodes;
}
Above is the definition of the Node, and I have no idea how to implement the sum of the binary tree.
public class TreeNode {
int val;
TreeNode left;
TreeNode right;
TreeNode(int x) {
val = x;
}
}
However, I can understand this version of node and the sum of nodes of binary tree can be implemented by recursion.
public static int sumTree(Node root) {
int sum = 0;
if (root == null) {
return 0;
}
// Line 1
for (int i = 0; i < root.childNodes.size(); i++) {
sum = sum + root.childNodes.get(i).value + sumTree(root.childNodes.get(i));
}
return sum;
}
Actually, this is a tree instead of binary tree. This is my code
The sum of the nodes in the tree is: value of node + sum of left tree + sum of right tree.
Therefore:
public static int sum(TreeNode node) {
if(node == null) {
return 0;
} else {
return node.getVal() + sum(node.getLeft()) + sum(node.getRight());
}
}
public int sum(Node root) {
if (root == null) {
return 0;
} else if ( root.childNodes == null) {
return root.value;
}
int sum = root.value;
for ( Node child : root.childNodes ) {
sum += sum(child);
}
return sum;
}

Get Words out of a Trie Data Structure

i have the following Trie Data Structure:
public class CDictionary implements IDictionary {
private static final int N = 'z' -'a'+1;
private static class Node {
private boolean end = false;
private Node[] next = new Node[N];
}
private int size = 0;
private Node root = new Node();
#Override
public boolean contains(String word) {
Node node = this.contains(root,word,0);
if (node == null) {
return false;
}
return node.end;
}
private Node contains(Node node, String str, int d) {
if (node == null) return null;
if (d == str.length()) return node;
char c = str.charAt(d);
return contains(node.next[c-'a'], str, d+1);
}
#Override
public void insert(String word) {
this.root = insert(this.root, word, 0);
this.size++;
}
private Node insert(Node node, String str, int d) {
if (node == null) node = new Node();
if (d == str.length()) {
node.end = true;
return node;
}
char c = str.charAt(d);
node.next[c-'a'] = this.insert(node.next[c-'a'], str, d+1);
return node;
}
#Override
public int size() {
return size;
}
The Trie is filled with some words like
for, the, each, home, is, it, egg, red...
Now i need a function to get all Words with a specific length for example the length 3
public List<String> getWords(int lenght) {
}
With the Words mentioned above it should return a list with the words
for,the,egg,red
The Problem is how can i restore these words out of the Trie Structur?
You need to recurse through your structure to a maximum depth of N (in this case 3)
You could do this by adding a couple of methods to your dictionary...
public List<String> findWordsOfLength(int length) {
// Create new empty list for results
List<String> results = new ArrayList<>();
// Start at the root node (level 0)...
findWordsOfLength(root, "", 0, length, results);
// Return the results
return results;
}
public void findWordsOfLength(Node node, String wordSoFar, int depth, int maxDepth, List<String> results) {
// Go through each "child" of this node
for(int k = 0; k < node.next.length; k++) {
Node child = node.next[k];
// If this child exists...
if(child != null) {
// Work out the letter that this child represents
char letter = 'a' + k;
// If we have reached "maxDepth" letters...
if(depth == maxDepth) {
// Add this letter to the end of the word so far and then add the word to the results list
results.add(wordSoFar + letter);
} else {
// Otherwise recurse to the next level
findWordsOfLength(child, wordSoDar + letter, depth + 1, maxDepth, results);
}
}
}
}
(I have not compiled / tested this, but it should give you an idea of what you need to do)
Hope this helps.

Tree Print Tree Method

I am going over my old test from Data Structures, and I cannot figure out how to implement the printtree(int level) method in my Tree class. I am restricted to using this structure. I cannot figure out an implementation to use without root.right or root.left, this is very frustrating.
/*
Exam 2. Problem 2. 03/09/2012
*/
import java.util.List;
import java.util.ArrayList;
/**
A tree in which each node has an arbitrary number of children.
*/
public class Tree
{
private Node root;
class Node
{
public Object data;
public List<Node> children;
/**
Computes the size of the subtree whose root is this node.
#return the number of nodes in the subtree
*/
public int size()
{
int sum = 0;
for (Node child : children) { sum = sum + child.size(); }
return 1 + sum;
}
public int leaves() {
int count = 0;
for (Node child : children) {
if (child.size() == 1) {
count = count + 1;
} else {
count = count + child.leaves();
}
}
if (count == 0) {
count = count + 1;
}
return count;
}
public String printTree(int level) {
String S = "";
S += root.data + " (level:" + level + ") ";
if (root != null) {
return S;
}
if (root.children != null) {
S += root.printTree(level + 1);
}
return S;
}
}
/**
Constructs an empty tree.
*/
public Tree()
{
root = null;
}
/**
Constructs a tree with one node and no children.
#param rootData the data for the root
*/
public Tree(Object rootData)
{
root = new Node();
root.data = rootData;
root.children = new ArrayList<Node>();
}
/**
Adds a subtree as the last child of the root.
*/
public void addSubtree(Tree subtree)
{
root.children.add(subtree.root);
}
/**
Computes the size of this tree.
#return the number of nodes in the tree
*/
public int size()
{
if (root == null) { return 0; }
else { return root.size(); }
}
public int leaves() {
Node newNode = root;
if (root == null) { return 0; }
else { return root.leaves(); }
}
public String printTree() {
return root.children.printTree(0);
}
}
you just need to change 3 things:
Change root to this every where in the printTree(int level) method
The placement of if(this == null) should be checked before anything else
Use a for loop to print all of the children
public String printTree(int level) {
String S = "";
// notice the change to '=='
if (this == null)
return S;
S += this.data + " (level:" + level + ") ";
// notice the for loop
if( this.children != null)
for(Node child : this.children)
S += child.printTree(level + 1);
return S;
}

Binary Heap Implemented via a Binary Tree Structure

For an assignment, we were instructed to create a priority queue implemented via a binary heap, without using any built-in classes, and I have done so successfully by using an array to store the queued objects. However, I'm interested in learning how to implement another queue by using an actual tree structure, but in doing so I've run across a bit of a problem.
How would I keep track of the nodes on which I would perform insertion and deletion? I have tried using a linked list, which appends each node as it is inserted - new children are added starting from the first list node, and deleted from the opposite end. However, this falls apart when elements are rearranged in the tree, as children are added at the wrong position.
Edit: Perhaps I should clarify - I'm not sure how I would be able to find the last occupied and first unoccupied leaves. For example, I would always be able to tell the last inserted leaf, but if I were to delete it, how would I know which leaf to delete when I next remove the item? The same goes for inserting - how would I know which leaf to jump to next after the current leaf has both children accounted for?
A tree implementation of a binary heap uses a complete tree [or almost full tree: every level is full, except the deepest one].
You always 'know' which is the last occupied leaf - where you delete from [and modifying it is O(logn) after it changed so it is not a problem], and you always 'know' which is the first non-occupied leaf, in which you add elements to [and again, modifying it is also O(logn) after it changed].
The algorithm idea is simple:
insert: insert element to the first non-occupied leaf, and use heapify [sift up] to get this element to its correct place in the heap.
delete_min: replace the first element with the last occupied leaf, and remove the last occupied leaf. then, heapify [sift down] the heap.
EDIT: note that delete() can be done to any element, and not only the head, however - finding the element you want to replace with the last leaf will be O(n), which will make this op expensive. for this reason, the delete() method [besides the head], is usually not a part of the heap data structure.
I really wanted to do this for almost a decade.Finally sat down today and wrote it.Anyone who wants it can use it.I got inspired by Quora founder to relearn Heap.Apparently he was asked how would you find K near points in a set of n points in his Google phone screen.Apparently his answer was to use a Max Heap and to store K values and remove the maximum element after the size of the heap exceeds K.The approach is pretty simple and the worst case is nlog K which is better than n^2 in most sorting cases.Here is the code.
import java.util.ArrayList;
import java.util.List;
/**
* #author Harish R
*/
public class HeapPractise<T extends Comparable<T>> {
private List<T> heapList;
public List<T> getHeapList() {
return heapList;
}
public void setHeapList(List<T> heapList) {
this.heapList = heapList;
}
private int heapSize;
public HeapPractise() {
this.heapList = new ArrayList<>();
this.heapSize = heapList.size();
}
public void insert(T item) {
if (heapList.size() == 0) {
heapList.add(item);
} else {
siftUp(item);
}
}
public void siftUp(T item) {
heapList.add(item);
heapSize = heapList.size();
int currentIndex = heapSize - 1;
while (currentIndex > 0) {
int parentIndex = (int) Math.floor((currentIndex - 1) / 2);
T parentItem = heapList.get(parentIndex);
if (parentItem != null) {
if (item.compareTo(parentItem) > 0) {
heapList.set(parentIndex, item);
heapList.set(currentIndex, parentItem);
currentIndex = parentIndex;
continue;
}
}
break;
}
}
public T delete() {
if (heapList.size() == 0) {
return null;
}
if (heapList.size() == 1) {
T item = heapList.get(0);
heapList.remove(0);
return item;
}
return siftDown();
}
public T siftDown() {
T item = heapList.get(0);
T lastItem = heapList.get(heapList.size() - 1);
heapList.remove(heapList.size() - 1);
heapList.set(0, lastItem);
heapSize = heapList.size();
int currentIndex = 0;
while (currentIndex < heapSize) {
int leftIndex = (2 * currentIndex) + 1;
int rightIndex = (2 * currentIndex) + 2;
T leftItem = null;
T rightItem = null;
int currentLargestItemIndex = -1;
if (leftIndex <= heapSize - 1) {
leftItem = heapList.get(leftIndex);
}
if (rightIndex <= heapSize - 1) {
rightItem = heapList.get(rightIndex);
}
T currentLargestItem = null;
if (leftItem != null && rightItem != null) {
if (leftItem.compareTo(rightItem) >= 0) {
currentLargestItem = leftItem;
currentLargestItemIndex = leftIndex;
} else {
currentLargestItem = rightItem;
currentLargestItemIndex = rightIndex;
}
} else if (leftItem != null && rightItem == null) {
currentLargestItem = leftItem;
currentLargestItemIndex = leftIndex;
}
if (currentLargestItem != null) {
if (lastItem.compareTo(currentLargestItem) >= 0) {
break;
} else {
heapList.set(currentLargestItemIndex, lastItem);
heapList.set(currentIndex, currentLargestItem);
currentIndex = currentLargestItemIndex;
continue;
}
}
}
return item;
}
public static void main(String[] args) {
HeapPractise<Integer> heap = new HeapPractise<>();
for (int i = 0; i < 32; i++) {
heap.insert(i);
}
System.out.println(heap.getHeapList());
List<Node<Integer>> nodeArray = new ArrayList<>(heap.getHeapList()
.size());
for (int i = 0; i < heap.getHeapList().size(); i++) {
Integer heapElement = heap.getHeapList().get(i);
Node<Integer> node = new Node<Integer>(heapElement);
nodeArray.add(node);
}
for (int i = 0; i < nodeArray.size(); i++) {
int leftNodeIndex = (2 * i) + 1;
int rightNodeIndex = (2 * i) + 2;
Node<Integer> node = nodeArray.get(i);
if (leftNodeIndex <= heap.getHeapList().size() - 1) {
Node<Integer> leftNode = nodeArray.get(leftNodeIndex);
node.left = leftNode;
}
if (rightNodeIndex <= heap.getHeapList().size() - 1) {
Node<Integer> rightNode = nodeArray.get(rightNodeIndex);
node.right = rightNode;
}
}
BTreePrinter.printNode(nodeArray.get(0));
}
}
public class Node<T extends Comparable<?>> {
Node<T> left, right;
T data;
public Node(T data) {
this.data = data;
}
}
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
class BTreePrinter {
public static <T extends Comparable<?>> void printNode(Node<T> root) {
int maxLevel = BTreePrinter.maxLevel(root);
printNodeInternal(Collections.singletonList(root), 1, maxLevel);
}
private static <T extends Comparable<?>> void printNodeInternal(
List<Node<T>> nodes, int level, int maxLevel) {
if (nodes.isEmpty() || BTreePrinter.isAllElementsNull(nodes))
return;
int floor = maxLevel - level;
int endgeLines = (int) Math.pow(2, (Math.max(floor - 1, 0)));
int firstSpaces = (int) Math.pow(2, (floor)) - 1;
int betweenSpaces = (int) Math.pow(2, (floor + 1)) - 1;
BTreePrinter.printWhitespaces(firstSpaces);
List<Node<T>> newNodes = new ArrayList<Node<T>>();
for (Node<T> node : nodes) {
if (node != null) {
String nodeData = String.valueOf(node.data);
if (nodeData != null) {
if (nodeData.length() == 1) {
nodeData = "0" + nodeData;
}
}
System.out.print(nodeData);
newNodes.add(node.left);
newNodes.add(node.right);
} else {
newNodes.add(null);
newNodes.add(null);
System.out.print(" ");
}
BTreePrinter.printWhitespaces(betweenSpaces);
}
System.out.println("");
for (int i = 1; i <= endgeLines; i++) {
for (int j = 0; j < nodes.size(); j++) {
BTreePrinter.printWhitespaces(firstSpaces - i);
if (nodes.get(j) == null) {
BTreePrinter.printWhitespaces(endgeLines + endgeLines + i
+ 1);
continue;
}
if (nodes.get(j).left != null)
System.out.print("//");
else
BTreePrinter.printWhitespaces(1);
BTreePrinter.printWhitespaces(i + i - 1);
if (nodes.get(j).right != null)
System.out.print("\\\\");
else
BTreePrinter.printWhitespaces(1);
BTreePrinter.printWhitespaces(endgeLines + endgeLines - i);
}
System.out.println("");
}
printNodeInternal(newNodes, level + 1, maxLevel);
}
private static void printWhitespaces(int count) {
for (int i = 0; i < 2 * count; i++)
System.out.print(" ");
}
private static <T extends Comparable<?>> int maxLevel(Node<T> node) {
if (node == null)
return 0;
return Math.max(BTreePrinter.maxLevel(node.left),
BTreePrinter.maxLevel(node.right)) + 1;
}
private static <T> boolean isAllElementsNull(List<T> list) {
for (Object object : list) {
if (object != null)
return false;
}
return true;
}
}
Please note that BTreePrinter is a code I took somewhere in Stackoverflow long back and I modified to use with 2 digit numbers.It will be broken if we move to 3 digit numbers and it is only for simple understanding of how the Heap structure looks.A fix for 3 digit numbers is to keep everything as multiple of 3.
Also due credits to Sesh Venugopal for wonderful tutorial on Youtube on Heap data structure
public class PriorityQ<K extends Comparable<K>> {
private class TreeNode<T extends Comparable<T>> {
T val;
TreeNode<T> left, right, parent;
public String toString() {
return this.val.toString();
}
TreeNode(T v) {
this.val = v;
left = null;
right = null;
}
public TreeNode<T> insert(T val, int position) {
TreeNode<T> parent = findNode(position/2);
TreeNode<T> node = new TreeNode<T>(val);
if(position % 2 == 0) {
parent.left = node;
} else {
parent.right = node;
}
node.parent = parent;
heapify(node);
return node;
}
private void heapify(TreeNode<T> node) {
while(node.parent != null && (node.parent.val.compareTo(node.val) < 0)) {
T temp = node.val;
node.val = node.parent.val;
node.parent.val = temp;
node = node.parent;
}
}
private TreeNode<T> findNode(int pos) {
TreeNode<T> node = this;
int reversed = 1;
while(pos > 0) {
reversed <<= 1;
reversed |= (pos&1);
pos >>= 1;
}
reversed >>= 1;
while(reversed > 1) {
if((reversed & 1) == 0) {
node = node.left;
} else {
node = node.right;
}
reversed >>= 1;
}
return node;
}
public TreeNode<T> remove(int pos) {
if(pos <= 1) {
return null;
}
TreeNode<T> last = findNode(pos);
if(last.parent.right == last) {
last.parent.right = null;
} else {
last.parent.left = null;
}
this.val = last.val;
bubbleDown();
return null;
}
public void bubbleDown() {
TreeNode<T> node = this;
do {
TreeNode<T> left = node.left;
TreeNode<T> right = node.right;
if(left != null && right != null) {
T max = left.val.compareTo(right.val) > 0 ? left.val : right.val;
if(max.compareTo(node.val) > 0) {
if(left.val.equals(max)) {
left.val = node.val;
node.val = max;
node = left;
} else {
right.val = node.val;
node.val = max;
node = right;
}
} else {
break;
}
} else if(left != null) {
T max = left.val;
if(left.val.compareTo(node.val) > 0) {
left.val = node.val;
node.val = max;
node = left;
} else {
break;
}
} else {
break;
}
} while(true);
}
}
private TreeNode<K> root;
private int position;
PriorityQ(){
this.position = 1;
}
public void insert(K val) {
if(val == null) {
return;
}
if(root == null) {
this.position = 1;
root = new TreeNode<K>(val);
this.position++;
return ;
}
root.insert(val, position);
position++;
}
public K remove() {
if(root == null) {
return null;
}
K val = root.val;
root.remove(this.position-1);
this.position--;
if(position == 1) {
root = null;
}
return val;
}
public static void main(String[] args) {
PriorityQ<Integer> q = new PriorityQ<>();
System.out.println(q.remove());
q.insert(1);
q.insert(11);
q.insert(111);
q.insert(1111);
q.remove();
q.remove();
q.remove();
q.remove();
q.insert(2);
q.insert(4);
}
}

Categories