I am implementing conflict-based backjumping with nqueen. I want to optimize my code especially in recursive call.

In short,backjumping is similar to backtracking and it uses conflict set. When checking failure, it stores the fail value in conflict set.When it needs to backtrack,it jumps from the conflict set and not as stack by stack like backtracking.

public class Backjumping {
int                             size;
List<Integer>                   columns;
int                             numberofplaces;
int                             numberofbacktracks;
HashMap<Integer, List<Integer>> conflict;
boolean                         noBreak = true;

Backjumping(int size) {
    this.size = size;
    columns = new ArrayList();
    conflict = new HashMap<>(size);
    for (int i = 0; i < size; i++) {
        conflict.put(i, new ArrayList<>());

List place(int startRow) {
    if (columns.size() == size) {
        System.out.println("Solution Found! The board size was :" + size);
        System.out.println(numberofplaces + " total nodes assigned were made.");
        System.out.println(numberofbacktracks + " total backtracks were executed.");
        return this.columns;
    } else {
        for (int row = 0; row < size; row++) {
            if (isSafe(columns.size(), row)) {
                if (indexExists(columns, columns.size()))
                    columns.set(columns.size(), row);
                    columns.add(columns.size(), row);

                numberofplaces += 1;
                return place(startRow);
        if (noBreak) {
            List<Integer> lastRowList = conflict.get(columns.size());
            numberofbacktracks += 1;

            List<Integer> key = new ArrayList<>();
            Counter<Integer> counts = new Counter<Integer>();
            lastRowList.forEach(i -> {
                if (!key.contains(i)) {

            Object[] keyContent = key.toArray();
            List<Integer> temp = new ArrayList<>();

            for (int i = 0; i < counts.size(); i++) {
                temp.add(counts.count((int) keyContent[i]));

            Integer value = Collections.max(temp);
            int index = temp.indexOf(value);
            int lastRow = (int) keyContent[index];

            conflict.replace(columns.size(), new ArrayList<>());
            int previous_variable = columns.remove(lastRow);
    return this.columns;

private boolean isSafe(int cols, int rows) {

    for (int threatrow : columns) {
        int threatcol = columns.indexOf(threatrow);
        if (rows == threatrow || cols == columns.indexOf(threatrow)) {
            return false;
        } else if ((threatrow + threatcol) == (rows + cols) || (threatrow - threatcol) == (rows - cols)) {
            return false;
    return true;

public boolean indexExists(final List list, final int index) {
    return index >= 0 && index < list.size();

public static void main(String[] args) {
    System.out.println("Enter the size of board");
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    Backjumping bj = new Backjumping(n);
    double start = System.currentTimeMillis();
    List cols = bj.place(2);
    double end = System.currentTimeMillis();
    System.out.println("Time to solve in second       = " + (end - start) * 0.001 + " s");
    System.out.print("Ths solution is : ");
    cols.forEach(i -> System.out.print(((int) i + 1) + ", "));
    System.out.println("\n\nPlotting CSP result on N_Queens board");
    bj.getBoardPic(n, cols);

public void getBoardPic(int size, List columns) {
    int[] cols = Ints.toArray(columns);

    int[][] matrix = new int[size][size];

    for (int a = 0; a < size; a++) {
        int j = cols[a];
        matrix[a][j] = 1;

    for (int a = 0; a < size; a++) {
        for (int b = 0; b < size; b++) {
            if (matrix[b][a] == 1)
                System.out.print(" Q ");
                System.out.print(" - ");

class Counter<T> {

final Map<T, Integer> counts = new HashMap<>();

public void add(T t) {
    counts.merge(t, 1, Integer::sum);

public int count(T t) {
    return counts.getOrDefault(t, 0);

public int size() {
    return counts.size();

  • \$\begingroup\$ Hello, you wrote my solution wrongs when N=6. Code Review is for reviewing code working and working as expected and this requisite seems not be satisfied by your code, for details you can check what topics can I ask about here?. \$\endgroup\$ Feb 6, 2020 at 8:50
  • \$\begingroup\$ Welcome to CodeReview@SE. (Please put spaces after punctuation marks instead of before.) \$\endgroup\$
    – greybeard
    Feb 6, 2020 at 8:55
  • \$\begingroup\$ Ok,Thanks for your advice.I will edit it. \$\endgroup\$
    – Cecelia
    Feb 6, 2020 at 9:10
  • \$\begingroup\$ Hello again, please format your code and split it into distinct classes, if you have test cases (input values and output values expected) add them to you post, this will help your question to obtain more answers. \$\endgroup\$ Feb 6, 2020 at 11:07
  • \$\begingroup\$ My IDE complains, first about missing imports; more seriously: what, in getBoardPic(), is Ints? \$\endgroup\$
    – greybeard
    Feb 6, 2020 at 19:05

1 Answer 1


I haven't look too much at your algorithm, however there's a few things that stand out that you might want to look at.


You're passing start row into place. The only time you use it is when you pass it into the recursive calls. Are you supposed to be using it to limit the scope of the search, or is it simply unnecessary?


There's a similar issue with noBreak. You set it when constructing your class to true and nothing ever changes it. If it's unnecessary, then it allows you to remove the level of nesting in your if block if(noBreak, since it's always true and so always going to be executed.


The body of both your if clauses is the same, really you're doing if(A|B|C|D), rather than if(A|B) else if(C|D). I'd combine the clauses to make it more obvious that this is the case.

range checking

The application doesn't seem to work when its size is 3 or less. Consider adding some validation on the input.

+= 1

It's unusual to see += 1, I'd expect ++.


Class fields are usually marked as private, you've left them as the default of package private. Naming also usually follows the standard camelCase convention, you seem to have mixed an matched between it and alllowercase which is less easy to read.


It's naming suggests that it returns a picture of the board (possibly in a string), however it actually prints the board to the console. This is a bit misleading.


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