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Return array with common elements in all matrix row-s with repetition

Currently working on a method that takes a n*n matrix as input and returns an array consisting of all elements that are found in each sub-array. However, since I need it to also include duplicates etc, it's harder than I thought.
Googled the hell out of it, however, yet to find a solution which matches my criteria of repetition.
Currently I have this, which compares the element's of the first row with every other row and all their elements. If the counter gets to the length where it confirms that the element indeed is present in all rows, it adds it to the array. However, this has faults in it. First of all, since I create a set array in the beginning with the maximum possible length, it might return an array with non-needed 0's in it. And second, the duplicate part is not working correctly, struggling to implement a check there.
Examples of input/output that I need:
Input matrix: {{2,2,1,4},{4,1,2,2},{7,1,2,2},{2,10,2,1}}
Desired output: {1, 2, 2}
My output: {2, 2, 1, 0}
Input matrix: {{2,2,1,4},{4,1,3,2},{7,1,9,2},{2,10,2,1}}
Desired output: {1, 2}
My output: {2, 2, 1, 0}
public static int[] common_elements(int[][] matrix){
int[] final_array = new int[matrix.length];
for (int i = 0; i < matrix.length; i++) {
int counter = 0;
for (int j = 1; j < matrix.length; j++) {
for (int k = 0; k < matrix.length; k++) {
if(matrix.[0][i] == matrix.[j][k]){
counter += 1;
break;
}
}
}
if(counter == a.length-1){
final_array[i] = a[0][i];
}
}
return final_array;
}
EDIT: This is what I finally got together that fits my requirements and works flawlessly, with comments
public static int[] repetitiveInts(int[][] a){
//This is a method declared outside for sorting every row of the matrix ascending-ly before I do the element search.
for (int i = 0; i < a.length; i++) {
sorting(a[i]);
}
//Declaring a LinkedList in order to add elements on the go
LinkedList<Integer> final_list= new LinkedList<Integer>();
//Iterating through the matrix with every element of the first row, counting if it appears in every row besides the first one.
for (int i = 0; i < a.length; i++) {
int counter = 0;
for (int j = 1; j < a.length; j++) {
for (int k = 0; k < a.length; k++) {
//Checking if an element from the other rows match
if(a[0][i] == a[j][k]){
a[j][k] = a[0][i]-1; //If a match is found, the element is changed so finding duplicates is possible.
counter += 1;
break; //Breaking and checking the next row after one row checks out successfully.
}
}
}
//If the element is indeed in every row, adds it to the lit.
if(counter == a.length-1){
final_list.add(a[0][i]);
}
}
//Since I had to return a regular int[] array, converting the LinkedList into an array.
int[] final_realarray= new int[final_list.size()];
for (int i = 0; i < final_list.size(); i++) {
final_realarray[i] = final_list.get(i);
}
return final_realarray;
Grateful for help :)

The most efficient way to solve this problem is by creating a histogram of frequencies for each nested array in the matrix (i.e. determine the number of occurrences for every element in the nested array).
Every histogram will be represented by a Map<Integer, Integer> (array element as a key, its occurrences as a value). To generate a histogram only a single pass through the array is needed. In the solution below this logic resides inside the getFrequencies() method.
After creating all histograms we have to merge them. In terms of set theory we are looking for an intersection of keys in all histograms. I.e. we need only those keys that appear at least once in every histogram and a value for each key will be the smallest in all histograms for that key. This logic is placed in the getCommonElements().
In order to create a merged histogram, we can pick any of the histograms (in the code below the first histogram is used frequencies.get(0).keySet()) and iterate over its keys. Then in the nested loop, for every key, we need to find the minimum value associated with that in every histogram in a list (reminder: that will be the smallest number of occurrences for the key).
At the same time, while merging histograms we can also find the length of the resulting array by adding all the minimal frequencies together. That small optimization will allow to avoid doing the second iteration over the merged map.
The last step required is to populate the resulting array commonElements with keys from the merged histogram. Value of every key denotes how many times it has to be placed in the resulting array.
public static void main(String[] args) {
System.out.println(Arrays.toString(commonElements(new int[][]{{2,2,1,4},{4,1,2,2},{7,1,2,2},{2,10,2,1}})));
System.out.println(Arrays.toString(commonElements(new int[][]{{2,2,1,4},{4,1,3,2},{7,1,9,2},{2,10,2,1}})));
}
public static int[] commonElements(int[][] matrix){
List<Map<Integer, Integer>> frequencies = getFrequencies(matrix);
return getCommonElements(frequencies);
}
private static List<Map<Integer, Integer>> getFrequencies(int[][] matrix) {
List<Map<Integer, Integer>> frequencies = new ArrayList<>();
for (int[] arr: matrix) {
Map<Integer, Integer> hist = new HashMap<>(); // a histogram of frequencies for a particular array
for (int next: arr) {
// hist.merge(next, 1, Integer::sum); Java 8 alternative to if-else below
if (hist.containsKey(next)) {
hist.put(next, hist.get(next) + 1);
} else {
hist.put(next, 1);
}
}
frequencies.add(hist);
}
return frequencies;
}
private static int[] getCommonElements(List<Map<Integer, Integer>> frequencies) {
if (frequencies.isEmpty()) { // return an empty array in case if no common elements were found
return new int[0];
}
Map<Integer, Integer> intersection = new HashMap<>();
int length = 0;
for (Integer key: frequencies.get(0).keySet()) { //
int minCount = frequencies.get(0).get(key); // min number of occurrences of the key in all maps
for (Map<Integer, Integer> map: frequencies) {
int nextCount = map.getOrDefault(key, 0);
minCount = Math.min(nextCount, minCount); // getOrDefault is used because key might not be present
if (nextCount == 0) { // this key isn't present in one of the maps, no need to check others
break;
}
}
if (minCount > 0) {
intersection.put(key, minCount);
length += minCount;
}
}
int[] commonElements = new int[length];
int ind = 0;
for (int key: intersection.keySet()) {
int occurrences = intersection.get(key);
for (int i = 0; i < occurrences; i++) {
commonElements[ind] = key;
ind++;
}
}
return commonElements;
}
output
[1, 2, 2]
[1, 2]
Side note: don't violate the naming conventions, use camel-case for method and variable names.
Update
I've managed to implement a brute-force solution based on arrays and lists only as required.
The most important thing is that for this task you need two lists: one to store elements, another to store frequencies. Lists are bound together via indices. And these two lists are basically mimic a map, frankly saying a very inefficient one (but that's a requirement). Another possibility is to implement a class with two int fields that will represent the data for a common element, and then store the instances of this class in a single list. But in this case, the process of checking whether a particular element already exists in the list will be much more verbose.
The overall logic has some similarities with the solution above.
First, we need to pick a single array in the matrix (matrix[0]) and compare all its unique elements against the contents of all other arrays. Every element with non-zero frequency will be reflected in the list of elements and in the list of frequencies at the same index in both. And when the resulting array is being created the code relies on the corresponding indices in these lists.
public static int[] commonElements(int[][] matrix){
if (matrix.length == 0) { // case when matrix is empty - this condition is required because farther steps will lead to IndexOutOfBoundsException
return new int[0];
}
if (matrix.length == 1) { // a small optimization
return matrix[0];
}
// Map<Integer, Integer> frequencyByElement = new HashMap<>(); // to lists will be used instead of Map, because of specific requirement for this task
List<Integer> frequencies = new ArrayList<>(); // lists will be bind together by index
List<Integer> elements = new ArrayList<>();
int length = 0; // length of the resulting array
for (int i = 0; i < matrix[0].length; i++) {
if (elements.contains(matrix[0][i])) { // that means this element is a duplicate, no need to double-count it
continue;
}
int currentElement = matrix[0][i];
int minElementCount = matrix[0].length; // min number of occurrences - initialized to the max possible number of occurrences for the current array
// iterating over the all nested arrays in matrix
for (int row = 0; row < matrix.length; row++) {
int localCount = 0; // frequency
for (int col = 0; col < matrix[row].length; col++) {
if(matrix[row][col] == currentElement){
localCount++;
}
}
if (localCount == 0) { // element is absent in this array and therefore has to be discarded
minElementCount = 0;
break; // no need to iterate any farther, breaking the nested loop
}
minElementCount = Math.min(localCount, minElementCount); // adjusting the value the min count
}
// frequencyByElement.put(currentElement, minElementCount); // now we are sure that element is present in all nested arrays
frequencies.add(minElementCount);
elements.add(currentElement);
length += minElementCount; // incrementing length
}
return getFinalArray(frequencies, elements, length);
}
private static int[] getFinalArray(List<Integer> frequencies,
List<Integer> elements,
int length) {
int[] finalArray = new int[length];
int idx = 0; // array index
for (int i = 0; i < elements.size(); i++) {
int element = elements.get(i);
int elementCount = frequencies.get(i);
for (int j = 0; j < elementCount; j++) {
finalArray[idx] = element;
idx++;
}
}
return finalArray;
}

How to return all array permutations iteratively into a two-dimensional array?

I am trying to write a program that will iterate through all possible permutations of a String array, and return a two dimensional array with all the permutations. Specifically, I am trying to use a String array of length 4 to return a 2D array with 24 rows and 4 columns.
I have only found ways to print the Strings iteratively but not use them in an array. I have also found recursive ways of doing it, but they do not work, as I am using this code with others, and the recursive function is much more difficult.
For what I want the code to do, I know the header should be:
public class Permutation
{
public String[][] arrayPermutation(String[] str)
{
//code to return 2D array
}
}
//I tried using a recursive method with heap's algorithm, but it is very //complex with its parameters.
I am very new to programming and any help would be greatly appreciated.

Your permutation-problem is basically just an index-permutation problem.
If you can order the numbers from 0 to n - 1 in all possible variations, you can use them as indexes of your input array, and simply copy the Strings. The following algorithm is not optimal, but it is graphic enough to explain and implement iteratively.
public static String[][] getAllPermutations(String[] str) {
LinkedList<Integer> current = new LinkedList<>();
LinkedList<Integer[]> permutations = new LinkedList<>();
int length = str.length;
current.add(-1);
while (!current.isEmpty()) {
// increment from the last position.
int position = Integer.MAX_VALUE;
position = getNextUnused(current, current.pop() + 1);
while (position >= length && !current.isEmpty()) {
position = getNextUnused(current, current.pop() + 1);
}
if (position < length) {
current.push(position);
} else {
break;
}
// fill with all available indexes.
while (current.size() < length) {
// find first unused index.
int unused = getNextUnused(current, 0);
current.push(unused);
}
// record result row.
permutations.add(current.toArray(new Integer[0]));
}
// select the right String, based on the index-permutation done before.
int numPermutations = permutations.size();
String[][] result = new String[numPermutations][length];
for (int i = 0; i < numPermutations; ++i) {
Integer[] indexes = permutations.get(i);
String[] row = new String[length];
for (int d = 0; d < length; ++d) {
row[d] = str[indexes[d]];
}
result[i] = row;
}
return result;
}
public static int getNextUnused(LinkedList<Integer> used, Integer current) {
int unused = current != null ? current : 0;
while (used.contains(unused)) {
++unused;
}
return unused;
}
The getAllPermutations-method is organized in an initialization part, a loop collecting all permutations (numeric), and finally a convertion of the found index-permutation into the String-permutations.
As the convertion from int to String is trivial, I'll just explain the collection part. The loop iterates as long, as the representation is not completely depleted, or terminated from within.
First, we increment the representation (current). For that, we take the last 'digit' and increment it to the next free value. Then we pop, if we are above length, and look at the next digit (and increment it). We continue this, until we hit a legal value (one below length).
After that, we fill the remainder of the digits with all still remaining digits. That done, we store the current representation to the list of arrays.
This algorithm is not optimal in terms of runtime! Heap is faster. But implementing Heap's iteratively requires a non-trivial stack which is tiresome to implement/explain.

How can I implement the recursion in my Quicksort algorithm?

I'm trying to implement quicksort in Java to learn basic algorithms. I understand how the algo works (and can do it on paper) but am finding it hard to write it in code. I've managed to do step where we put all elements smaller than the pivot to the left, and larger ones to the right (see my code below). However, I can't figure out how to implement the recursion part of the algo, so sort the left and right sides recursively. Any help please?
public void int(A, p, q){
if(A.length == 0){ return; }
int pivot = A[q];
j = 0; k = 0;
for(int i = 0; i < A.length; i++){
if(A[i] <= pivot){
A[j] = A[i]; j++;
}
else{
A[k] = A[i]; k++;
}
}
A[j] = pivot;
}

Big Disclaimer: I did not write this piece of code, so upvotes is not needed. But I link to a tutorial which explains quicksort in detail. Gave me a much needed refreshment on the algorithm as well! The example given has very good comments that might just help you to wrap your head around it.
I suggest you adapt it to your code and write som tests for it to verify it works
Quicksort is a fast, recursive, non-stable sort algorithm which works by the divide and conquer principle. Quicksort will in the best case divide the array into almost two identical parts. It the array contains n elements then the first run will need O(n). Sorting the remaining two sub-arrays takes 2 O(n/2). This ends up in a performance of O(n log n).
In the worst case quicksort selects only one element in each iteration. So it is O(n) + O(n-1) + (On-2).. O(1) which is equal to O(n^2).*
public class Quicksort {
private int[] numbers;
private int number;
public void sort(int[] values) {
// check for empty or null array
if (values ==null || values.length==0){
return;
}
this.numbers = values;
number = values.length;
quicksort(0, number - 1);
}
private void quicksort(int low, int high) {
int i = low, j = high;
// Get the pivot element from the middle of the list
int pivot = numbers[low + (high-low)/2];
// Divide into two lists
while (i <= j) {
// If the current value from the left list is smaller than the pivot
// element then get the next element from the left list
while (numbers[i] < pivot) {
i++;
}
// If the current value from the right list is larger than the pivot
// element then get the next element from the right list
while (numbers[j] > pivot) {
j--;
}
// If we have found a value in the left list which is larger than
// the pivot element and if we have found a value in the right list
// which is smaller than 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--;
}
}
// This is the recursion part you had trouble with i guess?
// Recursion
if (low < j)
quicksort(low, j);
if (i < high)
quicksort(i, high);
}
private void exchange(int i, int j) {
int temp = numbers[i];
numbers[i] = numbers[j];
numbers[j] = temp;
}
}
Link to tutorial

How to implement a k-way merge sort?

I need to implement a function which does a k-way merge sort on an unsorted array or integers.
The function takes in two parameters, an integer K, which is the "way" of the sort and always a power of 2. The second parameter is the array of integers to be sorted, whose length is also a power of 2.
The function is to return an array containing the sorted elements. So far, I know how to implement a regular merge sort. How would I modify this code so that it implements a K-way merge sort? (Note: this function doesn't return the sorted array, I need help with that as well. It also doesn't take in K, since its a regular merge sort)
Below code:
public class MergeSort {
public static void main(String[] args) {
}
public static void mergeSort(int[] inputArray) {
int size = inputArray.length;
if (size < 2)
return;
int mid = size / 2;
int leftSize = mid;
int rightSize = size - mid;
int[] left = new int[leftSize];
int[] right = new int[rightSize];
for (int i = 0; i < mid; i++) {
left[i] = inputArray[i];
}
for (int i = mid; i < size; i++) {
right[i - mid] = inputArray[i];
}
mergeSort(left);
mergeSort(right);
merge(left, right, inputArray);
}
public static void merge(int[] left, int[] right, int[] arr) {
int leftSize = left.length;
int rightSize = right.length;
int i = 0, j = 0, k = 0;
while (i < leftSize && j < rightSize) {
if (left[i] <= right[j]) {
arr[k] = left[i];
i++;
k++;
} else {
arr[k] = right[j];
k++;
j++;
}
}
while (i < leftSize) {
arr[k] = left[i];
k++;
i++;
}
while (j < leftSize) {
arr[k] = right[j];
k++;
j++;
}
}
}

Regular merge sort is two-way sorting. You compare elements from the first and the second halves of array and copy smallest to output array.
For k-way sorting you divide input array into K parts. K indexes point to the first elements of every part. To effectively choose the smallest of them, use priority queue (based on binary heap) and pop the smallest element from the heap top at every step. When you pop element belonging to the m-th part, push the next element from the same part (if it still exists)
Let you have array length 16 and k = 4.
The first recursion level calls 4 mergesorts for arrays copied from indexes 0..3, 4..7, 8..11, 12..15.
The second recursion level gets length 4 array and calls 4 mergesorts for 1-element arrays.
The third recursion level gets length 1 array and immediately returns (such array is sorted).
Now at the second recursion level you merge 4 one-element arrays into one sorted array.
Now at the first recursion level you merge 4 four-element arrays into one sorted array length 16

Algorithm to partition the array using the pivot element

I was trying to solve following programming exercise from some java programming book
Write method that partitions the array using the first element, called a pivot. After the partition, the elements in the list are rearranged so that all the elements before the pivot are less than or equal to the pivot and the elements after the pivot are greater than the pivot. The method returns the index where the pivot is located in the new list. For example, suppose the list is {5, 2, 9, 3, 6, 8}. After the partition, the list becomes {3, 2, 5, 9, 6, 8}. Implement the method in a way that takes at most array.length comparisons.
I've implemented solution, but it takes much more than array.length comparisons.
The book itself has solution, but unfortunately it's just plain wrong (not working with some inputs). I've seen the answer to this similar question, and understood "conquer" part of Quicksort algorithm, but in this algorithm values are partitioned using mid-value, but in my case using of 1st array value as a pivot is required.

This is the pivot routine from the linked answer (adapted from source here).
int split(int a[], int lo, int hi) {
// pivot element x starting at lo; better strategies exist
int x=a[lo];
// partition
int i=lo, j=hi;
while (i<=j) {
while (a[i]<x) i++;
while (a[j]>x) j--;
if (i<=j) swap(a[i++], a[j--]);
}
// return new position of pivot
return i;
}
The number of inter-element comparisons in this algorithm is either n or n+1; because in each main loop iteration, i and j move closer together by at exactly c units, where c is the number of comparisons performed in each of the inner while loops. Look at those inner loops - when they return true, i and j move closer by 1 unit. And if they return false, then, at the end of the main loop, i and j will move closer by 2 units because of the swap.
This split() is readable and short, but it also has a very bad worst-case (namely, the pivot ending at either end; follow the first link to see it worked out). This will happen if the array is already sorted either forwards or backwards, which is actually very frequent. That is why other pivot positions are better: if you choose x=a[lo+hi/2], worst-case will be less common. Even better is to do like Java, and spend some time looking for a good pivot to steer clear from the worst case. If you follow the Java link, you will see a much more sophisticated pivot routine that avoids doing extra work when there are many duplicate elements.

It seem that the algorithm (as taken from "Introduction to algorihtm 3rd ed") can be implemented as follows (C++) should be similar in Java`s generics:
template <typename T> void swap_in_place(T* arr, int a, int b)
{
T tmp = arr[a];
arr[a] = arr[b];
arr[b] = tmp;
}
template <typename T> int partition(T* arr, int l, int r)
{
T pivot = arr[r];
int i = l-1;
int j;
for(j=l; j < r; j++) {
if (arr[j] < pivot /* or cmp callback */) {
// preincrement is needed to move the element
swap_in_place<T>(arr, ++i, j);
}
}
// reposition the pivot
swap_in_place(arr, ++i, j);
return i;
}
template <typename T> void qsort(T* arr, int l, int r)
{
if ( l < r ) {
T x = partition<T>(arr, l, r);
qsort(arr, l, x-1);
qsort(arr, x+1, r);
}
}
However, its a simple pseudocode implementation, I dont know if it`s the best pivot to pick from. Maybe (l+r)/2 would be more proper.

Pretty simple solution with deque:
int [] arr = {3, 2, 5, 9, 6, 8};
Deque<Integer> q = new LinkedBlockingDeque<Integer>();
for (int t = 0; t < arr.length; t++) {
if (t == 0) {
q.add(arr[t]);
continue;
}
if (arr[t] <= arr[0])
q.addFirst(arr[t]);
else
q.addLast(arr[t]);
}
for (int t:q) {
System.out.println(t);
}
Output is:
2
3
5 <-- pivot
9
6
8

There is video that I made on Pivot based partition I explained both the methods of patitioning.
https://www.youtube.com/watch?v=356Bffvh1dA
And based on your(the other) approach
https://www.youtube.com/watch?v=Hs29iYlY6Q4
And for the code. This is a code I wrote for pivot being the first element and it takes O(n) Comparisons.
void quicksort(int a[],int l,int n)
{
int j,temp;
if(l+1 < n)
{
int p=l;
j=l+1;
for(int i=l+1;i<n;++i)
{
if(a[i]<a[p])
{
temp=a[i];
a[i]=a[j];
a[j]=temp;
j++;
}
}
temp=a[j-1];
a[j-1]=a[p];
a[p]=temp;
quicksort(a,l,j);
quicksort(a,j,n);
}
}

The partition function below works as follow:
The last variable points to the last element in the array that has not been compared to the pivot element and can be swapped.
If the element directly next to the pivot element is less than the pivot
element. They are swapped.
Else if the pivot element is less than the next element, the nextelement is swapped with the element whose index is the last variable.
static int partition(int[] a){
int pivot = a[0];
int temp, index = 0;
int last = a.length -1;
for(int i = 1; i < a.length; i++){
//If pivot > current element, swap elements
if( a[i] <= pivot){
temp = a[i];
a[i] = pivot;
a[i-1] = temp;
index = i;
}
//If pivot < current elmt, swap current elmt and last > index of pivot
else if( a[i] > pivot && last > i){
temp = a[i];
a[i] = a[last];
a[last] = temp;
last -= 1;
i--;
}
else
break;
}
return index;
}