八皇后问题独立解JAVA代码

import java.util.HashMap;
import java.util.Map;

/**
 * 八皇后问题
 * 
 * @author Watson Xu
 * @since 2016年4月8日 v1.0.0
 */
public class Queens {
	private Integer queens;

	// 同栏是否有皇后，1表示有
	private Integer[] column;

	// 右上至左下是否有皇后
	private Integer[] rup;

	// 左上至右下是否有皇后
	private Integer[] lup;

	// 解答
	private Integer[] queen;
	
	// 独立解 及其对称图形
	private Map<String, String> results = new HashMap<String, String>();

	// 解答编号
	private int num;

	public Queens(int queens) {
		this.queens = queens;
		column = new Integer[queens + 1];
		rup = new Integer[(2 * queens) + 1];
		lup = new Integer[(2 * queens) + 1];
		queen = new Integer[queens + 1];
		
		for (int i = 0; i <= queens; i++) {
			column[i] = queen[i] = 0;
		}

		for (int i = 0; i <= (2 * queens); i++) {
			rup[i] = lup[i] = 0; // 初始定义全部无皇后
		}

		
	}

	public void backtrack(int i) {
		if (i > queens) {
			showAnswer();
		} else {
			for (int j = 1; j <= queens; j++) {
				if ((column[j] == 0) && (rup[i + j] == 0) && (lup[i - j + queens] == 0)) {
					// 若无皇后
					queen[i] = j;
					// 设定为占用
					column[j] = rup[i + j] = lup[i - j + queens] = 1;
					backtrack(i + 1); // 循环调用
					column[j] = rup[i + j] = lup[i - j + queens] = 0;
				}
			}
		}
	}

	protected void showAnswer() {
		num++;
		if(!isIndependence(num)) return;
		System.out.println("解答" + num + ":");
		for (int y = 1; y <= queens; y++) {
			for (int x = 1; x <= queens; x++) {
				if (queen[y] == x) {
					System.out.print(" Q");
				} else {
					System.out.print(" .");
				}
			}
			System.out.println(" ");
		}
		System.out.println();
	}
	
	protected boolean isIndependence(int number) {
		// 自身
		String newSolution = resultToString(queen);
		String flag = results.get(newSolution);

		if (flag != null) {
			//System.out.println("非独立解答解答, 同解答 " + flag + " 对称。");
			return false;
		}

		// 左右对称
		Integer[] leftRight = new Integer[queen.length];
		// 上下对称
		Integer[] upDown = new Integer[queen.length];
		// 左上右下对称
		Integer[] lurd = new Integer[queen.length];
		// 右上左下对称
		Integer[] ruld = new Integer[queen.length];
		// 顺时针第1次旋转
		Integer[] cw1 = new Integer[queen.length];
		for (int i = 1; i < queen.length; i++) {
			leftRight[i] = queen[queen.length - i];
			upDown[i] = queen.length - queen[i];
			lurd[queen.length - queen[i]] = queen.length - i;
			ruld[queen[i]] = i;
			cw1[queen[i]] = queen.length - i;
		}
		// 顺时针第2次旋转
		Integer[] cw2 = new Integer[queen.length];
		for (int i = 1; i < queen.length; i++) {
			cw2[cw1[i]] = queen.length - i;
		}
		// 顺时针第3次旋转
		Integer[] cw3 = new Integer[queen.length];
		for (int i = 1; i < queen.length; i++) {
			cw3[cw2[i]] = queen.length - i;
		}

		results.put(newSolution, number + "_self");
		putNewSolution(leftRight, number + "_lr");
		putNewSolution(upDown, number + "_ud");
		putNewSolution(lurd, number + "_lurd");
		putNewSolution(ruld, number + "_ruld");
		putNewSolution(cw1, number + "_cw1");
		putNewSolution(cw2, number + "_cw2");
		putNewSolution(cw3, number + "_cw3");

		return true;
	}
	
	protected void putNewSolution(Integer[] temp, String mark) {
		String newSolution = resultToString(temp);
		String flag = results.get(newSolution);
		
		if(flag == null) {
			results.put(newSolution, mark);
		}
	}
	
	protected String resultToString(Integer[] result) {
		StringBuilder sb = new StringBuilder();
		for (int i = 1; i < queen.length; i++) {
			sb.append(result[i]);
		}
		return sb.toString();
	}
	
	// 计算复杂度 15720
	public static void main(String[] args) {
		Queens queen = new Queens(8);
		queen.backtrack(1);
	}
	
}