I am trying to insert in a maxHeap in java and then bubble up the object. This is what I have done, I am not sure how I should approach the bubble up method.
I do understand the algorithm behind bubble up, which is as follows:
get parent node
see if L_childNode is less than parent Node. If Yes, then swap parent with L_child.
see if R_childNode is less than parent Node. If Yes, then swap parent with L_child.
Please point out what am I doing wrong?
private int getLeftChild(int n){
return x*2+1;
}
private int getRightChild(int n){
return x*2+2;
}
public void insert (E item) {
//Integer pos_lastEl= new Integer (heapArray.lastElement());
heapArray.add(item);
bubbleUp(item);
}
//To use to reheap up when item inserted at end of heap (complete tree)
private void bubbleUp(E x){
int place = heapArray.size()-1;
int parent=(place-1)/2;
if ((parent>=0) && (parent.compareTo(heapArray.get(getLeftChild))<0)){
swap(place,parent);
}else ((parent>=0 && (parent.compareTo(heapArray.get(getRightChild))<0))){
swap(place,parent);
}
}
//swaps two objects at index i and j
private void swap(int i, int j){
int max=heapArray.size();
if(i>=0 && i<max && j>=0 && j<max){
E temp=heapArray.get(i);
//put J item in I
heapArray.set(i,heapArray.get(j));
heapArray.set(j,temp);
}
}
Your major problem is using if instead of while to bubble up the newly added element to the proper position.
And there are also some other issues in your code, sorry I had to do some refactoring to make it clean enough:
public class MaxHeapTest<E extends Comparable<E>> {
List<E> heapArray = new ArrayList<>();
public static void main(String... args) {
int N = 13;
MaxHeapTest<Integer> maxHeap = new MaxHeapTest();
for (int i = 0; i < N; ++i) { // ascending;
maxHeap.insert(i);
}
while (!maxHeap.isEmpty()) { // descending now;
System.out.print(maxHeap.delMax() + " ");
}
}
public E delMax() {
E e = heapArray.get(0);
swap(0, heapArray.size() - 1);
heapArray.remove(heapArray.size() - 1);
sinkDown(0);
return e;
}
public void insert(E item) {
heapArray.add(item);
bubbleUp(item);
}
public boolean isEmpty() {
return heapArray.isEmpty();
}
private void bubbleUp(E x) {
int k = heapArray.indexOf(x);
int j = (k - 1) / 2;
while (j >= 0) {
if (heapArray.get(j).compareTo(heapArray.get(k)) < 0) {
swap(k, j);
k = j;
j = (j - 1) / 2;
} else break;
}
}
private void sinkDown(int k) {
int j = 2 * k + 1;
while (j < heapArray.size()) {
if (j < heapArray.size() - 1 && heapArray.get(j).compareTo(heapArray.get(j + 1)) < 0) j++;
if (heapArray.get(k).compareTo(heapArray.get(j)) < 0) {
swap(k, j);
k = j;
j = 2 * j + 1;
} else break;
}
}
private void swap(int i, int j) {
E temp = heapArray.get(i);
heapArray.set(i, heapArray.get(j));
heapArray.set(j, temp);
}
}
After the maxHeap, we can easily output the descending numbers as:
12 11 10 9 8 7 6 5 4 3 2 1 0
Related
I am writing a bin packing program in one dimension. I want only one possible bin. So it does not include a lot of bin its only one. This program is only searching quad groups and explode if quad groups are not equal to the searching number. I want to search every possible group that is bigger than quads.
In example we have 60 60 50 40 45 35 25 15 and we are looking for summing equal to 180 and answer is 60 60 45 15 that's fine but if we search 250 it will not working.
Can you help me?
That's the link for program https://github.com/omerbguclu/BinPacking1D
That's the code for the algorithm o array is the numbers, a array is the location of answers
public BinPacking() {
}
public void binpack(ArrayList<Integer> o, ArrayList<Integer> a, int wanted) {
int sum = 0;
if (wanted > 0) {
control(o, a, wanted);
if (is) {
return;
}
for (int i = 0; i < o.size(); i++) {
sum += o.get(i);
summing(o, a, wanted - sum, i + 1);
if (is) {
a.add(i);
return;
}
for (int j = i; j < o.size(); j++) {
if (i != j) {
sum += o.get(j);
summing(o, a, wanted - sum, j + 1);
if (is) {
a.add(i);
a.add(j);
return;
}
sum -= o.get(j);
}
}
sum -= o.get(i);
// "/////////////*******************////////////////////");
}
if (wanted != sum) {
System.out.println("There is not an answer with quad summing method");
}
}
}
public void summing(ArrayList<Integer> o, ArrayList<Integer> a, int wanted, int loop) {
int sum = 0;
if (loop < o.size() && wanted > 0) {
for (int i = loop; i < o.size(); i++) {
if (wanted == o.get(i)) {
a.add(i);
is = true;
return;
}
for (int j = loop; j < o.size(); j++) {
if (i != j) {
sum = o.get(i) + o.get(j);
if (wanted != sum) {
sum = 0;
} else {
a.add(i);
a.add(j);
is = true;
return;
}
}
// System.out.println("///////////////////////////////////");
}
}
System.out.println("There is not an answer with binary summing method");
}
}
public void control(ArrayList<Integer> o, ArrayList<Integer> a, int wanted) {
for (int i = 0; i < o.size(); i++) {
if (o.get(i) == wanted) {
a.add(i);
is = true;
break;
}
}
}
There is a pretty well established and efficient mechanism for getting every possible combination of a set of objects. Essentially you treat membership of the combination as a BitSet which represents whether each member of the set is in the combination. Then visiting every combination is just visiting every BitSet combination.
Here's how I tend to implement it:
public class Combo<T> implements Iterable<List<T>> {
private final List<T> set;
public Combo(List<T> set) {
this.set = set;
}
public Iterator<List<T>> iterator() {
BitSet combo = new BitSet(set.size());
return new Iterator<List<T>>() {
public boolean hasNext() {
return combo.cardinality() < set.size();
}
public List<T> next() {
int i = 0;
while (combo.get(i))
combo.clear(i++);
combo.set(i);
return combo.stream().mapToObj(set::get).collect(Collectors.toList());
}
};
}
}
So your solution would become:
for (List<Integer> combo: new Combo<>(...)) {
if (combo.size >= 4 && combo.stream.reduce(0, Integer::sum) == total)
....
}
A hackier version of the same idea would be:
for (long l = 0; l < 1 << (input.size() - 1); l++) {
List<Integer> combo = BitSet.valueOf(new long[]{l}).stream()
.mapToObj(input::get).collect(Collectors.toList());
if (combo.stream().mapToInt(n -> n).sum() == total) {
System.out.println(combo);
}
}
I am trying to write a program which can solve the 8-Puzzle problem.I am using the A* algorithm to find the solution.
I have reviewed my code many times and also tried making some changes.
Even my friends tried to help me find the bug,but they couldn't. I still don't understand where i went wrong.I used javadocs to see if I did something wrong,even that din't solve my problem. I have created three classes to solve this problem.
import java.util.*;
public class Solver implements Iterable<State>
{
ArrayList<State> queue,solQueue;
public int sol[][] = { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 0 } };
int temp[][],i;
int moves;
int leastPriority,removeIndex;
State removeTemp;
public Solver(State initial)
{
queue = new ArrayList<State>();
solQueue = new ArrayList<State>();
queue.ensureCapacity(16);
solQueue.ensureCapacity(16);
temp = new int[3][3];
i=1;
leastPriority = 100;
removeTemp=initial;
queue.add(removeTemp);
Iterator<State> qu = queue.iterator();
while(removeTemp.m!=sol)
{
leastPriority = 100;
i=0;
queue.iterator();
for (State s : queue)
{
if((s.mh + s.count) <leastPriority)
{
leastPriority = (s.mh + s.count);
removeIndex = i;
}
if(qu.hasNext())
i++;
}
for(State s : removeTemp.neighbours() )
{
queue.add(s);
}
removeTemp=queue.remove(removeIndex);
solQueue.add(removeTemp);
}
this.moves();
this.solution();
}
public int moves()
{
System.out.print("Solution found out in "+ moves+" moves");
moves = removeTemp.count;
return moves;
}
public Iterable<State> solution()
{
for(State s : solQueue)
{
System.out.println(s.m);
System.out.println("");
}
return solQueue;
}
#SuppressWarnings({ "unchecked", "rawtypes" })
#Override
public Iterator iterator() {
return null;
}
}
And the JVM is throwing an exception.
Exception in thread "main" java.lang.IndexOutOfBoundsException: Index: 0,Size: 0
at java.util.ArrayList.rangeCheck(Unknown Source)
at java.util.ArrayList.get(Unknown Source)
at Solver.<init>(Solver.java:41)
at Main.main(Main.java:13)
What i don't understand is that how can the size of the ArrayList be 1 when i have explicitly state it as 16.
The State Class has the heuristic function which is suppose to make the algorithm efficient.The following is the State Class.
import java.util.ArrayList;
import java.util.Iterator;
public class State implements Iterable<State>
{
public int sol[][] = { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 0 } };
int m[][], bi, bj, count, priority, si, sj;
int i,j,tempm[][];
int mh = 0;
boolean isInitialState, isRepeatedState;
State previousState, tempState;
ArrayList<State> neighbourStates;
public State(State s, int c, int[][] array)
{
neighbourStates = new ArrayList<State>();
neighbourStates.ensureCapacity(16);
tempState =this;
m = new int[3][3];
m=array;
if (s == null)
{
isInitialState = true;
count = 0;
previousState =null;
}
else
{
previousState = s;
count = c+1;
}
this.findZero();
this.manhattanHeuristic();
}
private void findZero()
{
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
{
if(m[i][j]==0)
{
bi=i;
bj=j;
}
}
}
private void manhattanHeuristic() {
int n = 1;
mh = 0;
for (int i = 0; i < 3; i++)
Z: for (int j = 0; j < 3; j++) {
if ((i == bi) && (j == bj)) {
continue Z;
}
else if (m[i][j] == n) {
n++;
}
else {
this.getSolutionIndex();
mh = mh + Math.abs(i - si) + Math.abs(j - sj);
}
}
}
void getSolutionIndex() {
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++) {
if (m[i][j] == 0) {
si = i;
sj = j;
}
}
}
public Iterable<State> neighbours()
{
tempm = m;
this.up();
if(!(equals(tempm)))
{
tempState = new State(this,count,tempm);
neighbourStates.add(tempState);
}
this.down();
if(!(equals(tempm)))
{
tempState = new State(this,count,tempm);
neighbourStates.add(tempState);
}
this.left();
if(!(equals(tempm)))
{
tempState = new State(this,count,tempm);
neighbourStates.add(tempState);
}
this.right();
if(!(equals(tempm)))
{
tempState = new State(this,count,tempm);
neighbourStates.add(tempState);
}
return neighbourStates;
}
public boolean equals(int s[][])
{
if((isInitialState==false)&&(previousState.m == s))
return true;
else
return false;
}
#Override
public Iterator<State> iterator() {
// TODO Auto-generated method stub
return null;
}
public void up()
{
if ((bi > 1) && (bi < 2) && (bj < 3)&& (bj > 1))
{
i = bi;
i = i + 1;
this.move(i,bj);
}
}
public void down()
{
if ((bi > 2) && (bi < 3) && (bj < 3) && (bj > 1))
{
i = bi;
i = i - 1;
this.move(i,bj);
}
}
public void left()
{
if ((bi > 1) && (bi < 3) && (bj < 2)&& (bj > 1)) {
j = bj;
j = j + 1;
this.move(bi, j);
}
}
public void right()
{
if ((bi > 1) && (bi < 3) && (bj < 3) && (bj > 2)) {
j = bj;
j = j - 1;
this.move(bi, j);
}
}
public void move(int x, int y) {
{
tempm = m;
}
if ((tempm[x + 1][y] == 0) || (tempm[x - 1][y] == 0) || (tempm[x][y + 1] == 0)|| (tempm[x][y - 1] == 0)) {
tempm[bi][bj] = tempm[x][y];
tempm[x][y] = 0;
bi = x;
bj = y;
}
}
}
And the finally the class with the main function.
import java.util.Scanner;
public class Main {
public static void main(String[] args)
{
#SuppressWarnings("resource")
Scanner sc = new Scanner(System.in);
int[][] tiles = new int[3][3];
System.out.println("Enter the elements");
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
tiles[i][j] = sc.nextInt();
State initial = new State(null,0,tiles);
Solver solver = new Solver(initial);
solver.solution();
System.out.println("Minimum number of moves = " + solver.moves());
}
}
What i don't understand is that how can the size of the ArrayList be 1 when i have explicitly state it as 16.
You did not set the size of the ArrayList to 16. You've set the capacity:
queue.ensureCapacity(16);
solQueue.ensureCapacity(16);
This does not make the ArrayList have a size of 16.
An ArrayList has an array to hold its data. When you add more elements to the ArrayList and its internal array is full, it will have to allocate a larger array and copy the content of what it currently holds plus the new element.
The capacity of the ArrayList is the minimum size that the internal array has. You can use ensureCapacity to make sure that the ArrayList doesn't have to resize too often (resizing and copying the content is an expensive operation). So, ensureCapacity is a call you make to make it work effiently.
It does not make the ArrayList have 16 elements; it only makes sure that the ArrayList has room for at least 16 elements.
If you want the ArrayList to have 16 elements, you'll have to add those elements one by one.
Size of the collection and the capacity are 2 different concepts.
capacity represents the maximum size of items a collection can hold without a reallocation.
size represents the current number of items in the collection.
IndexOutOfBoundsException is saying that you are trying to access an item with index that does not exist in the collection.
please try the below code in Solver.java
if(!queue.isEmpty())
removeTemp=queue.remove(removeIndex);
else
break;
I tried to build a minHeap using java, this is my code:
public class MyMinHeap {
private ArrayList<Node> heap;
public MyMinHeap() {
heap = new ArrayList<Node>();
}
public MyMinHeap(ArrayList<Node> nodeList) {
heap = nodeList;
buildHeap();
}
public void buildHeap() {
int i = heap.size() / 2;
while (i >= 0) {
minHeapify(i);
i--;
}
}
public Node extractMin() {
if (heap.size() <= 0) return null;
Node minValue = heap.get(0);
heap.set(0, heap.get(heap.size() - 1));
heap.remove(heap.size() - 1);
minHeapify(0);
return minValue;
}
public String toString() {
String s = "";
for (Node n : heap) {
s += n + ",";
}
return s;
}
public void minHeapify(int i) {
int left = 2 * i + 1;
int right = 2 * i + 2;
int smallest = i;
if (left < heap.size() - 1 && lessThan(left, smallest))
smallest = left;
if (right < heap.size() - 1 && lessThan(right, smallest))
smallest = right;
if (smallest != i) {
swap(smallest, i);
minHeapify(smallest);
}
}
private void swap(int i, int j) {
Node t = heap.get(i);
heap.set(i, heap.get(j));
heap.set(j, t);
}
public boolean lessThan(int i, int j) {
return heap.get(i)
.compareTo(heap.get(j)) < 0;
}
public static void main(String[] args) {
char[] chars = {'a', 'b', 'c', 'd', 'e', 'f'};
int[] freqs = {45, 13, 12, 16, 9, 5};
ArrayList<Node> data = new ArrayList<Node>();
for (int i = 0; i < chars.length; i++) {
data.add(new Node(chars[i], freqs[i]));
}
MyMinHeap heap = new MyMinHeap(data);
System.out.println("print the heap : " + heap);
for (int i = 0; i < chars.length; i++) {
System.out.println("Smallest is :" + heap.extractMin());
}
}
}
The output should be:5,9,12,13,16,45,
but what I got is : 9,13,12,16,45
I have debugged this but still can't figure out, anybody help? thanks a lot.
Insert :
When we insert into a min-heap, we always start by inserting the element at the bottom. We insert at the
rightmost spot so as to maintain the complete tree property.
Then, we "fix" the tree by swapping the new element with its parent, until we find an appropriate spot for
the element. We essentially bubble up the minimum element.
This takes 0 (log n) time, where n is the number of nodes in the heap.
Extract Minimum Element :
Finding the minimum element of a min-heap is easy: it's always at the top. The trickier part is how to remove
it. (I n fact, this isn't that tricky.)
First, we remove the minimum element and swap it with the last element in the heap (the bottommost,
rightmost element). Then, we bubble down this element, swapping it with one of its children until the minheap
property is restored.
Do we swap it with the left child or the right child? That depends on their values. There's no inherent
ordering between the left and right element, but you'll need to take the smaller one in order to maintain
the min-heap ordering.
public class MinHeap {
private int[] heap;
private int size;
private static final int FRONT = 1;
public MinHeap(int maxSize) {
heap = new int[maxSize + 1];
size = 0;
}
private int getParent(int position) {
return position / 2;
}
private int getLeftChild(int position) {
return position * 2;
}
private int getRightChild(int position) {
return position * 2 + 1;
}
private void swap(int position1, int position2) {
int temp = heap[position1];
heap[position1] = heap[position2];
heap[position2] = temp;
}
private boolean isLeaf(int position) {
if (position > size / 2) {
return true;
}
return false;
}
public void insert(int data) {
heap[++size] = data;
int currentItemIndex = size;
while (heap[currentItemIndex] < heap[getParent(currentItemIndex)]) {
swap(currentItemIndex, getParent(currentItemIndex));
currentItemIndex = getParent(currentItemIndex);
}
}
public int delete() {
int item = heap[FRONT];
swap(FRONT, size--); // heap[FRONT] = heap[size--];
heapify(FRONT);
return item;
}
private void heapify(int position) {
if (isLeaf(position)) {
return;
}
if (heap[position] > heap[getLeftChild(position)]
|| heap[position] > heap[getRightChild(position)]) {
// if left is smaller than right
if (heap[getLeftChild(position)] < heap[getRightChild(position)]) {
// swap with left
swap(heap[position], heap[getLeftChild(position)]);
heapify(getLeftChild(position));
} else {
// swap with right
swap(heap[position], heap[getRightChild(position)]);
heapify(getRightChild(position));
}
}
}
#Override
public String toString() {
StringBuilder output = new StringBuilder();
for (int i = 1; i <= size / 2; i++) {
output.append("Parent :" + heap[i]);
output
.append("LeftChild : " + heap[getLeftChild(i)] + " RightChild :" + heap[getRightChild(i)])
.append("\n");
}
return output.toString();
}
public static void main(String... arg) {
System.out.println("The Min Heap is ");
MinHeap minHeap = new MinHeap(15);
minHeap.insert(5);
minHeap.insert(3);
minHeap.insert(17);
minHeap.insert(10);
minHeap.insert(84);
minHeap.insert(19);
minHeap.insert(6);
minHeap.insert(22);
minHeap.insert(9);
System.out.println(minHeap.toString());
System.out.println("The Min val is " + minHeap.delete());
}
}
The problem is in your minHeapify function. You have:
public void minHeapify(int i) {
int left = 2 * i + 1;
int right = 2 * i + 2;
int smallest = i;
if (left < heap.size() - 1 && lessThan(left, smallest))
smallest = left;
if (right < heap.size() - 1 && lessThan(right, smallest))
smallest = right;
Now, let's say that your initial array list is {3,2}, and you call minHeapify(0).
left = 2 * i + 1; // = 1
right = 2 * i + 2; // = 2
smallest = i; // 0
Your next statement:
if (left < heap.size() - 1 && lessThan(left, smallest))
At this point, left = 1, and heap.size() returns 2. So left isn't smaller than heap.size() - 1. So your function exits without swapping the two items.
Remove the - 1 from your conditionals, giving:
if (left < heap.size() && lessThan(left, smallest))
smallest = left;
if (right < heap.size() && lessThan(right, smallest))
smallest = right;
I have two Arrays 1 with strings and another one with ints.
I have to use insertion sorts to print this list in acceding order numerical wise this is my code so far
these are the arrays:
String[]bn={"Cardinals","BlueJays","Albatross","Vultures","Crows","Mockingbirds","Condors","BaldEagles","Pigeons","RedHeadWoodPecker","Hummingbirds","Dodos"};
int[]bq={40,15,1,3,10,2,12,25,7,6,88,15};
public static void SortNumericalOrdernsert (String[] bn,int[] bq){
for(int i=1;i<bq.length;i++){
int next=bq[i];
String y=bn[i];
//find all the insertion location
//Move all the larger elements up
int j=i;
while(j>0 && bq[j-1]>next){
bn[j]=bn[j-1];
bq[j]=bq[j-1];
j--;
}
//insert the element
bq[j]=next;
bn[j]=y;
}
}}
Where am i doing it wrong?
// edited
You want to do like this?
public static void SortNumericalOrdernsert(String[] bn, int[] bq) {
for (int i = 1; i < bq.length; i++) {
int next = bq[i];
// find all the insertion location
// Move all the larger elements up
int j = i;
while (j > 0 && bq[j - 1] > next) {
bq[j] = bq[j - 1];
j--;
}
bq[j] = next;
}
for (int i = 1; i < bn.length; i++) {
String y = bn[i];
int j = i;
while (j > 0 && isBigger(bn[j - 1], y)) {
bn[j] = bn[j - 1];
j--;
}
bn[j] = y;
}
}
private static boolean isBigger(String left, String right) {
return left.compareTo(right) > 0;
}
The purpose of this program is to find the kth smallest element in an array without sorting the array using a recursive and nonrecursive decrease and conquer type method.
I was hoping someone could look over my code and try to help me with my array out of bounds error(s).
The method that is throwing these errors is the recursive selection the non recursive selection works fine.
My driver is also attached and everything should compile if you want to test my code.
public class KthSmallest
{
private int counter;
private int term;
private int[] A;
int SelectionNonRecursive(int A[], int kthSmallest, int sizeOfA)
{
this.A = A;
if(kthSmallest == 1 || kthSmallest == sizeOfA)
{
return (LinearSearch(kthSmallest, sizeOfA));
}
else
{
for(int i = 0; i<sizeOfA; i++)
{
counter = 0;
for(int j = 0; j<sizeOfA; j++)
{
if(A[i] < A[j])
{
counter++;
}
}
if((sizeOfA - counter) == kthSmallest)
{
return A[i];
}
}
}
return 0;
}
int SelectionRecursive(int A[], int kthSmallest, int sizeOfA)
{
this.A = A;
return Selection_R(0, sizeOfA - 1, kthSmallest);
}
int Selection_R(int l, int r, int kthSmallest)
{
if(l<r)
{
if(kthSmallest == 1 || kthSmallest == A.length)
{
return (LinearSearch(kthSmallest, A.length));
}
else
{
int s = LomutoPartition(l, r);
if(s == kthSmallest - 1)
{
return A[s];
}
else if(s > (A[0] + kthSmallest - 1))
{
Selection_R(l, s-1, kthSmallest);
}
else
{
Selection_R(s+1, r, kthSmallest);
}
}
}
return 0;
}
int LomutoPartition(int l, int r)
{
int pivot = A[l];
int s = l;
for(int i = l+1; i<r; i++)
{
if(A[i] < pivot)
{
s += 1;
swap(A[s], A[i]);
}
}
swap(A[l], A[s]);
return s;
}
public void swap(int i, int j)
{
int holder = A[i];
A[i] = A[j];
A[j] = holder;
}
int LinearSearch(int kthSmallest, int sizeOfA)
{
term = A[0];
for(int i=1; i<sizeOfA; i++)
{
if(kthSmallest == 1)
{
if(term > A[i])
{
term = A[i];
}
}
else
{
if(term < A[i])
{
term = A[i];
}
}
}
return term;
}
}
public class KthDriver
{
public static void main(String[] args)
{
KthSmallest k1 = new KthSmallest();
int[] array = {7,1,5,9,3};
System.out.print(k1.SelectionRecursive(array, 3, array.length));
}
}
Inside your LomutoPartition method, you are passing the array elements in your swap method: -
swap(A[s], A[i]); // Inside for loop
and
swap(A[l], A[s]); // Outside for loop
And your swap method considers them as indices: -
public void swap(int i, int j) <-- // `i` and `j` are elements A[s] and A[i]
{
int holder = A[i]; <-- // You are accessing them as indices(A[i] -> A[A[s]])
A[i] = A[j];
A[j] = holder;
}
That is why you are getting that exception. Because, if any element in array is greater than size, it will blast out.
You should change your invocation to: -
swap(s, i); // Inside for loop
and
swap(l, s); // Outside for loop
respectively. And leave your method as it is.
Note that, you should pass array indices, and not array elements. If you pass array elements, then the swapping in the method will not be reflected in your array. Because, your method will have its own copy of your elements.