I am learning sorting algorithms. I have gone through a program given on the following link. For the sake of simplicity I am attaching both link and program itself.
public class Mergesort {
private int[] numbers;
private int[] helper;
private int number;
public void sort(int[] values) {
this.numbers = values;
number = values.length;
this.helper = new int[number];
mergesort(0, number - 1);
}
private void mergesort(int low, int high) {
if (low < high) {
int middle = low + (high - low) / 2;
mergesort(low, middle);
mergesort(middle + 1, high);
merge(low, middle, high);
}
}
private void merge(int low, int middle, int high) {
for (int i = low; i <= high; i++) {
helper[i] = numbers[i];
}
int i = low;
int j = middle + 1;
int k = low;
while (i <= middle && j <= high) {
if (helper[i] <= helper[j]) {
numbers[k] = helper[i];
i++;
} else {
numbers[k] = helper[j];
j++;
}
k++;
}
while (i <= middle) {
numbers[k] = helper[i];
k++;
i++;
}
}
}
I am not getting any clue that in merge method why this last while(i<=middle) is included. Means while(j<=high) was also there, but this condition was ignored.
The link where I got this program is http://www.vogella.com/tutorials/JavaAlgorithmsMergesort/article.html
Sorry for my bad explanation. Hope someone can explain it to me.
The clue is actually in the referenced article:
// Copy the rest of the left side of the array into the target array
while (i <= middle) {
numbers[k] = helper[i];
k++;
i++;
}
Consider the case when numbers in the first half are all greater than the numbers in the second half. Then in the first while cycle you'll only increase j, you will not copy any numbers from the first half. The second while cycle copies the remaining numbers from the first half.
A good question is why you actually don't need to copy tthe remaining numbers from the second half. I'll leave it to you. :)
I am trying to implement quick sort using Java.The partition function does what it should do.That is,partition the array around the pivot(I've chosen the element as the pivot). But the final output is not in sorted order.I cannot figure the error out.Can someone help?
public class Quick_sort {
public static int arr[] = {11, 2, 7, 1, 5, 4, 12, 65, 23};
public static int temp = 0;
public static void main(String args[]) {
int p=0;
int r=arr.length;
quick_sort(p,r);
for(int i: arr)
System.out.println(i);
}
public static int partition(int p, int r) {
if(p < r) {
int pivot=arr[p];
int i=1;
for(int j=1;j<r;j++) {
if(arr[j]<pivot) {
temp=arr[j];
arr[j]=arr[i];
arr[i]=temp;
i++;
}
}
temp=arr[i-1];
arr[i-1]=arr[p];
arr[p]=temp;
for(int m=0;m<r;m++) {
if(arr[m]==pivot) {
temp=m;
}
}
}
return temp;
}
public static void quick_sort(int p,int r) {
if(p>=r) return;
int index=partition(p,r);
quick_sort(p,index-1);
quick_sort(index+1,r-1);
}
}
In your last line
quick_sort(index+1,r-1);
You skip the last element of the array. But the last element should be sorted as well. Try it with:
quick_sort(index+1,r);
And it is better to adapt the variables i and j in the partition method to the current processed part of the array.
So I tried to fix it. Try it with (main function):
int r=arr.length-1;
and change the partition function to:
public static int partition(int p, int r) {
if(p < r) {
int pivot=arr[p];
int i= p ;
for(int j=(p+1);j<=r;j++) {
if(arr[j]<pivot) {
temp=arr[j];
arr[j]=arr[i + 1];
arr[i + 1] = arr[i];
arr[i] = temp;
i++;
}
}
temp = i;
}
return temp;
}
as well as the in the quick-sort method:
quick_sort(p,index-1);
quick_sort(index+1,r);
Do you see your problem? Your main problem was to not adapt the variables to the smaller parts you are actually looking at at the moment. It did well for the first partition round, but not for the following, as you had the former variables.
This is a complete example of a QuickSort implementation :
public class QuickSort {
public static void main(String[] args) {
int[] x = { 9, 2, 4, 7, 3, 7, 10 };
System.out.println(Arrays.toString(x));
int low = 0;
int high = x.length - 1;
quickSort(x, low, high);
System.out.println(Arrays.toString(x));
}
public static void quickSort(int[] arr, int low, int high) {
if (arr == null || arr.length == 0)
return;
if (low >= high)
return;
// pick the pivot
int middle = low + (high - low) / 2;
int pivot = arr[middle];
// make left < pivot and right > pivot
int i = low, j = high;
while (i <= j) {
while (arr[i] < pivot) {
i++;
}
while (arr[j] > pivot) {
j--;
}
if (i <= j) {
int temp = arr[i];
arr[i] = arr[j];
arr[j] = temp;
i++;
j--;
}
}
// recursively sort two sub parts
if (low < j)
quickSort(arr, low, j);
if (high > i)
quickSort(arr, i, high);
}
}
you can find more here.
I'm trying to count minimum swaps(only consecutive swaps) in an array sorted by mergesort. It works for some cases but this case doesn't work for example: http://puu.sh/kC9mg/65e055807f.png. The first number is how many numbers it should sort, then you enter the numbers. In that case it should print 1 because the number of minimum consecutive swaps is 1 in this case which will swap 4 and 3.
This is the code I have:
public class MergeSort {
private int[] numbers;
private int[] helper;
private int number;
private long swapCounter = 0;
public MergeSort(int[] inputNumbers)
{
numbers = inputNumbers;
number = inputNumbers.length;
helper = new int[number];
mergesort(0, number-1);
}
private void mergesort(int low, int high) {
// check if low is smaller then high, if not then the array is sorted
if (low < high) {
// Get the index of the element which is in the middle
int middle = low + (high - low) / 2;
// Sort the left side of the array
mergesort(low, middle);
// Sort the right side of the array
mergesort(middle + 1, high);
// Combine them both
merge(low, middle, high);
}
}
private void merge(int low, int middle, int high) { // Merge it
long internCounter = 0;
for (int i = low; i <= high; i++) { // Copy both parts into the helper array
helper[i] = numbers[i];
}
int i = low;
int j = middle + 1;
int k = low;
while (i <= middle && j <= high) { // Copy the smallest values from either the left or the right side back to the original array
if (helper[i] < helper[j]) {
numbers[k] = helper[i];
i++;
internCounter++;
} else {
numbers[k] = helper[j];
j++;
swapCounter += internCounter;
}
k++;
}
while (i <= middle) { // Copy the rest of the left side of the array into the target array
numbers[k] = helper[i];
k++;
i++;
swapCounter += internCounter;
}
}
public long getCounter() // Get the counter
{
return this.swapCounter;
}
}
And this is my main class:
import java.util.Scanner;
public class Fr {
public static void main(String[] args)
{
Scanner input = new Scanner(System.in);
int numberOfStudents;
int[] inputNumbers2;
numberOfStudents = input.nextInt();
inputNumbers2 = new int[numberOfStudents];
for(int i = 0; i < numberOfStudents; i++)
{
inputNumbers2[i] = input.nextInt();
}
MergeSort ms = new MergeSort(inputNumbers2);
System.out.println(ms.getCounter());
input.close();
}
}
Do anyone have any thoughts what could be wrong?
I don't think you need the intern counter at all. Just count how many positions you swap an element when taking an element from the high half:
public class MergeSort {
private int[] numbers;
private int[] helper;
private int number;
private long swapCounter = 0;
public MergeSort(int[] inputNumbers)
{
numbers = inputNumbers;
number = inputNumbers.length;
helper = new int[number];
mergesort(0, number-1);
}
private void mergesort(int low, int high) {
// check if low is smaller then high, if not then the array is sorted
if (low < high) {
// Get the index of the element which is in the middle
int middle = low + (high - low) / 2;
// Sort the left side of the array
mergesort(low, middle);
// Sort the right side of the array
mergesort(middle + 1, high);
// Combine them both
merge(low, middle, high);
}
}
private void merge(int low, int middle, int high) { // Merge it
for (int i = low; i <= high; i++) { // Copy both parts into the helper array
helper[i] = numbers[i];
}
int i = low;
int j = middle + 1;
int k = low;
while (i <= middle && j <= high) { // Copy the smallest values from either the left or the right side back to the original array
if (helper[i] < helper[j]) {
numbers[k] = helper[i];
i++;
} else {
numbers[k] = helper[j];
swapCounter += (j-k);
j++;
}
k++;
}
while (i <= middle) { // Copy the rest of the left side of the array into the target array
numbers[k] = helper[i];
k++;
i++;
}
}
public long getCounter() // Get the counter
{
return this.swapCounter;
}
}
I'm a programming student and rather than post the whole assignment I'll just ask for help solving what I've tried for hours now to understand. I'm tasked with sorting an array of strings using the quicksort method. Everything else I've been tasked with as part of this problem is fine but when I tested the sorting method by printing out the String Array, it's completely jumbled up without any seeming rhyme or reason. Please help me pinpoint the error in my code, or the several glaring errors I've overlooked. The array of strings provided is this list of 65 names: http://pastebin.com/jRrgeV1E and the method's code is below:
private static void quickSort(String[] a, int start, int end)
{
// index for the "left-to-right scan"
int i = start;
// index for the "right-to-left scan"
int j = end;
// only examine arrays of 2 or more elements.
if (j - i >= 1)
{
// The pivot point of the sort method is arbitrarily set to the first element int the array.
String pivot = a[i];
// only scan between the two indexes, until they meet.
while (j > i)
{
// from the left, if the current element is lexicographically less than the (original)
// first element in the String array, move on. Stop advancing the counter when we reach
// the right or an element that is lexicographically greater than the pivot String.
while (a[i].compareTo(pivot) < 0 && i <= end && j > i){
i++;
}
// from the right, if the current element is lexicographically greater than the (original)
// first element in the String array, move on. Stop advancing the counter when we reach
// the left or an element that is lexicographically less than the pivot String.
while (a[j].compareTo(pivot) > 0 && j >= start && j >= i){
j--;
}
// check the two elements in the center, the last comparison before the scans cross.
if (j > i)
swap(a, i, j);
}
// At this point, the two scans have crossed each other in the center of the array and stop.
// The left partition and right partition contain the right groups of numbers but are not
// sorted themselves. The following recursive code sorts the left and right partitions.
// Swap the pivot point with the last element of the left partition.
swap(a, start, j);
// sort left partition
quickSort(a, start, j - 1);
// sort right partition
quickSort(a, j + 1, end);
}
}
/**
* This method facilitates the quickSort method's need to swap two elements, Towers of Hanoi style.
*/
private static void swap(String[] a, int i, int j)
{
String temp = a[i];
a[i] = a[j];
a[j] = temp;
}
Ok, i was mistaken that it would work and found your tiny mistake.
Take a look at wikipedias pseudo code
You will notice that your conditions in the while loop are causing the error
if you change (a[i].compareTo(pivot) < 0 && i <= end && j > i) and (a[j].compareTo(pivot) > 0 && j >= start && j >= i) to
(a[i].compareTo(pivot) <= 0 && i < end && j > i) and (a[j].compareTo(pivot) >= 0 && j > start && j >= i).
Thought this would help for those who seek for a string sorting algorithm based on quick sorting method.
public class StringQuickSort {
String names[];
int length;
public static void main(String[] args) {
StringQuickSort sorter = new StringQuickSort();
String words[] = {"zz", "aa", "cc", "hh", "bb", "ee", "ll"}; // the strings need to be sorted are put inside this array
sorter.sort(words);
for (String i : words) {
System.out.print(i);
System.out.print(" ");
}
}
void sort(String array[]) {
if (array == null || array.length == 0) {
return;
}
this.names = array;
this.length = array.length;
quickSort(0, length - 1);
}
void quickSort(int lowerIndex, int higherIndex) {
int i = lowerIndex;
int j = higherIndex;
String pivot = this.names[lowerIndex + (higherIndex - lowerIndex) / 2];
while (i <= j) {
while (this.names[i].compareToIgnoreCase(pivot) < 0) {
i++;
}
while (this.names[j].compareToIgnoreCase(pivot) > 0) {
j--;
}
if (i <= j) {
exchangeNames(i, j);
i++;
j--;
}
}
//call quickSort recursively
if (lowerIndex < j) {
quickSort(lowerIndex, j);
}
if (i < higherIndex) {
quickSort(i, higherIndex);
}
}
void exchangeNames(int i, int j) {
String temp = this.names[i];
this.names[i] = this.names[j];
this.names[j] = temp;
}
}
I am trying to make a merge sort method, but it keeps on giving the wrong sorts. Where do I have change to make it actually sort the array? What part of the code has to be different? Thank you for your time.
public static void mergeSort(int[] array, int left, int lHigh, int right, int rHigh) {
int elements = (rHigh - lHigh +1) ;
int[] temp = new int[elements];
int num = left;
while ((left <= lHigh) && (right <= rHigh)){
if (a[left] <= array[right]) {
temp[num] = array[left];
left++;
}
else {
temp[num] = array[right];
right++;
}
num++;
}
while (left <= right){
temp[num] = array[left]; // I'm getting an exception here, and is it because of the num???
left += 1;
num += 1;
}
while (right <= rHigh) {
temp[num] = array[right];
right += 1;
num += 1;
}
for (int i=0; i < elements; i++){
array[rHigh] = temp[rHigh];
rHigh -= 1;
}
EDIT: now the mergeSort doesn't really sort the numbers, can someone tell me where it specifically is? especially when I print the "Testing merge sort" part.
First of all, I'm assuming this is academic rather than practical, since you're not using a built in sort function. That being said, here's some help to get you moving in the right direction:
Usually, one can think of a merge sort as two different methods: a merge() function that merges two sorted lists into one sorted list, and mergeSort() which recursively breaks the list into single element lists. Since a single element list is sorted already, you then merge all the lists together into one big sorted list.
Here's some off-hand pseudo-code:
merge(A, B):
C = empty list
While A and B are not empty:
If the first element of A is smaller than the first element of B:
Remove first element of A.
Add it to the end of C.
Otherwise:
Remove first element of B.
Add it to the end of C.
If A or B still contains elements, add them to the end of C.
mergeSort(A):
if length of A is 1:
return A
Split A into two lists, L and R.
Q = merge(mergeSort(L), mergeSort(R))
return Q
Maybe that'll help clear up where you want to go.
If not, there's always MergeSort at wikipedia.
Additional:
To help you out, here are some comments inline in your code.
public static void mergeSort(int[] array, int left, int lHigh, int right, int rHigh) {
// what do lHigh and rHigh represent?
int elements = (rHigh - lHigh +1) ;
int[] temp = new int[elements];
int num = left;
// what does this while loop do **conceptually**?
while ((left <= lHigh) && (right <= rHigh)){
if (a[left] <= a[right]) {
// where is 'pos' declared or defined?
temp[pos] = a[left];
// where is leftLow declared or defined? Did you mean 'left' instead?
leftLow ++;
}
else {
temp[num] = a[right];
right ++;
}
num++;
}
// what does this while loop do **conceptually**?
while (left <= right){
// At this point, what is the value of 'num'?
temp[num] = a[left];
left += 1;
num += 1;
}
while (right <= rHigh) {
temp[num] = a[right];
right += 1;
num += 1;
}
// Maybe you meant a[i] = temp[i]?
for (int i=0; i < elements; i++){
// what happens if rHigh is less than elements at this point? Could
// rHigh ever become negative? This would be a runtime error if it did
a[rHigh] = temp[rHigh];
rHigh -= 1;
}
I'm purposefully being vague so you think about the algorithm. Try inserting your own comments into the code. If you can write what is conceptually happening, then you may not need Stack Overflow :)
My thoughts here are that you are not implementing this correctly. This is because it looks like you're only touching the elements of the array only once (or close to only once). This means you have a worst case scenario of O(N) Sorting generally takes at least O(N * log N) and from what I know, the simpler versions of merge sort are actually O(N^2).
More:
In the most simplistic implementation of merge sort, I would expect to see some sort of recursion in the mergeSort() method. This is because merge sort is generally defined recursively. There are ways to do this iteratively using for and while loops, but I definitely don't recommend it as a learning tool until you get it recursively.
Honestly, I suggest taking either my pseudo-code or the pseudo-code you may find in a wikipedia article to implement this and start over with your code. If you do that and it doesn't work correctly still, post it here and we'll help you work out the kinks.
Cheers!
And finally:
// Precondition: array[left..lHigh] is sorted and array[right...rHigh] is sorted.
// Postcondition: array[left..rHigh] contains the same elements of the above parts, sorted.
public static void mergeSort(int[] array, int left, int lHigh, int right, int rHigh) {
// temp[] needs to be as large as the number of elements you're sorting (not half!)
//int elements = (rHigh - lHigh +1) ;
int elements = rHigh - left;
int[] temp = new int[elements];
// this is your index into the temp array
int num = left;
// now you need to create indices into your two lists
int iL = left;
int iR = right;
// Pseudo code... when you code this, make use of iR, iL, and num!
while( temp is not full ) {
if( left side is all used up ) {
copy rest of right side in.
make sure that at the end of this temp is full so the
while loop quits.
}
else if ( right side is all used up) {
copy rest of left side in.
make sure that at the end of this temp is full so the
while loop quits.
}
else if (array[iL] < array[iR]) { ... }
else if (array[iL] >= array[iR]) { ... }
}
}
public class MergeSort {
public static void main(String[] args) {
int[] arr = {5, 4, 7, 2, 3, 1, 6, 2};
print(arr);
new MergeSort().sort(arr, 0, arr.length - 1);
}
private void sort(int[] arr, int lo, int hi) {
if (lo < hi) {
int mid = (lo + hi) / 2;
sort(arr, lo, mid); // recursive call to divide the sub-list
sort(arr, mid + 1, hi); // recursive call to divide the sub-list
merge(arr, lo, mid, hi); // merge the sorted sub-lists.
print(arr);
}
}
private void merge(int[] arr, int lo, int mid, int hi) {
// allocate enough space so that the extra 'sentinel' value
// can be added. Each of the 'left' and 'right' sub-lists are pre-sorted.
// This function only merges them into a sorted list.
int[] left = new int[(mid - lo) + 2];
int[] right = new int[hi - mid + 1];
// create the left and right sub-list for merging into original list.
System.arraycopy(arr, lo, left, 0, left.length - 1);
System.arraycopy(arr, mid + 1, right, 0, left.length - 1);
// giving a sentinal value to marking the end of the sub-list.
// Note: The list to be sorted is assumed to contain numbers less than 100.
left[left.length - 1] = 100;
right[right.length - 1] = 100;
int i = 0;
int j = 0;
// loop to merge the sorted sequence from the 2 sub-lists(left and right)
// into the main list.
for (; lo <= hi; lo++) {
if (left[i] <= right[j]) {
arr[lo] = left[i];
i++;
} else {
arr[lo] = right[j];
j++;
}
}
}
// print the array to console.
private static void print(int[] arr) {
System.out.println();
for (int i : arr) {
System.out.print(i + ", ");
}
}
}
Here's another!
private static int[] mergeSort(int[] input){
if (input.length == 1)
return input;
int length = input.length/2;
int[] left = new int[length];
int[] right = new int[input.length - length];
for (int i = 0; i < length; i++)
left[i] = input[i];
for (int i = length; i < input.length; i++)
right[i-length] = input[i];
return merge(mergeSort(left),mergeSort(right));
}
private static int[] merge(int[] left, int[] right){
int[] merged = new int[left.length+right.length];
int lengthLeft = left.length;
int lengthRight = right.length;
while (lengthLeft > 0 && lengthRight > 0){
if (left[left.length - lengthLeft] < right[right.length - lengthRight]){
merged[merged.length -lengthLeft-lengthRight] = left[left.length - lengthLeft];
lengthLeft--;
}else{
merged[merged.length - lengthLeft-lengthRight] = right[right.length - lengthRight];
lengthRight--;
}
}
while (lengthLeft > 0){
merged[merged.length - lengthLeft] = left[left.length-lengthLeft];
lengthLeft--;
}
while (lengthRight > 0){
merged[merged.length - lengthRight] = right[right.length-lengthRight];
lengthRight--;
}
return merged;
}
static void mergeSort(int arr[],int p, int r) {
if(p<r) {
System.out.println("Pass "+k++);
int q = (p+r)/2;
mergeSort(arr,p,q);
mergeSort(arr,q+1,r);
//System.out.println(p+" "+q+" "+r);
merge(arr,p,q,r);
}
}
static void merge(int arr[],int p,int q,int r) {
int temp1[],temp2[];
//lower limit array
temp1 = new int[q-p+1];
//upper limit array
temp2 = new int[r-q];
for(int i=0 ; i< (q-p+1); i++){
temp1[i] = arr[p+i];
}
for(int j=0; j< (r-q); j++){
temp2[j] = arr[q+j+1];
}
int i = 0,j=0;
for(int k=p;k<=r;k++){
// This logic eliminates the so called sentinel card logic mentioned in Coreman
if(i!= temp1.length
&& (j==temp2.length || temp1[i] < temp2[j])
) {
arr[k] = temp1[i];
// System.out.println(temp1[i]);
i++;
}
else {
//System.out.println(temp2[j]);
arr[k] = temp2[j];
j++;
}
}
}
>
Merge Sort Using Sentinel
This codes works perfectly fine.
public void mergeSort(int a[], int low, int high) {
if (low < high) {
int mid = (low + high) / 2;
mergeSort(a, low, mid);
mergeSort(a, mid + 1, high);
merge(a, low, mid, high);
}
}
public void merge(int a[], int low, int mid, int high) {
int n1 = mid - low + 1;// length of an array a1
int n2 = high - mid; // length of an array a2
int a1[] = new int[n1 + 1];
int a2[] = new int[n2 + 1];
int lowRange = low;
for (int i = 0; i < n1; i++) {
a1[i] = a[lowRange];
lowRange++;
}
for (int j = 0; j < n2; j++) {
a2[j] = a[mid + j + 1];
}
a1[n1] = Integer.MAX_VALUE; // inserting sentinel at the end of array a1
a2[n2] = Integer.MAX_VALUE; // inserting sentinel at the end of array a2
int i = 0;
int j = 0;
int k = low;
for (k = low; k <= high; k++) {
if (a1[i] >= a2[j]) {
a[k] = a2[j];
j++;
} else {
a[k] = a1[i];
i++;
}
}
if (a2.length >= a1.length) {
for (int ab = k; ab < a2.length; ab++) {
a[k] = a2[ab];
k++;
}
} else if (a1.length >= a2.length) {
for (int ab = k; ab < a1.length; ab++) {
a[k] = a1[ab];
k++;
}
}
}
Here's another alternative:
public class MergeSort {
public static void merge(int[]a,int[] aux, int f, int m, int l) {
for (int k = f; k <= l; k++) {
aux[k] = a[k];
}
int i = f, j = m+1;
for (int k = f; k <= l; k++) {
if(i>m) a[k]=aux[j++];
else if (j>l) a[k]=aux[i++];
else if(aux[j] > aux[i]) a[k]=aux[j++];
else a[k]=aux[i++];
}
}
public static void sort(int[]a,int[] aux, int f, int l) {
if (l<=f) return;
int m = f + (l-f)/2;
sort(a, aux, f, m);
sort(a, aux, m+1, l);
merge(a, aux, f, m, l);
}
public static int[] sort(int[]a) {
int[] aux = new int[a.length];
sort(a, aux, 0, a.length-1);
return a;
}
}
Here is a simple merge sort algorithm in Java:
Good Tip: Always use int middle = low + (high-low)/2 instead of int middle = (low + high)/2.
public static int[] mergesort(int[] arr) {
int lowindex = 0;
int highindex = arr.length-1;
mergesort(arr, lowindex, highindex);
return arr;
}
private static void mergesort(int[] arr, int low, int high) {
if (low == high) {
return;
} else {
int midIndex = low + (high-low)/2;
mergesort(arr, low, midIndex);
mergesort(arr, midIndex + 1, high);
merge(arr, low, midIndex, high);
}
}
private static void merge(int[] arr, int low, int mid, int high) {
int[] left = new int[mid-low+2];
for (int i = low; i <= mid; i++) {
left[i-low] = arr[i];
}
left[mid-low+1] = Integer.MAX_VALUE;
int[] right = new int[high-mid+1];
for (int i = mid+1; i <= high; i++) {
right[i-mid-1] = arr[i];
}
right[high - mid] = Integer.MAX_VALUE;
int i = 0;
int j = 0;
for (int k = low; k <= high; k++) {
if (left[i] <= right[j]) {
arr[k] = left[i];
i++;
} else {
arr[k] = right[j];
j++;
}
}
}
package com.sortalgo;
import java.util.Arrays;
public class MyMSort {
private static void merge(int[] array, int[] result, int low, int mid, int high) {
int k =low, i=low; int j=mid+1;
while(i<=mid && j<=high) {
if(array[i]<= array[j]) {
result[k++]=array[i++];
}else {
result[k++]=array[j++];
}
}
while(i<=mid) {
result[k++]=array[i++];
}
while(j<=high) {
result[k++]=array[j++];
}
for(i=low;i<=high;i++) {
array[i]=result[i];
}
}
private static void mergeSort(int[] array, int[] result, int low, int high) {
if(high == low) {
return ;
}
int mid = (low + high)/2;
mergeSort(array,result, low, mid );
mergeSort(array,result, mid+1, high );
merge(array, result, low, mid, high);
}
public static void main(String[] args) {
int[] array = {8,4,3,12,25,6,13,10};
int[] result = new int[array.length];
mergeSort(array, result, 0, array.length-1 );
for(int i=0; i<=array.length-1;i++) {
System.out.println(array[i]);
}
}
}