I was learning to merge sort an integer array, when I noticed that while copying the sorted array elements to the original array, we need two separate loop variables to run simultaneously, while the values at those indices are copied to the original array. Here is the code for reference:
class MergeSort {
public static void sort(int arr[], int si, int ei, int mid) {
int merged[] = new int[ei - si + 1];
int index1 = si; // tracks the first array
int index2 = mid + 1; // tracks the second array
int i = 0;
while (index1 <= mid && index2 <= ei) {
if (arr[index1] <= arr[index2]) {
merged[i++] = arr[index1++];
} else {
merged[i++] = arr[index2++];
}
} // end of while
while (index1 <= mid) {
merged[i++] = arr[index1++];
}
while (index2 <= ei) {
merged[i++] = arr[index2++];
}
// to copy merged[] to arr[]
int j = si;
for (i = 0; i < merged.length; i++, j++) {
arr[j] = merged[i];
}
} // end sort()
public static void divide(int arr[], int si, int ei) {
// base case
if (si >= ei) {
return;
} // end of base case
int mid = si + (ei - si) / 2; // same as (ei-si)/2 but with less space complexity
divide(arr, si, mid);
divide(arr, mid + 1, ei);
sort(arr, si, ei, mid);
} // end of divide
public static void main(String args[]) {
int arr[] = { 1, 8, 0, 7, -4 };
int n = arr.length;
divide(arr, 0, n - 1);
for (int i = 0; i < n; i++) {
System.out.print(arr[i] + " ");
} // end of for
} // end of main
} // end of class
Notice that while copying the values of the array merged[] to the array arr[], we are using two separate variables i and j. I did try using only one loop variable, which went like:
for (int i = 0; i < arr.length; i++) {
arr[i] = merged[i];
}
but received an incorrect output. If anyone knows why we need two separate variables for the operation, please let me know. Thank you :)
You could use a single variable in this final loop, but you must add the offset of the start of the slice in the destination array:
for (int i = 0; i < arr.length; i++) {
arr[si + i] = merged[i];
}
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 working on a program that uses quick sort to sort an array to display the running time. This program selects the median of three random numbers as the pivot. However, I am not sure if I am doing something wrong because every time I run this program I get the following errors:
"java.lang.StackOverflowError",
at java.util.Random.nextInt(Unknown Source)
at SortingItems.quickSort(SortingItems.java:31)
at SortingItems.quickSort(SortingItems.java:69) " I get this specific message multiple times"
This is the code:
import java.util.Random;
public class SortingItems {
static int x = 1000;
static int array [] = new int[x];
public static void main(String[] args) {
long time;
input(x, array);
time = System.nanoTime();
sort(array);
System.out.println("Running time in ascending order " + (System.nanoTime() - time));
}
public static void sort(int[] array) {
quickSort(array, 0, array.length - 1);
}
public static void quickSort(int[] array, int low, int high) {
if (array == null || array.length == 0)
return;
if (low >= high)
return;
// Generating random numbers from 0 to the last element of the array
Random f = new Random();
int first = f.nextInt(array.length - 1);
Random s = new Random();
int second = s.nextInt(array.length - 1);
Random t = new Random();
int third = t.nextInt(array.length - 1);
// Selecting the pivot
int pivot = Math.max(Math.min(array[first], array[second]),
Math.min(Math.max(array[first],array[second]), array[third]));
int i = low;
int j = high;
while (i <= j) {
while (array[i] < pivot) {
i++;
}
while (array[j] > pivot) {
j--;
}
if (i <= j) {
int temp = array[i];
array[i] = array[j];
array[j] = temp;
i++;
j--;
}
}
if (low < j)
quickSort(array, low, j);
if (high > i)
quickSort(array, i, high);
}
// Input in ascending order
public static int[] input(int x, int[] array) {
for (int k = 0; k < x; k++) {
array[k] = k;
}
return array;
}
}
The problem seems to be with how the median is being selected here. The pivots should be chosen from between the current high and low positions and not the entire array.
Note that your test-input is in ascending order. Now, as you select three random values from the entire array of size 1000 for pivoting, when it comes to the smaller recursive cases, the arrays tend to be lopsided with a very high probability. This means that another level of recursion would be called with the same input parameters. In the long run, this is likely to cause a stack overflow with a high probability.
The following change should fix your issue:
// Generating random numbers from low to high
Random f = new Random();
int first = f.nextInt(high-low) + low;
Random s = new Random();
int second = s.nextInt(high-low) + low;
Random t = new Random();
int third = t.nextInt(high-low) + low;
I am wondering why my code keeps having this "time limit exceed" on the uva-online judge page (http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=2511), it is supposed to execute in 1 second but I don't know which input they use (my code works and do exactly what it supposed).. I am wondering that maybe the while loop of the testCases have something to do, because when I remove it it says wrong answer.. this is my code:
public class Main {
private static final int TAM = 10000; // TAM equals to the posible numbers of houses
private static int[] auxHouses;
private static int nHouses[];
private static int testCases;
private static Scanner scanner = new Scanner(System.in);
public static void main(String[] args) {
nHouses = new int[TAM];
// First we read the input
// Read the variable of testCases
testCases = scanner.nextInt();
while (testCases > 0) {
float sol = binarySearch(testCases);
System.out.println(sol);
testCases--;
}
}
public static float binarySearch(int tC) {
int routers = 0, houses = 0;
int pivot = 0;
int hi = 0;
// While for the testCases
routers = scanner.nextInt();
houses = scanner.nextInt();
// Read the numbers of the houses
for (int i = 0; i < houses; i++) {
nHouses[i] = scanner.nextInt();
}
if (routers >= houses) {
return 0;
}
// First we sort the array
sortHouses(nHouses, houses);
// Prepare the variables of the index
int lo = 0;
hi = 2 * (nHouses[houses - 1] - nHouses[0] + 1); // 2*(loc[h-1]-loc[0]+1);
// Now we execute the binary search algorithm
while (hi > lo) {
pivot = (lo + hi) / 2;
int start = nHouses[0];
int need = 1;
for (int i = 0; i < houses; i++) {
if (nHouses[i] > start + pivot) {
start = nHouses[i];
need++;
}
}
if (need > routers) {
lo = pivot + 1;
} else {
hi = pivot;
}
}
return (float) hi / 2;
}
public static void sortHouses(int[] nhouses, int length) {
// First we check if the are actually values on the array
if (nhouses.length == 0) {
return;
}
// Copy the array of int into an auxiliary variable and the numbers of
// int in the array
auxHouses = nhouses;
int lengthArray = length;
quickSort(0, lengthArray - 1);
}
public static void quickSort(int low, int high) {
// System.out.println("Array " + Arrays.toString(auxHouses));
int i = low, j = high;
// Get the pivot element from the middle of the list
int pivot = auxHouses[low + (high - low) / 2];
// Divide into two lists
while (i <= j) {
// If the current value from the left list is smaller then the pivot
// element then get the next element from the left list
while (auxHouses[i] < pivot) {
i++;
}
// If the current value from the right list is larger then the pivot
// element then get the next element from the right list
while (auxHouses[j] > pivot) {
j--;
}
// If we have found a values in the left list which is larger then
// the pivot element and if we have found a value in the right list
// which is smaller then the pivot element then we exchange the
// values.
// As we are done we can increase i and j
if (i <= j) {
exchange(i, j);
i++;
j--;
}
}
// Recursion
if (low < j)
quickSort(low, j);
if (i < high)
quickSort(i, high);
}
private static void exchange(int i, int j) {
int temp = auxHouses[i];
auxHouses[i] = auxHouses[j];
auxHouses[j] = temp;
}
}
I have it with the quicksort implemented, but if you use Arrays.sort(..) method instead it says the same thing..TLE, what could be doing wrong?
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]);
}
}
}