BestSum memoization java - java

I have a function that receives a target and a numbers array, and the goal is to return the combination that uses less array numbers to achieve the target.
Example:
sum(8, [1,4,5]) should return [4,4]
sum(7, [5,3,4,7]) should return [7]`
sum(8, [2,3,5]) should return [3,5]
sum(100, [1,2,5,25]) should return [25, 25, 25, 25]
The function was working just fine before I attempted to do the memoization... Here is my code:
import java.util.ArrayList;
public class BestSum {
ArrayList<Integer> memoInt;
ArrayList<ArrayList<Integer>> memoList;
BestSum () {
memoList = new ArrayList<ArrayList<Integer>>();
memoInt = new ArrayList<Integer>();
}
public ArrayList<Integer> sum (int target, int nums[]) {
for(int i = 0; i < memoInt.size(); i++) {
if(memoInt.get(i) == target) {
return memoList.get(i);
}
}
if(target == 0) {
return new ArrayList<Integer>();
}
if(target < 0) {
return null;
}
ArrayList<Integer> shortestCombination = null;
for(int i = 0; i < nums.length; i++) {
int rest = target-nums[i];
ArrayList<Integer> currentCombination = sum(rest, nums);
if(currentCombination != null) {
currentCombination.add(nums[i]);
if(shortestCombination == null || currentCombination.size() < shortestCombination.size()){
shortestCombination = new ArrayList<Integer>();
shortestCombination = (ArrayList)currentCombination.clone();
}
}
}
memoInt.add(target);
memoList.add(shortestCombination);
return shortestCombination;
}
public static void main(String[] args) {
int target = 8;
int nums[] = {1,4,5};
BestSum bs = new BestSum();
System.out.println(bs.sum(target, nums).toString()); //[4,4]
}
}
However when I run this instead of [4,4], I get [4,1,4]... Any suggestions?

Ok So I fix the code :D
import java.util.ArrayList;
import java.util.*;
public class BestSum {
HashMap<Integer, ArrayList<Integer>> hp;
BestSum () {
hp = new HashMap<Integer, ArrayList<Integer>>();
}
public ArrayList<Integer> sum (int target, int nums[]) {
if(hp.containsKey(target)) {
return hp.get(target);
}
if(target == 0) {
return new ArrayList<Integer>();
}
if(target < 0) {
return null;
}
ArrayList<Integer> shortestCombination = null;
for(int i = 0; i < nums.length; i++) {
int rest = target-nums[i];
ArrayList<Integer> currentCombination = sum(rest, nums);
if(currentCombination != null) {
ArrayList<Integer> combination = new ArrayList<Integer>();
combination = (ArrayList)currentCombination.clone();
combination.add(nums[i]);
if(shortestCombination == null || combination.size() < shortestCombination.size()){
shortestCombination = new ArrayList<Integer>();
shortestCombination = (ArrayList)combination.clone();
}
}
}
hp.put(target, shortestCombination);
return shortestCombination;
}
public static void main(String[] args) {
int target = 8;
int nums[] = {1,4,5};
BestSum bs = new BestSum();
System.out.println(bs.sum(target, nums).toString()); //[4,4]
}
}

Tweaked the for loop a little,
for(int i = 0; i < nums.length; i++) {
int rest = target-nums[i];
ArrayList<Integer> currentCombination = sum(rest, nums);
if(currentCombination != null) {
ArrayList<Integer> tempCombination = new ArrayList<>(currentCombination);
tempCombination.add(nums[i]);
if(shortestCombination == null || tempCombination.size() < shortestCombination.size()){
shortestCombination = tempCombination;
}
}
}
It's an important step as the previous memory is being reassigned hence all the old values are pre-stored which caused the issue. I found out while debugging. Always a good idea to assign a new list while using recursion technique.

Related

I am trying to create a parallel implementation for selection sort but it ends up slower than serial

For my parallel computing class I have to think and create a parallel implementation of the selection sort algorithm. The idea is to be able to scale it to multiple threads so that it becomes faster than the serial implementation.
My idea was as follows:
Parallel selection sort idea
I have created the following implementation over the last few days but it is much slower than the serial algorithm. Whenever I use more threads it is also much slower vs when I use one thread. This is the first time I am working with threads as well so I am not sure if I implemented that correctly.
SelectionSort.java
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
public class SelectionSort {
private static final int availableProcessors = Runtime.getRuntime().availableProcessors();
private static final int NUMBER_COUNT = 10000;
private static List<Integer> sortedList = new ArrayList<>();
private static int[][] splitArray;
private static List<Integer> lowestNumbers = new ArrayList<>();
public static void main(String[] args) throws InterruptedException {
List<Integer> numbers = Numbers.GenerateNumber(NUMBER_COUNT);
class Lowest {
synchronized int getLowest(int index) {
int lowestInArray = Integer.MAX_VALUE;
for (int i = 0; i < splitArray[index].length; i++) {
if (splitArray[index][i] < lowestInArray) {
lowestInArray = splitArray[index][i];
}
}
return lowestInArray;
}
}
Lowest lowest = new Lowest();
class SelectionSortThread extends Thread {
private int splitArrayIndex;
private SelectionSortThread(int splitArrayIndex) {
this.splitArrayIndex = splitArrayIndex;
}
public void run() {
lowestNumbers.add(lowest.getLowest(splitArrayIndex));
}
}
long startingTime = System.currentTimeMillis();
for (int i = 0; i < NUMBER_COUNT; i++) {
List<Thread> threads = new ArrayList<>();
splitArray = fillSplitArray(availableProcessors, numbers);
lowestNumbers.clear();
for (int j = 0; j < availableProcessors; j++) {
if(splitArray[j] != null) {
threads.add(new SelectionSortThread(j));
}
}
for (Thread thread : threads) {
thread.start();
}
for (Thread thread : threads) {
thread.join();
}
int lowestInArray = getLowest(lowestNumbers);
numbers = swap(numbers, lowestInArray);
sortedList.add(numbers.get(0));
numbers.remove(0);
}
System.out.println("Sorted list: " + Arrays.toString(sortedList.toArray()));
System.out.println(System.currentTimeMillis() - startingTime);
}
private static int getLowest(List<Integer> lowestNumbers) {
int lowestInArray = Integer.MAX_VALUE;
for (Integer lowestNumber : lowestNumbers) {
if (lowestNumber < lowestInArray) {
lowestInArray = lowestNumber;
}
}
return lowestInArray;
}
private static List<Integer> swap(List<Integer> list, int lowest)
{
int n = list.size();
for(int i = 0; i < n; i++)
{
if(list.get(i) == lowest) {
Collections.swap(list, 0, i);
return list;
}
}
return null;
}
static int[][] fillSplitArray(int arrayAmount, List<Integer> listToUse) {
if (listToUse.size() == 0) {
return new int[0][0];
}
int splitLength = (int) Math.ceil((double) listToUse.size() / (double) arrayAmount);
int[][] splits = new int[arrayAmount][];
int j = 0;
int k = 0;
for (int i = 0; i < listToUse.size(); i++) {
if (k == splitLength) {
k = 0;
j++;
}
if (splits[j] == null) {
int remainingNumbers = listToUse.size() - i;
splits[j] = new int[Math.min(remainingNumbers, splitLength)];
}
splits[j][k++] = listToUse.get(i);
}
return splits;
};
}
Numbers.java
import java.util.ArrayList;
import java.util.List;
class Numbers {
static List<Integer> GenerateNumber(int numberCount) {
List<Integer> temp = new ArrayList<>();
for (int i = numberCount; i > 0; i--) {
temp.add(i);
}
return temp;
}
}
Is there anything I am doing totally wrong or that I could improve? I am expecting the parallel implementation to be faster than the serial one but so far this is not the case. It is currently a lot slower.

Constraining all combinations of an array-list

I know similar questions have been asked before but I have found the answers confusing. I am trying to make a program that will find every combination of an array-list with no repetitions and only of the maximum size. If the list has 4 items it should print out only the combinations with all 4 items present. This is what I have so far:
public main(){
UI.initialise();
UI.addButton("Test", this::testCreate);
UI.addButton("Quit", UI::quit);
}
public void createCombinations(ArrayList<String> list, String s, int depth) {
if (depth == 0) {
return;
}
depth --;
for (int i = 0; i < list.size(); i++) {
if (this.constrain(s + "_" + list.get(i), list.size())) {
UI.println(s + "_" + list.get(i));
}
createCombinations(list, s + "_" + list.get(i), depth);
}
}
public void testCreate() {
ArrayList<String> n = new ArrayList<String>();
n.add("A"); n.add("B"); n.add("C"); n.add("D");
this.createCombinations(n , "", n.size());
}
public boolean constrain(String s, int size) {
// Constrain to only the maximum length
if ((s.length() != size*2)) {
return false;
}
// Constrain to only combinations without repeats
Scanner scan = new Scanner(s).useDelimiter("_");
ArrayList<String> usedTokens = new ArrayList<String>();
String token;
while (scan.hasNext()) {
token = scan.next();
if (usedTokens.contains(token)) {
return false;
} else {
usedTokens.add(token);
}
}
// If we fully iterate over the loop then there are no repitions
return true;
}
public static void main(String[] args){
main obj = new main();
}
This prints out the following which is correct:
_A_B_C_D
_A_B_D_C
_A_C_B_D
_A_C_D_B
_A_D_B_C
_A_D_C_B
_B_A_C_D
_B_A_D_C
_B_C_A_D
_B_C_D_A
_B_D_A_C
_B_D_C_A
_C_A_B_D
_C_A_D_B
_C_B_A_D
_C_B_D_A
_C_D_A_B
_C_D_B_A
_D_A_B_C
_D_A_C_B
_D_B_A_C
_D_B_C_A
_D_C_A_B
_D_C_B_A
This works for small lists but is very inefficient for larger ones. I am aware that what I have done is completely wrong but I want to learn the correct way. Any help is really appreciated. Thanks in advance.
P.S. This is not homework, just for interest although I am a new CS student (if it wasn't obvious).
Implementing Heap's algorithm in Java:
import java.util.Arrays;
public class Main {
public static void swap(final Object[] array, final int index1, final int index2) {
final Object tmp = array[index1];
array[index1] = array[index2];
array[index2] = tmp;
}
public static void printPermutations_HeapsAlgorithm(final int n, final Object[] array) {
final int[] c = new int[n];
for (int i = 0; i < c.length; ++i)
c[i] = 0;
System.out.println(Arrays.toString(array)); //Consume first permutation.
int i=0;
while (i < n) {
if (c[i] < i) {
if ((i & 1) == 0)
swap(array, 0, i);
else
swap(array, c[i], i);
System.out.println(Arrays.toString(array)); //Consume permutation.
++c[i];
i=0;
}
else
c[i++] = 0;
}
}
public static void main(final String[] args) {
printPermutations_HeapsAlgorithm(4, new Character[]{'A', 'B', 'C', 'D'});
}
}
Possible duplicate of this.

Recursive Coin Change Making by printing all possible ways

I have tried to print all the paths which give the given amount. But my code does not work properly. I think I am missing some points to print all possible combinations. For example;
if amount: 7 and startCoin = 25, the program needs to give me:
{5,1,1} and {1,1,1,1,1,1,1}.
Can you help me to fix these problem?
Note: Preferably Java Solutions
class Solution {
static int[] coinSet = {1,5,10,25};
static List<List<Integer>> possibleWays = new ArrayList<>();
static List<Integer> currentWay = new ArrayList<>();
private static int makeChange(int amount, int startCoin){
boolean flag = false;
for(int i =0 ; i < coinSet.length ; i++){
if(coinSet[i] == startCoin) {
flag =true;
}
}
if(!flag){
throw new IllegalArgumentException("startCoin has to be in the specified range");
}
int nextCoin = 0;
switch(startCoin) {
case 25:
nextCoin = 10;
break;
case 10:
nextCoin = 5;
break;
case 5:
nextCoin = 1;
break;
case 1:
possibleWays.add(currentWay);
currentWay = new ArrayList<>();
return 1;
}
int ways = 0;
for(int count = 0; count * startCoin <= amount; count++){
ways += makeChange(amount - (count * startCoin),nextCoin);
}
return ways;
}
public int calculateNumberOfWays(int amount, int startCoin) throws Exception {
if (amount == 0) {
throw new Exception(); }
return makeChange(amount, startCoin);
}
public static void main(String[] args) {
System.out.println(makeChange(5,25));
System.out.println(possibleWays);
}
}
This can be solved using backtracking but that is not very efficient, below is the working java code
/**
* Created by sumit sharma on 3/1/2016.
*/
import java.util.ArrayList;
import java.util.Date;
import java.util.List;
import java.util.Random;
public class Main {
static int[] coinSet = {1,5,10,25};
static List<List<Integer>> possibleWays = new ArrayList<>();
static List<Integer> currentWay = new ArrayList<>();
public static void main(String[] args) {
List<Integer> countOfCoins = new ArrayList<>();
makeChange(7, 0, countOfCoins);
//System.out.print(possibleWays);
}
private static int makeChange(int amount, int startCoinIdx, List<Integer> coinsSoFar) {
if(startCoinIdx == coinSet.length){
if(amount == 0){
possibleWays.add(coinsSoFar);
System.out.println(coinsSoFar);
}
//System.out.println(coinsSoFar);
return 0;
}
for(int count = 0;(count*coinSet[startCoinIdx]) <= amount;count++){
List<Integer> temp = new ArrayList<>();
for(int i = 0;i < coinsSoFar.size();i++) temp.add(coinsSoFar.get(i));
for(int i = 0;i < count;i++) temp.add(coinSet[startCoinIdx]);
makeChange(amount - (count * coinSet[startCoinIdx]),startCoinIdx+1, temp);
temp.clear();
}
return 0;
}
}
Link to solution on Ideone : http://ideone.com/kIckmG

Merge sort in ArrayList in Java

I am learning how to implement basic algorithms in Java, so i am a newbie in this environment. I am trying to implement Merge Sort algorithm using ArrayList where program will read data (Integer in each line) from file and produce sorting result using Merge Sort. However, my code is showing same result as it has not sorted anything out! I would be very glad if someone can identify where did I do my mistake. As i am a beginner, the code is very simple, not optimized and not very fast in performance probably.
Here is my code:
public class MergeSortExp1 {
public static void main(String[] args) {
ArrayList<Integer>number = new ArrayList<Integer>();
Scanner myScanner = null;
try {
myScanner = new Scanner(new File("/Users/Sabbir/Desktop/workload.txt"));
} catch (FileNotFoundException e) {
e.printStackTrace();
}
while(myScanner.hasNextInt()){
number.add(myScanner.nextInt());
}
System.out.println("Before sorting" +number);
number=mergeSort(number);
System.out.println("Sorted Array =" +number);
}
public static ArrayList<Integer> mergeSort( ArrayList<Integer> Input)
{
if (Input.size() ==1){
return Input;
}
else {
int mid= Input.size()/2;
ArrayList<Integer> left= new ArrayList<Integer>(mid);
ArrayList<Integer> right=new ArrayList<Integer>(Input.size()-mid);
for (int i = 0; i < mid; i++) {
left.add(Input.get(i));
}
for (int i = 0; i < Input.size()-mid; i++) {
right.add(Input.get(i));
}
left=mergeSort(left);
right=mergeSort(right);
merge(left,right,Input);
}
return Input;
}
public static void merge (ArrayList<Integer>left,ArrayList<Integer>right,ArrayList<Integer>Input)
{
int i1=0;// left Index
int i2=0;// right Index
int InputIndex=0;
for (int i = 0; i < Input.size(); i++) {
if (i2>=right.size() || (i1<left.size() && left.get(i)<=right.get(i)))
{
Input.set(InputIndex,left.get(i1));
InputIndex++;
}
else {
Input.set(InputIndex, right.get(i2));
InputIndex++;
}
}
}
}
If your merge method is Ok (I don't test it), you forget to merge left and right to input, edit your code as shown below and re-try:
// This is called recursion. Calling a method again within the
//method until the value of left and right becomes 1.
left=mergeSort(left);
right=mergeSort(right);
merge(left,right,Input);
hope helped you!
One more variant:
private static <T extends Comparable<T>> List<T> mergeSort(List<T> unsortedList) {
if (unsortedList.size() <= 1) {
return unsortedList;
}
List<T> sortedList = new ArrayList<>(unsortedList.size());
List<T> leftList = mergeSort(unsortedList.subList(0, unsortedList.size() / 2));
List<T> rightList = mergeSort(unsortedList.subList(unsortedList.size() / 2, unsortedList.size()));
int leftIdx = 0;
int rightIdx = 0;
int resultIdx = 0;
while (leftIdx < leftList.size() && rightIdx < rightList.size()) {
if (leftList.get(leftIdx).compareTo(rightList.get(rightIdx)) <= 0) {
sortedList.add(resultIdx, leftList.get(leftIdx));
leftIdx++;
} else {
sortedList.add(resultIdx, rightList.get(rightIdx));
rightIdx++;
}
resultIdx++;
}
while (leftIdx < leftList.size()) {
sortedList.add(resultIdx, leftList.get(leftIdx));
leftIdx++;
resultIdx++;
}
while (rightIdx < rightList.size()) {
sortedList.add(resultIdx, rightList.get(rightIdx));
rightIdx++;
resultIdx++;
}
return sortedList;
}
import java.util.ArrayList;
import java.io.*;
import java.util.*;
public class Mergesort1 {
public static void main(String[] args) {
ArrayList<Integer> values = new ArrayList<Integer>();
int zeilen = 0;
try{
FileInputStream in = new FileInputStream(args[0]);
BufferedReader reader = new BufferedReader(new InputStreamReader(in));
String line;
while((line = reader.readLine()) != null){
values.add(Integer.parseInt(line));
zeilen++;
}
try{
FileOutputStream out = new FileOutputStream(args[1]);
BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(out));
sort(values); //sortien array list
for (int i=0; i<values.size(); i++){
writer.write("" + values.get(i));
writer.newLine();
}
writer.close();
}
catch(Exception e){
System.out.println(e);
}
}
catch(Exception e){
System.out.println(e);
}
}
public static ArrayList<Integer> sort( ArrayList<Integer> values)
{
if (values.size() ==1){
return values;
}
else {
int mid= values.size()/2;
ArrayList<Integer> left= new ArrayList<Integer>(mid);
ArrayList<Integer> right=new ArrayList<Integer>(values.size()-mid);
for (int i = 0; i < mid; i++) {
left.add(values.get(i));
}
for (int i = mid; i < values.size(); i++) {
right.add(values.get(i));
}
left=sort(left);
right=sort(right);
merge(left,right,values);
}
return values;
}
public static void merge (ArrayList<Integer>left,ArrayList<Integer>right,ArrayList<Integer>values)
{
int i1=0;// left Index
int i2=0;// right Index
int InputIndex=0;
for (int i = 0; i < values.size(); i++) {
if(i1==left.size()){
values.set(i, right.get(i2));
i2++;
}
else{
if (i2==right.size()){
values.set(i,left.get(i1));
i1++;
}
else{
if (left.get(i1)<=right.get(i2)) {
values.set(i,left.get(i1));
i1++;
}
else {
if (left.get(i1)>=right.get(i2)) {
values.set(i, right.get(i2));
i2++;
}
}
}
}
}
}
}

recursive method not properly executing

I have a programming assignment for an introductory level Java class (the subset sum problem) - for some reason, my recursive method isn't executing properly (it just goes straight to the end of the method and prints out the sorted list). Any help would be appreciated - I'm a newbie and recursive functions are really confusing to me.
package programmingassignment3;
import java.io.*;
import java.util.*;
public class ProgrammingAssignment3 {
static int TARGET = 10;
static ArrayList<Integer> list = new ArrayList<>();
static int SIZE = list.size();
public static void main(String[] args) {
populateSortSet();
sumInt(list);
recursiveSS(list);
}//main
public static void populateSortSet() {
try {
File f = new File("set0.txt");
Scanner input = new Scanner(f);
while (input.hasNext()) {
int ele = input.nextInt();
if (ele < TARGET && !list.contains(ele)) {
list.add(ele);
}//if
}//while
Collections.sort(list);
}//try
catch (IOException e) {
e.printStackTrace();
}//catch
}//populateSet
public static void recursiveSS(ArrayList<Integer> Alist) {
if (Alist.size() == SIZE) {
if (sumInt(Alist) == TARGET) {
System.out.println("The integers that equal " + TARGET + "are: " + Alist);
} //if==TARGET
}//if==SIZE
else {
for (int i = 0; i < SIZE; i++) {
ArrayList<Integer> list1 = new ArrayList<>(Alist);
ArrayList<Integer> list0 = new ArrayList<>(Alist);
list1.add(1);
list0.add(0);
if (sumInt(list0) < TARGET) {
recursiveSS(list0);
}//if
if (sumInt(list1) < TARGET) {
recursiveSS(list1);
}//if
}//for
}//else
System.out.println("echo" + Alist);
}//recursiveSS
public static int sumInt(ArrayList<Integer> Alist) {
int sum = 0;
for (int i = 0; i < SIZE - 1; i++) {
sum += Alist.get(i);
}//for
if (Alist.size() == TARGET) {
sum += Alist.get(Alist.size() - 1);
}//if
return sum;
}//sumInt
}//class
This thing that you do at class level:
static ArrayList<Integer> list = new ArrayList<>();
static int SIZE = list.size();
means that SIZE will be initiated to 0, and stay 0 (even if you add elements to the list.)
This means that the code inside the for-loop will be executed 0 times.
Try something like:
public class ProgrammingAssignment3 {
private static int initialSize;
//...
public static void populateSortSet() {
//populate the list
initialSize = list.size();
}
So you don't set the value of the size variable until the list is actually populated.
That being said, there a quite a few other strange things in your code, so I think you need to specify exactly what you are trying to solve here.
Here's how I'd do it. I hope it clarifies the stopping condition and the recursion. As you can see, static methods are not an issue:
import java.util.ArrayList;
import java.util.List;
/**
* Demo of recursion
* User: mduffy
* Date: 10/3/2014
* Time: 10:56 AM
* #link http://stackoverflow.com/questions/26179574/recursive-method-not-properly-executing?noredirect=1#comment41047653_26179574
*/
public class RecursionDemo {
public static void main(String[] args) {
List<Integer> values = new ArrayList<Integer>();
for (String arg : args) {
values.add(Integer.valueOf(arg));
}
System.out.println(String.format("input values : %s", values));
System.out.println(String.format("iterative sum: %d", getSumUsingIteration(values)));
System.out.println(String.format("recursive sum: %d", getSumUsingRecursion(values)));
}
public static int getSumUsingIteration(List<Integer> values) {
int sum = 0;
if (values != null) {
for (int value : values) {
sum += value;
}
}
return sum;
}
public static int getSumUsingRecursion(List<Integer> values) {
if ((values == null) || (values.size() == 0)) {
return 0;
} else {
if (values.size() == 1) { // This is the stopping condition
return values.get(0);
} else {
return values.get(0) + getSumUsingRecursion(values.subList(1, values.size())); // Here is recursion
}
}
}
}
Here is the case I used to test it:
input values : [1, 2, 3, 4, 5, 6]
iterative sum: 21
recursive sum: 21
Process finished with exit code 0
Thanks everyone. I really appreciate the help. I did figure out the problem and the solution is as follows (closing brace comments removed for the reading pleasure of #duffymo ):
public class ProgrammingAssignment3 {
static int TARGET = 6233;
static ArrayList<Integer> set = new ArrayList<>();
static int SIZE;
static int count = 0;
public static void populateSortSet() {
try {
File f = new File("set3.txt");
Scanner input = new Scanner(f);
while (input.hasNext()) {
int ele = input.nextInt();
if (ele < TARGET && !set.contains(ele)) {
set.add(ele);
}
}
Collections.sort(set);
SIZE = set.size();
System.out.println("The original sorted set: " + set + "\t subset sum = " + TARGET);
}
catch (IOException e) {
e.printStackTrace();
}
}
public static void recursiveSS(ArrayList<Integer> list) {
if (list.size() == SIZE) {
if (sumInt(list) == TARGET) {
System.out.print("The Bit subset is: " + list + "\t");
System.out.println("The subset is: " + getSubset(list));
count++;
}
}
else {
ArrayList<Integer> list1 = new ArrayList<>(list);//instantiate list1
ArrayList<Integer> list0 = new ArrayList<>(list);//instantiate list0
list1.add(1);
list0.add(0);
if (sumInt(list0) <= TARGET) {
recursiveSS(list0);
}
if (sumInt(list1) <= TARGET) {
recursiveSS(list1);
}
}
}
public static int sumInt(ArrayList<Integer> list) {
int sum = 0;
for (int i = 0; i < list.size(); i++) {
if (list.get(i) == 1) {
sum += set.get(i);
}
}
return sum;
}
public static ArrayList<Integer> getSubset(ArrayList<Integer> list) {
ArrayList<Integer> l = new ArrayList<>();
for (int i = 0; i < list.size(); i++) {
if (list.get(i) == 1) {
l.add(set.get(i));
}
}
return l;
}
}

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