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I am implementing the quick-select algorithm to get the kth element in an array, and I am stuck at a place where I don't know how to resolve. Here is my code that doesn't work:
public static void main (String[] args) {
int[] arr = new int[]{7,6,5,4,3,2,1};
int k = 4;
quickSort(arr, 0, arr.length - 1, k);
return arr[k];
}
private static void quickSelect(int[] nums, int start, int end, int k) {
if (start < end) {
int partitionIndex = getPartitionIndex(nums, start, end);
if (partitionIndex == k) {
return;
}
quickSelect(nums, start, partitionIndex - 1, k);
quickSelect(nums, partitionIndex + 1, end, k);
}
}
private int getPartitionIndex(int[] nums, int start, int end) {
int pivot = nums[end];
int index = start;
for (int i = start; i <= end; i++) {
int current = nums[i];
if (current < pivot) {
swap(nums, index, i);
index++;
}
}
swap(nums, index, end);
return index;
}
private void swap(int[] nums, int i, int j) {
if (i == j) {
return;
}
nums[i] = nums[i] ^ nums[j];
nums[j] = nums[i] ^ nums[j];
nums[i] = nums[i] ^ nums[j];
}
Sure, if I remove these lines:
if (partitionIndex == k) {
return;
}
It becomes quicksort and works fine. And I understand why it's not working, it is since the array I am getting from 0 to k might not be sorted as I return at the above condition. But I am not able to find the right conditions where I sort only the first k elements in the array and leave out the rest, so that I don't do any extra work. I've looked at some implementations online and spent some time on the above, but not able to figure it out, so reaching out for help.
If k < partitionIndex, only check the left partition, else only check the right partition.
if (k < partitionIndex)
quickSelect(nums, start, partitionIndex - 1, k);
else
quickSelect(nums, partitionIndex + 1, end, k);
I am trying to calculate the running time of hybrid quickSort - insertionSort. However, when presented with a larger array (~500k elements), I get a java.lang.StackOverflowError. Can I somehow overcome this? Not using recursion is not an option.
Here's the code:
public class QuickSort2 {
private static void swap(int[] arr, int x, int y){
int temp = arr[x];
arr[x] = arr[y];
arr[y] = temp;
}
private static int partition(int[] arr, int lo, int hi){
int pivot = arr[hi];
int index = lo - 1;
for(int i = lo; i < hi; i++){
if(arr[i] < pivot){
index++;
swap(arr, index, i);
}
}
swap(arr, index + 1, hi);
return index + 1;
}
public static void quickSort(int[] arr, int lo, int hi){
if(lo < hi && hi-lo > 10){
int q = partition(arr, lo, hi);
quickSort(arr,lo,q-1);
quickSort(arr,q+1,hi);
}else{
InsertionSort.insertSort(arr);
}
}
}
and also, the insertionSort:
public class InsertionSort {
static void insertSort(int[] arr){
int n = arr.length;
for (int j = 1; j < n; j++){
int key = arr[j];
int i = j-1;
while ((i >= 0) && (arr[i] > key)){
arr[i+1] = arr[i];
i--;
}
arr[i+1] = key;
}
}
The lines where the error occurs:
quickSort(arr,lo,q-1);
quickSort(arr,q+1,hi);
and also the calling code:
public class RunningTime {
public static void main(String[] args) {
int[] arr = ReadTest.readToArray("int500k");
int lo = 0;
int hi = arr.length - 1;
long startTime = System.currentTimeMillis();
QuickSort2.quickSort(arr, lo, hi);
long stopTime = System.currentTimeMillis();
long elapsedTime = stopTime - startTime;
System.out.println("Running time: " + elapsedTime);
System.out.println("Array is sorted: " + isSorted(arr));
}
}
You should restrict insertion sort to work only on the subset of the array.
Besides this, I don't see any other issues with your code.
Is the file int500k sorted? If so this is the worst case scenario for quick sort, which means that the recursion will be 500k levels deep.
To fix it you can for instance choose the pivot randomly instead of arr[hi].
I'm running this and I am being told it would not run fast enough. What is a good way to increase the speed of this running class? I am guessing I would need to change my nested while loops. That is the only thing I can think of. The if statements should all be linear...
import java.io.File;
import java.io.FileNotFoundException;
import java.util.*;
public class QSortLab {
static int findpivot(Comparable[] A, int i, int j) {
return (i + j) / 2;
}
static <E> void swap(E[] A, int p1, int p2) {
E temp = A[p1];
A[p1] = A[p2];
A[p2] = temp;
}
static void quicksort(Comparable[] A, int i, int j) { // Quicksort
int pivotindex = findpivot(A, i, j); // Pick a pivot
swap(A, pivotindex, j); // Stick pivot at end
int k = partition(A, i, j-1, A[j]);
swap(A, k, j); // Put pivot in place
if ((k-i) > 1) quicksort(A, i, k-1); // Sort left partition
if ((j-k) > 1) quicksort(A, k+1, j); // Sort right partition
}
static int partition(Comparable[] A, int left, int right, Comparable pivot) {
while (left <= right) { // Move bounds inward until they meet
while (A[left].compareTo(pivot) < 0) left++;
while ((right >= left) && (A[right].compareTo(pivot) >= 0)) right--;
if (right > left) swap(A, left, right); // Swap out-of-place values
}
return left; // Return first position in right partition
}
}
What do you mean you need to change your nested while loops? Quick Sort is defined by those features. Removing wouldn't function properly.
As for optimization, by default it should be known that primitives vs objects tend to be different. E.g. primitives on stack/heap to keep stack small & heap stores object with refs able to be on stack.
So let's test some stuff
primitive quick sort (from here)
Integer quick sort (same code as above, but with Integer class)
Your original posted code
Your original posted code (w/ several edits)
Here's the entire code I used.
import java.util.Random;
public class App {
public static final int ARR_SIZE = 1000;
public static final int TEST_ITERS = 10000;
public static Random RANDOM = new Random();
public static void main(String[] args) {
int[] a = new int[ARR_SIZE];
Integer[] b = new Integer[ARR_SIZE];
Integer[] c = new Integer[ARR_SIZE];
Integer[] d = new Integer[ARR_SIZE];
long sum = 0, start = 0, end = 0;
for (int i = 0; i < TEST_ITERS; ++i) {
for (int j = 0; j < ARR_SIZE; ++j)
a[j] = RANDOM.nextInt();
start = System.nanoTime();
quickSort(a, 0, a.length - 1);
end = System.nanoTime();
sum += (end - start);
}
System.out.println((sum / TEST_ITERS) + " nano, qs avg - 'int'");
sum = 0;
for (int i = 0; i < TEST_ITERS; ++i) {
for (int j = 0; j < ARR_SIZE; ++j)
b[j] = RANDOM.nextInt();
start = System.nanoTime();
quickSort(b, 0, b.length - 1);
end = System.nanoTime();
sum += (end - start);
}
System.out.println((sum / TEST_ITERS) + " nano, qs avg - 'Integer'");
sum = 0;
for (int i = 0; i < TEST_ITERS; ++i) {
for (int j = 0; j < ARR_SIZE; ++j)
c[j] = RANDOM.nextInt();
start = System.nanoTime();
quicksort(c, 0, c.length - 1);
end = System.nanoTime();
sum += (end - start);
}
System.out.println((sum / TEST_ITERS) + " nano, qs avg - 'Comparable' (SO user code)");
sum = 0;
for (int i = 0; i < TEST_ITERS; ++i) {
for (int j = 0; j < ARR_SIZE; ++j)
d[j] = RANDOM.nextInt();
start = System.nanoTime();
qs_quicksort(d, 0, d.length - 1);
end = System.nanoTime();
sum += (end - start);
}
System.out.println((sum / TEST_ITERS) + " nano, qs avg - 'Comparable' (SO user code - edit)");
for (int i = 0; i < ARR_SIZE; ++i) {
final int n = RANDOM.nextInt();
a[i] = n;
b[i] = n;
c[i] = n;
d[i] = n;
}
quickSort(a, 0, a.length - 1);
Integer[] aConv = new Integer[ARR_SIZE];
for (int i = 0; i < ARR_SIZE; ++i)
aConv[i] = a[i];
quickSort(b, 0, b.length - 1);
quicksort(c, 0, c.length - 1);
qs_quicksort(d, 0, d.length - 1);
isSorted(new Integer[][] { aConv, b, c, d });
System.out.println("All properly sorted");
}
public static void isSorted(Integer[][] arrays) {
if (arrays.length != 4) {
System.out.println("error sorting, input arr len");
return;
}
for (int i = 0; i < ARR_SIZE; ++i) {
int val1 = arrays[0][i].compareTo(arrays[1][i]);
int val2 = arrays[1][i].compareTo(arrays[2][i]);
int val3 = arrays[2][i].compareTo(arrays[3][i]);
if (val1 != 0 || val2 != 0 || val3 != 00) {
System.out.printf("Error [i = %d]: a = %d, b = %d, c = %d", i, arrays[0][i], arrays[1][i], arrays[2][i], arrays[3][i]);
break;
}
}
}
public static int partition(int arr[], int left, int right) {
int i = left, j = right;
int tmp;
int pivot = arr[(left + right) / 2];
while (i <= j) {
while (arr[i] < pivot)
i++;
while (arr[j] > pivot)
j--;
if (i <= j) {
tmp = arr[i];
arr[i] = arr[j];
arr[j] = tmp;
i++;
j--;
}
}
return i;
}
public static void quickSort(int arr[], int left, int right) {
int index = partition(arr, left, right);
if (left < index - 1)
quickSort(arr, left, index - 1);
if (index < right)
quickSort(arr, index, right);
}
public static int partition(Integer[] arr, int left, int right) {
int i = left, j = right;
Integer pivot = arr[(left + right) / 2];
while (i <= j) {
while (arr[i].compareTo(pivot) < 0)
i++;
while (arr[j].compareTo(pivot) > 0)
j--;
if (i <= j) {
Integer temp = arr[i];
arr[i] = arr[j];
arr[j] = temp;
i++;
j--;
}
}
return i;
}
public static void quickSort(Integer[] arr, int left, int right) {
int index = partition(arr, left, right);
if (left < index - 1)
quickSort(arr, left, index - 1);
if (index < right)
quickSort(arr, index, right);
}
static int findpivot(Comparable[] A, int i, int j)
{
return (i+j)/2;
}
static <E> void swap(E[] A, int p1, int p2) {
E temp = A[p1];
A[p1] = A[p2];
A[p2] = temp;
}
static void quicksort(Comparable[] A, int i, int j) { // Quicksort
int pivotindex = findpivot(A, i, j); // Pick a pivot
swap(A, pivotindex, j); // Stick pivot at end
int k = partition(A, i, j-1, A[j]);
swap(A, k, j); // Put pivot in place
if ((k-i) > 1) quicksort(A, i, k-1); // Sort left partition
if ((j-k) > 1) quicksort(A, k+1, j); // Sort right partition
}
static int partition(Comparable[] A, int left, int right, Comparable pivot) {
while (left <= right) { // Move bounds inward until they meet
while (A[left].compareTo(pivot) < 0) left++;
while ((right >= left) && (A[right].compareTo(pivot) >= 0)) right--;
if (right > left) swap(A, left, right); // Swap out-of-place values
}
return left; // Return first position in right partition
}
static <E> void qs_swap(E[] A, int p1, int p2) {
E temp = A[p1];
A[p1] = A[p2];
A[p2] = temp;
}
static void qs_quicksort(Comparable[] A, int i, int j) { // Quicksort
int pivotindex = (i+j)/2;
qs_swap(A, pivotindex, j); // Stick pivot at end
int k = qs_partition(A, i, j-1, A[j]);
qs_swap(A, k, j); // Put pivot in place
if ((k-i) > 1) qs_quicksort(A, i, k-1); // Sort left partition
if ((j-k) > 1) qs_quicksort(A, k+1, j); // Sort right partition
}
static int qs_partition(Comparable[] A, int left, int right, Comparable pivot) {
while (left <= right) { // Move bounds inward until they meet
while (A[left].compareTo(pivot) < 0) left++;
while ((right >= left) && (A[right].compareTo(pivot) >= 0)) right--;
if (right > left) { qs_swap(A, left, right); // Swap out-of-place values
left++; right--;}
}
return left; // Return first position in right partition
}
}
This produces the output:
56910 nano, qs avg - 'int'
69498 nano, qs avg - 'Integer'
76762 nano, qs avg - 'Comparable' (SO user code)
71846 nano, qs avg - 'Comparable' (SO user code - edit)
All properly sorted
Now, breaking down the results
The 'int' vs 'Integer' shows great diff when simply using primitives vs non-primitives (I'm sure at some points in the code there may be boxing but hopefully not in critical spots ;) - please edit this if so). The 'int' vs 'Integer' uses same code with exception of 'int' 'Integer'. See the following four method signatures that are used in this comparison, 'int'
public static int partition(int arr[], int left, int right)
public static void quickSort(int arr[], int left, int right)
and 'Integer'
public static int partition(Integer[] arr, int left, int right)
public static void quickSort(Integer[] arr, int left, int right)
respectively.
Then there are the method signatures related to the original code you posted,
static int findpivot(Comparable[] A, int i, int j)
static <E> void swap(E[] A, int p1, int p2)
static void quicksort(Comparable[] A, int i, int j)
static int partition(Comparable[] A, int left, int right, Comparable pivot)
and the modified ones,
static <E> void qs_swap(E[] A, int p1, int p2)
static void qs_quicksort(Comparable[] A, int i, int j)
static int qs_partition(Comparable[] A, int left, int right, Comparable pivot)
As you can see, in the modified code, findpivot was removed directly and replaced into the calling spot in quicksort. Also, the partition method gained counters for left and right respectively. left++; right--;
And finally, to ensure these 4 variations of quicksort actually did the sole purpose, sort, I added a method, isSorted() to check the validity of the same generated content and that it's sorted accordingly based on each of the 4 different sorts.
In conclusion, I think my edits may have saved a portion of time/nanoseconds, however I wasn't able to achieve the same time as the Integer test. Hopefully I've not missed anything obvious and edits are welcome if need be. Cheers
Well, I couldn't tell from testing whether this makes any difference at all because the timer on my machine is terrible , but I think most of the work in this algo is done with the swap function, so thinking about how to make that in particular more efficient, maybe the function call/return itself consumes cycles, and perhaps the creation of the temp variable each time the function is called also takes cycles, so maybe the code would be more efficient if the swap work was done in line. It was not obvious though when I tested on my machine as the nanotimer returned results +/- 20% each time I ran the program
public class QSort2 {
static int findpivot(Comparable[] A, int i, int j) {
return (i + j) / 2;
}
static Comparable temp;
static void quicksort(Comparable[] A, int i, int j) { // Quicksort
int pivotindex = findpivot(A, i, j); // Pick a pivot
// swap(A, pivotindex, j); // Stick pivot at end
temp = A[pivotindex];
A[pivotindex] = A[j];
A[j] = temp;
int k = partition(A, i, j - 1, A[j]);
//swap(A, k, j); // Put pivot in place
temp = A[k];
A[k] = A[j];
A[j] = temp;
if ((k - i) > 1) quicksort(A, i, k - 1); // Sort left partition
if ((j - k) > 1) quicksort(A, k + 1, j); // Sort right partition
}
static int partition(Comparable[] A, int left, int right, Comparable pivot) {
while (left <= right) { // Move bounds inward until they meet
while (A[left].compareTo(pivot) < 0) left++;
while ((right >= left) && (A[right].compareTo(pivot) >= 0)) right--;
if (right > left) {
//swap(A, left, right);} // Swap out-of-place values
temp = A[left];
A[left] = A[right];
A[right] = temp;
}
}
return left; // Return first position in right partition
}
}
I try to use "randomized pivot" method to find the Kth min elem among given array.
[The code]
public class FindKthMin {
// Find the Kth min elem by randomized pivot.
private static void exchange (int[] givenArray, int firstIndex, int secondIndex) {
int tempElem = givenArray[firstIndex];
givenArray[firstIndex] = givenArray[secondIndex];
givenArray[secondIndex] = tempElem;
}
private static int partition (int[] givenArray, int start, int end, int pivotIndex) {
// Debug:
//System.out.println("debug: start = " + start);
//System.out.println(">> end = " + end);
//System.out.println(">> pivotIndex = " + pivotIndex);
int pivot = givenArray[pivotIndex];
int left = start - 1;
int right = end;
boolean hasDone = false;
while (!hasDone) {
while (!hasDone) {
left ++;
if (left == right) {
hasDone = true;
break;
}
if (givenArray[left] >= pivot) {
// Exchange givenArray[left] and the givenArray[right].
exchange(givenArray, left, right);
break;
}
}
while (!hasDone) {
right --;
if (left == right) {
hasDone = true;
break;
}
if (givenArray[right] < pivot) {
// Exchange the givenArray[right] and the givenArray[left].
exchange(givenArray, right, left);
break;
}
}
}
givenArray[right] = pivot;
// Debug:
//System.out.println(">> split = " + right);
//System.out.println();
return right;
}
private static int findKthMin_RanP_Helper (int[] givenArray, int start, int end, int k) {
if (start > end) return -1;
// Generate a random num in the range[start, end].
int rand = (int)(start + Math.random() * (end - start + 1));
// Using this random num as the pivot index to partition the array in the current scope.
int split = partition(givenArray, start, end, rand);
if (k == split + 1) return givenArray[split];
else if (k < split + 1) return findKthMin_RanP_Helper(givenArray, start, split - 1, k);
else return findKthMin_RanP_Helper(givenArray, split + 1, end, k);
}
public static int findKthMin_RanP (int[] givenArray, int k) {
int size = givenArray.length;
if (k < 1 || k > size) return -1;
return findKthMin_RanP_Helper(givenArray, 0, size - 1, k);
}
// Main method to test.
public static void main (String[] args) {
// Test data: {8, 9, 5, 2, 8, 4}.
int[] givenArray = {8, 9, 5, 2, 8, 4};
// Test finding the Kth min elem by randomized pivot method.
System.out.println("Test finding the Kth min elem by randomized pivot method, rest = " + findKthMin_RanP(givenArray, 1));
}
}
But the result is unstable, sometimes right and sometimes wrong.
Please have a look at the 5th row of findKthMin_RanP_Helper method:
If I change this int split = partition(givenArray, start, end, rand); to int split = partition(givenArray, start, end, end);, the result is always correct. I really can not find what's wrong with this.
EDIT:
The problem comes from the "partition", the new partition should like this:
private static int partition_second_version (int[] givenArray, int start, int end, int pivotIndex) {
int pivot = givenArray[pivotIndex];
int left = start;
int right = end;
while (left <= right) {
while (givenArray[left] < pivot) left ++;
while (givenArray[right] > pivot) right --;
if (left <= right) {
// Exchange givenArray[left] and givenArray[right].
exchange(givenArray, left, right);
left ++;
right --;
}
}
return left;
}
And the findKthMin_RanP_Helper should be changed like this:
private static int findKthMin_RanP_Helper (int[] givenArray, int start, int end, int k) {
if (start > end) return -1;
// Generate a random num in the range[start, end].
int rand = start + (int)(Math.random() * ((end - start) + 1));
// Using this random num as the pivot index to partition the array in the current scope.
int split = partition_second_version (givenArray, start, end, rand);
if (k == split) return givenArray[split - 1];
else if (k < split) return findKthMin_RanP_Helper(givenArray, start, split - 1, k);
else return findKthMin_RanP_Helper(givenArray, split, end, k);
}
Your partition routine could be simplified...
private static int partition(int[] givenArray, int start, int end, int pivotIndex) {
final int pivot = givenArray[pivotIndex];
int left = start;
int right = end;
while (left < right) {
while (left < givenArray.length && givenArray[left] <= pivot) {
left++;
}
while (right > -1 && givenArray[right] > pivot) {
right--;
}
if (left >= right) {
break;
}
exchange(givenArray, right, left);
}
return right;
}
The one bug I see in your code is your partition routine. In the first exchange call, it is not guaranteed that the right index will always point to a value which is < pivot.
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]);
}
}
}