N皇后问题

Posted 2022-05-26 leodaxin

/**
 * 如何判断是否是对角线，对应坐标相减结果绝对值相等则对角线: Math.abs(x1 - x2) == Math.abs(y1 - y2);
 */

N皇后第一版代码：性能较差，但是完全由自己写粗来的，基于此版本优化：

 

package com.javartisan.redpacket;

import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;

/**
 * 如何判断是否是对角线，对应坐标相减结果绝对值相等则对角线: Math.abs(x1 - x2) == Math.abs(y1 - y2);
 */
class Solution 

    public static List<List<String>> solveNQueens(int n) 

        List<List<String>> ans = new ArrayList<>();
        byte[][] mtx = new byte[n][n];
        ArrayList<String> an = new ArrayList<>();
        for (int i = 0; i < n; i++) 
            an.add("");
        
        trace(ans, an, n, n, mtx);
        HashSet<List<String>> set = new HashSet<>(ans);
        return new ArrayList<>(set);
    

    public static void trace(List<List<String>> ans, ArrayList<String> an, int n, int cur, byte[][] mtx) 

        if (cur == 0) 
            ans.add((List<String>) an.clone());
            return;
        
        for (int i = 0; i < n; i++) 
            for (int j = 0; j < n; j++) 
                if (check(mtx, i, j, n)) 
                    mtx[i][j] = 1;
                    StringBuilder sb = new StringBuilder();
                    for (int k = 0; k < n; k++) 
                        if (k == j) 
                            sb.append("Q");
                         else 
                            sb.append(".");
                        
                    
                    an.set(i, sb.toString());
                    trace(ans, an, n, --cur, mtx);
                    an.set(i, "");
                    mtx[i][j] = 0;
                    cur++;
                
            
        

    


    public static boolean check(byte[][] mtx, int x, int y, int n) 

        boolean status = true;

        for (int i = 0; i < n && status; i++) 
            if (mtx[x][i] == 1) 
                status = false;
                break;
            
        

        for (int i = 0; i < n && status; i++) 
            if (mtx[i][y] == 1) 
                status = false;
                break;
            
        

        for (int i = x, j = y; i > 0 && j > 0 && status; i--, j--) 
            if (mtx[i - 1][j - 1] == 1) 
                status = false;
                break;
            
        

        for (int i = x, j = y; i < n - 1 && j < n - 1 && status; i++, j++) 

            if (mtx[i + 1][j + 1] == 1) 
                status = false;
                break;
            
        

        for (int i = x, j = y; i < n - 1 && j > 0 && status; i++, j--) 

            if (mtx[i + 1][j - 1] == 1) 
                status = false;
                break;
            
        

        for (int i = x, j = y; i > 0 && j < n - 1 && status; i--, j++) 

            if (mtx[i - 1][j + 1] == 1) 
                status = false;
                break;
            
        

        return status;
    

    public static void main(String[] args) 

        byte[][] mtx = 
                0, 0, 1, 0,
                0, 0, 0, 0,
                0, 0, 0, 0,
                0, 0, 0, 0,
        ;

        int n =7;
        long start = System.currentTimeMillis();
        System.out.println(solveNQueens(n));
        System.out.println(System.currentTimeMillis() - start);
        System.out.println(solveNQueens(n).size());

    

 

简单优化版：

import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;

/**
 * 如何判断是否是对角线，对应坐标相减结果绝对值相等则对角线: Math.abs(x1 - x2) == Math.abs(y1 - y2);
 */
class Solution 


    public static List<List<String>> solveNQueens(int n) 

        byte[] x = new byte[n];
        byte[] y = new byte[n];

        List<List<String>> ans = new ArrayList<>();
        byte[][] mtx = new byte[n][n];
        ArrayList<String> an = new ArrayList<>();
        for (int i = 0; i < n; i++) 
            an.add("");
        
        trace(ans, an, n, n, mtx, x, y);
        HashSet<List<String>> set = new HashSet<>(ans);
        return new ArrayList<>(set);
    

    public static void trace(List<List<String>> ans, ArrayList<String> an, int n, int cur, byte[][] mtx, byte[] usedX, byte[] usedY) 

        if (cur == 0) 
            ans.add((List<String>) an.clone());
            return;
        
        for (int i = 0; i < n; i++) 
            if (usedX[i] == 1) 
                continue;
            
            for (int j = 0; j < n; j++) 
                if (usedY[j] != 1 && check(mtx, i, j, n)) 
                    mtx[i][j] = 1;
                    usedX[i] = 1;
                    usedY[j] = 1;
                    StringBuilder sb = new StringBuilder();
                    for (int k = 0; k < n; k++) 
                        if (k == j) 
                            sb.append("Q");
                         else 
                            sb.append(".");
                        
                    
                    an.set(i, sb.toString());
                    trace(ans, an, n, --cur, mtx, usedX, usedY);
                    an.set(i, "");
                    mtx[i][j] = 0;
                    usedX[i] = 0;
                    usedY[j] = 0;
                    cur++;
                
            
        

    


    public static boolean check(byte[][] mtx, int x, int y, int n) 

        boolean status = true;

        for (int i = 0; i < n && status; i++) 
            if (mtx[x][i] == 1) 
                status = false;
                break;
            
        

        for (int i = 0; i < n && status; i++) 
            if (mtx[i][y] == 1) 
                status = false;
                break;
            
        

        for (int i = x, j = y; i > 0 && j > 0 && status; i--, j--) 
            if (mtx[i - 1][j - 1] == 1) 
                status = false;
                break;
            
        

        for (int i = x, j = y; i < n - 1 && j < n - 1 && status; i++, j++) 

            if (mtx[i + 1][j + 1] == 1) 
                status = false;
                break;
            
        

        for (int i = x, j = y; i < n - 1 && j > 0 && status; i++, j--) 

            if (mtx[i + 1][j - 1] == 1) 
                status = false;
                break;
            
        

        for (int i = x, j = y; i > 0 && j < n - 1 && status; i--, j++) 

            if (mtx[i - 1][j + 1] == 1) 
                status = false;
                break;
            
        

        return status;
    

    public static void main(String[] args) 

        byte[][] mtx = 
                0, 0, 1, 0,
                0, 0, 0, 0,
                0, 0, 0, 0,
                0, 0, 0, 0,
        ;

        System.out.println(solveNQueens(4).size());


        int n = 7;
        long start = System.currentTimeMillis();
        System.out.println(solveNQueens(n));
        System.out.println(System.currentTimeMillis() - start);
        start = System.currentTimeMillis();
        System.out.println(solveNQueens(8).size());
        System.out.println(System.currentTimeMillis() - start);