105-算法应用【N皇后问题】代码实现

问题应用：N皇后问题

算法主要思想：动态规划（构建树解）、BFS

算法核心代码实现：

//https://www.cnblogs.com/cheng2839
class QueensContainer {
    int n = -1;//n代表容器大小，及放置n个皇后
    int[][] containers; //容器;0:可放置，1:皇后，-1:不可放置
    State solvedTree;
    List<int[][]> result = new ArrayList<>();

    public QueensContainer(int n) {
        this.n = n;
        containers = new int[n][n];

        State solvedTreeRoot = new State();
        solvedTreeRoot.cs = this.containers;
        for (int i = 0; i < containers.length; i++) {
            State s = new State();
            s.h++;
            int[][] cs = clone(containers);
            cs[0][i] = 1;
            update(0, i, cs);
            s.cs = cs;
            solvedTreeRoot.children.add(s);
        }
        this.buildSolvedTree(solvedTreeRoot.children);

        this.solvedTree = solvedTreeRoot;
    }

    class State {
        int h = 0;
        int[][] cs;
        List<State> children = new ArrayList<>();
    }

    //原文：https://www.cnblogs.com/cheng2839
    void buildSolvedTree(List<State> root) {
        if (null == root || root.size() == 0)
            return;
        for (State state : root) {
            int h = state.h;
            if (h == state.cs.length)
                continue;

            int[] is = state.cs[h];
            for (int i = 0; i < is.length; i++) {
                if (is[i] == 0) {
                    State s = new State();
                    s.h = h + 1;
                    int[][] cs = clone(state.cs);
                    cs[h][i] = 1;
                    update(h, i, cs);
                    s.cs = cs;
                    state.children.add(s);
                }
            }
            buildSolvedTree(state.children);
        }
    }

    //原文：https://www.cnblogs.com/cheng2839
    void bfs(List<State> root) {
        if (null == root || root.size() == 0)
            return;
        for (State s : root) {
            if (null == s.children || s.children.size() == 0) {
                int n = 0;
                for (int i = 0; i < s.cs.length; i++) {
                    for (int j = 0; j < s.cs[i].length; j++) {
                        n += s.cs[i][j]==1 ? 1 : 0;
                    }
                }
                if (n == s.cs.length)
                    result.add(s.cs);
                continue;
            }
            bfs(s.children);
        }
    }

    //第i，j位置放置皇后，更新容器
    //原文：https://www.cnblogs.com/cheng2839
    boolean update(int i, int j, int[][] con) {
        for (int k = 0; k < con.length; k++) {
            for (int l = 0; l < con[k].length; l++) {
                int d = con[k][l];
                if (k == i && l == j) {
                    continue;
                }

                boolean dead = false;
                if (k == i) {
                    dead = true;
                }
                if (l == j) {
                    dead = true;
                }
                if (k-i == l-j) {
                    dead = true;
                }
                if (k-i == j-l) {
                    dead = true;
                }
                if (dead && d == 0) {
                    con[k][l] = -1;
                    continue;
                }
                if (dead && d == -1) {
                    continue;
                }
                if (dead && d == 1) {
                    return false;
                }
            }
        }
        return true;
    }

    public void print(int[][] con) {
        StringBuilder stringBuilder = new StringBuilder();
        for (int i = 0; i < con.length; i++) {
            for (int j = 0; j < con[i].length; j++) {
                stringBuilder.append(con[i][j]==-1?0:con[i][j]);
                if (j < con[i].length-1) {
                    stringBuilder.append(", ");
                }
            }
            if (i < con.length-1) {
                stringBuilder.append("
");
            }
        }
        System.out.println(stringBuilder.toString());
    }

    int[][] clone(int[][] con) {
        int[][] newCon = new int[con.length][con[0].length];
        for (int i = 0; i < con.length; i++) {
            for (int j = 0; j < con[i].length; j++) {
                newCon[i][j] = con[i][j];
            }
        }
        return newCon;
    }
}

结果展示：

（输出分控制台打印和可视图形化）可视化图形可通过按键（上下/左右）查看结果

import javax.swing.*;
import java.awt.*;
import java.awt.event.KeyAdapter;
import java.awt.event.KeyEvent;
import java.util.ArrayList;
import java.util.List;

/**
 * @Description N皇后问题
 * @Author https://www.cnblogs.com/cheng2839
 * @Date 2021年3月22日
 * @Version v1.0
 */
public class NQueens {

    static class MyFrame extends JPanel {
        JFrame jFrame = new JFrame();
        static final int SIZE = 50;
        static final int L = 3;
        int[][] data = null; //一个解
        static int DATA_INDEX = 0;
        static List<int[][]> result; //全部解
        public MyFrame(int n, List<int[][]> result) {
            MyFrame.result = result;
            jFrame.setTitle(n+"皇后问题—第"+(DATA_INDEX+1)+"/"+result.size()+"个解");
            data = result.get(DATA_INDEX);
            jFrame.setLayout(new CardLayout());
            jFrame.setBounds(0, 0, 500, 500);
            this.setBackground(Color.WHITE);
            jFrame.addKeyListener(new KeyAdapter() {
                public void keyReleased(KeyEvent e) {
                    if (e.getKeyCode() == KeyEvent.VK_RIGHT || e.getKeyCode() == KeyEvent.VK_UP) {
                        DATA_INDEX = Math.min(DATA_INDEX+1, result.size()-1);
                    } else if (e.getKeyCode() == KeyEvent.VK_LEFT || e.getKeyCode() == KeyEvent.VK_DOWN) {
                        DATA_INDEX = Math.max(DATA_INDEX-1, 0);
                    }
                    data = result.get(DATA_INDEX);
                    jFrame.setTitle(n+"皇后问题—第"+(DATA_INDEX+1)+"/"+result.size()+"个解");
                    MyFrame.this.repaint();
                }
            });
            /*new Thread(()->{
                while (true)
                    this.repaint(50);
            }).start();*/
            jFrame.add(this);
            jFrame.setVisible(true);
            jFrame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        }

        @Override
        public void paintComponent(Graphics g0) {
            if (null == data)return;
            Graphics2D g = (Graphics2D) g0;
            int w, h = -L;
            for (int i = 0; i < data.length; i++) {
                w = 0; h += L;
                for (int j = 0; j < data[i].length; j++) {
                    g.setColor(data[i][j] == 1 ? Color.RED : Color.LIGHT_GRAY);
                    g.fillRect(i * SIZE + h, j * SIZE + w, SIZE, SIZE);
                    w += L;
                }
            }
        }
    }

    public static void main(String[] args) {
        int n = 8;
        QueensContainer qc = new QueensContainer(n);
        QueensContainer.State root = qc.solvedTree;
        qc.bfs(root.children);
        List<int[][]> result = qc.result;

        //可视化图形界面
        new MyFrame(n, result);

        //控制台打印方式
        /*System.out.println("一共求出"+result.size()+"组解。");
        for (int[][] rs : result) {
            qc.print(rs);
            System.out.print("
");
        }*/
    }
}