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‎src/problems/leetcode/NQueens.java‎

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package problems.leetcode;
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import java.util.ArrayList;
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import java.util.Collections;
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import java.util.List;
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// https://leetcode.com/problems/n-queens/
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public class NQueens {
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public static List<List<String>> solveNQueens(int n) {
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if (n == 0) {
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return Collections.emptyList();
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}
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List<List<String>> result = new ArrayList<>();
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for (int col = 0; col < n; col++) {
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// System.out.println("col=" + col);
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Occupied current = new Occupied(n);
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Pos pos = new Pos(0, col);
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current.occupy(pos);
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solve(n, result, current, pos);
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}
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return result;
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// n = 5
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// x . . . .
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// . . . x .
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// . x . . .
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// . . . . x
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// . . x . .
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// x . . . .
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// . . x . .
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// . . . . x
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// . x . . .
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// . . . x .
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// . x . . .
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// . . . x .
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// x . . . .
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// . . x . .
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// . . . . x
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// . x . . .
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// . . . . x
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// . . x . .
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// x . . . .
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// . . . x .
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// . . x . .
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// . . . . x
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// x . . . .
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// . . . x .
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// . x . . .
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// . . x . .
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// x . . . .
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// . . . . x
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// . x . . .
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// . . . x .
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// . . . x .
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// . x . . .
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// . . . . x
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// . . x . .
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// x . . . .
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// . . . x .
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// x . . . .
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// . . x . .
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// . . . . x
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// . x . . .
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// . . . . x
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// . x . . .
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// . . . x .
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// x . . . .
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// . . x . .
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// . . . . x
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// . . x . .
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// x . . . .
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// . . . x .
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// . x . . .
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// solve it for cols = 0 to ceil(n/2)
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// d1 = x - y
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//
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}
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private static void solve(int boardSize, List<List<String>> result, Occupied current, Pos prev) {
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if (current.size() == boardSize) {
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result.add(current.toBoardString());
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return;
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}
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// System.out.println("current=" + current + ", prev=" + prev);
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// System.out.println("nexts-" + nextPositions);
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for (Pos next : prev.nextPositions(boardSize, current)) {
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current.occupy(next);
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solve(boardSize, result, current, next);
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current.deleteLast();;
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}
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}
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private static class Pos {
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int x;
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int y;
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Pos(int x, int y) {
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this.x = x;
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this.y = y;
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}
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List<Pos> nextPositions(int boardSize, Occupied occupied) {
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List<Pos> result = new ArrayList<>();
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for (int j = y + 2; j < boardSize; j++) {
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if (x + 1 < boardSize && !occupied.canAttack(x + 1, j)) {
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result.add(new Pos(x + 1, j));
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}
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if (x > 0 && !occupied.canAttack(x - 1, j)) {
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result.add(new Pos(x - 1, j));
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}
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}
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for (int j = y - 2; j >= 0; j--) {
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if (x + 1 < boardSize && !occupied.canAttack(x + 1, j)) {
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result.add(new Pos(x + 1, j));
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}
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if (x > 0 && !occupied.canAttack(x - 1, j)) {
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result.add(new Pos(x - 1, j));
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}
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}
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return result;
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}
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@Override
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public String toString() {
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return "{x=" + x + ", y=" + y + "}";
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}
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}
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private static class Occupied {
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int n;
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boolean rows[];
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boolean cols[];
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boolean diag1[];
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boolean diag2[];
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List<Pos> positions = new ArrayList<>();
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Occupied(int n) {
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this.n = n;
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this.rows = new boolean[n];
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this.cols = new boolean[n];
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this.diag1 = new boolean[n * 2 - 1];
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this.diag2 = new boolean[n * 2 - 1];
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}
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boolean canAttack(int x, int y) {
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return rows[x] || cols[y] || diag1[n - 1 - (x - y)] || diag2[x + y];
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}
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void occupy(Pos pos) {
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rows[pos.x] = true;
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cols[pos.y] = true;
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diag1[n - 1 - (pos.x - pos.y)] = true;
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diag2[pos.x + pos.y] = true;
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positions.add(pos);
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}
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void deleteLast() {
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Pos pos = positions.remove(positions.size() - 1);
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rows[pos.x] = false;
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cols[pos.y] = false;
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diag1[n - 1 - (pos.x - pos.y)] = false;
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diag2[pos.x + pos.y] = false;
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}
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int size() {
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return positions.size();
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}
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List<String> toBoardString() {
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char[][] board = new char[n][n];
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for (int i = 0; i < n; i++) {
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for (int j = 0; j < n; j++) {
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board[i][j] = '.';
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}
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}
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for (Pos pos : positions) {
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board[pos.x][pos.y] = 'Q';
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}
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List<String> rows = new ArrayList<>();
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for (char[] b : board) {
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rows.add(new String(b));
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}
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return rows;
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}
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}
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public static void main(String[] args) {
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// System.out.println(new Pos(0, 0).canAttack(new Pos(0, 0)));
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// System.out.println(new Pos(0, 0).canAttack(new Pos(2, 0)));
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// System.out.println(new Pos(0, 0).canAttack(new Pos(0, 3)));
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// System.out.println(new Pos(0, 0).canAttack(new Pos(2, 2)));
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// System.out.println(new Pos(1, 2).canAttack(new Pos(2, 3)));
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// System.out.println(new Pos(2, 0).canAttack(new Pos(0, 2)));
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for (List<String> l : solveNQueens(5)) {
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System.out.println("#############");
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for (String s : l) {
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System.out.println(s);
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}
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}
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// [["Q....","..Q..","....Q",".Q...","...Q."],
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// ["Q....","...Q.",".Q...","....Q","..Q.."],
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// [".Q...","...Q.","Q....","..Q..","....Q"],
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// [".Q...","....Q","..Q..","Q....","...Q."],
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// ["..Q..","Q....","...Q.",".Q...","....Q"],
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// ["..Q..","....Q",".Q...","...Q.","Q...."],
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// ["...Q.","Q....","..Q..","....Q",".Q..."],
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// ["...Q.",".Q...","....Q","..Q..","Q...."],
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// ["....Q",".Q...","...Q.","Q....","..Q.."],
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// ["....Q","..Q..","Q....","...Q.",".Q..."]]
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// n-1-(x-y)
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// 8 0-4
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// 7 0-3, 1-4
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// 6 0-2, 1-3, 2-4
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// 5 0-1, 1-2, 2-3, 3-4
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// 4 0-0, 1-1, 2-2, 3-3, 4-4
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// 3 1-0, 2-1, 3-2, 4-3
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// 2 2-0, 3-1, 4-2
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// 1 3-0, 4-1
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// 0 4-0
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// [".Q...",
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// "...Q.",
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// "Q....",
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// "..Q..",
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// "....Q"]
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}
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}

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