POJ 3239 Solution to the n Queens Puzzle

最新推荐文章于 2018-06-23 10:05:23 发布

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最新推荐文章于 2018-06-23 10:05:23 发布

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分类专栏： poj 文章标签： poj

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本文介绍了一种解决N皇后问题的有效算法。通过递归搜索和冲突检查，文章提供了一个能够找到任意大小N×N棋盘上皇后放置方案的C++程序实现。特别地，对于N大于3的情况，给出了一个预设的解决方案。

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Solution to the n Queens Puzzle

Time Limit: 1000MS		Memory Limit: 131072K
Total Submissions: 3469		Accepted: 1275		Special Judge

Description

The eight queens puzzle is the problem of putting eight chess queens on an 8 × 8 chessboard such that none of them is able to capture any other. The puzzle has been generalized to arbitrary n × n boards. Given n, you are to find a solution to the n queens puzzle.

POJ 3239 Solution to the n Queens Puzzle - Night - Time Ends.

Input

The input contains multiple test cases. Each test case consists of a single integer n between 8 and 300 (inclusive). A zero indicates the end of input.

Output

For each test case, output your solution on one line. The solution is a permutation of {1, 2, …, n}. The number in the ith place means the ith-column queen in placed in the row with that number.

Sample Input

8
0

Sample Output

5 3 1 6 8 2 4 7

Source

POJ Monthly--2007.06.03, Yao, Jinyu

N皇后问题，主要是为了测试代码:

#include <iostream>
#include <vector>
using namespace std;

class Queen {
public:
    char QChar, BChar;  // 代表皇后和空白的字符
    int * q_in_row;  // q_in_row[i] = j表示在第i行第j列有个皇后
    bool * col_free;  // col_free[i] = true表示第i列没有皇后
    bool * up_free;  // 从右上到左下的对角线是否可以放置皇后
    bool * down_free;  // 从左上到右下的对角线是否可以放置皇后
    int N;  // 皇后个数、正方形棋盘的边长
    bool ONE, NUM, ALL;  // 由于只有一个递归函数，三个变量用于区分是哪一个问题
    bool ONE_FINISH;  // 判断只返回一个解的问题是否已经解决
    int num;  // 所有解的个数
    vector<vector<char> > oneAns;  // 一个解
    vector<vector<vector<char> > > allAns;  // 所有解

    Queen() {
        QChar = 'Q';
        BChar = '.';
        ONE = NUM = ALL = ONE_FINISH = false;
    }

    void changeChar(char q, char b) {  // 可以改变代表皇后和空白的字符
        QChar = q;
        BChar = b;
    }

    void makeBoard(int n) {
        N = n;
        q_in_row = new int[N];
        col_free = new bool[N];
        up_free = new bool[2 * N - 1];
        down_free = new bool[2 * N - 1];
        for (int i = 0; i < N; i++) q_in_row[i] = col_free[i] = true;
        for (int i = 0; i < 2 * N - 1; i++) up_free[i] = down_free[i] = true;
    }

    void deleteBoard() {
        delete []q_in_row;
        delete []col_free;
        delete []up_free;
        delete []down_free;
    }

    void construct_solution() {
        int row = 0;
        if (N % 6 != 2 && N % 6 != 3) {
            if (N % 2 == 0) {
                for (int i = 2; i <= N; i += 2) q_in_row[row++] = i - 1;
                for (int i = 1; i <= N - 1; i += 2) q_in_row[row++] = i - 1;
            } else {
                for (int i = 2; i <= N - 1; i += 2) q_in_row[row++] = i - 1;
                for (int i = 1; i <= N; i += 2) q_in_row[row++] = i - 1;
            }
        } else {
            if (N % 2 == 0) {
                if ((N / 2) % 2 == 0) {
                    for (int i = N / 2; i <= N; i += 2) q_in_row[row++] = i - 1;
                    for (int i = 2; i <= N / 2 - 2; i += 2) q_in_row[row++] = i - 1;
                    for (int i = N / 2 + 3; i <= N - 1; i += 2) q_in_row[row++] = i - 1;
                    for (int i = 1; i <= N / 2 + 1; i += 2) q_in_row[row++] = i - 1;
                } else {
                    for (int i = N / 2; i <= N - 1; i += 2) q_in_row[row++] = i - 1;
                    for (int i = 1; i <= N / 2 - 2; i += 2) q_in_row[row++] = i - 1;
                    for (int i = N / 2 + 3; i <= N; i += 2) q_in_row[row++] = i - 1;
                    for (int i = 2; i <= N / 2 + 1; i += 2) q_in_row[row++] = i - 1;
                }
            } else {
                if ((N / 2) % 2 == 0) {
                    for (int i = N / 2; i <= N - 1; i += 2) q_in_row[row++] = i - 1;
                    for (int i = 2; i <= N / 2 - 2; i += 2) q_in_row[row++] = i - 1;
                    for (int i = N / 2 + 3; i <= N - 2; i += 2) q_in_row[row++] = i - 1;
                    for (int i = 1; i <= N / 2 + 1; i += 2) q_in_row[row++] = i - 1;
                    q_in_row[row++] = N - 1;
                } else {
                    for (int i = N / 2; i <= N - 2; i += 2) q_in_row[row++] = i - 1;
                    for (int i = 1; i <= N / 2 - 2; i += 2) q_in_row[row++] = i - 1;
                    for (int i = N / 2 + 3; i <= N - 1; i += 2) q_in_row[row++] = i - 1;
                    for (int i = 2; i <= N / 2 + 1; i += 2) q_in_row[row++] = i - 1;
                    q_in_row[row++] = N - 1;
                }
            }
        }
        write_in(oneAns);
    }

    vector<vector<char> > Return_an_ans(int n) {
        makeBoard(n);

        if (n > 3) {
            construct_solution();
            deleteBoard();
            return oneAns;
        }

        ONE = true;
        dfs(0);
        deleteBoard();
        return oneAns;
    }

    int Return_all_ans_num(int n) {
        makeBoard(n);
        NUM = true;
        num = 0;
        dfs(0);
        deleteBoard();
        return num;
    }

    vector<vector<vector<char> > > Return_all_ans(int n) {
        makeBoard(n);
        ALL = true;
        dfs(0);
        deleteBoard();
        return allAns;
    }

    void write_in(vector<vector<char> > & a) {
        a.resize(N);
        for (int i = 0; i < N; i++) {
            a[i].resize(N);
            for (int j = 0; j < N; j++) {
                if (q_in_row[i] == j) a[i][j] = QChar;
                else a[i][j] = BChar;
            }
        }
    }

    void dfs(int now) {

        if (now == N) {
            if (ONE) {
                ONE_FINISH = true;
                write_in(oneAns);
                return;
            }
            if (NUM) {
                num++;
                return;
            }
            if (ALL) {
                vector<vector<char> > a;
                write_in(a);
                allAns.push_back(a);
                return;
            }
        }

        for (int col = 0; col < N; col++) {
            if (col_free[col] && up_free[now + col] && down_free[now - col + N - 1]) {
                q_in_row[now] = col;
                col_free[col] = up_free[now + col] = down_free[now - col + N - 1] = false;
                dfs(now + 1);
                if (ONE && ONE_FINISH) return;
                col_free[col] = up_free[now + col] = down_free[now - col + N - 1] = true;
            }
        }
    }
};

int main() {

    std::cout.sync_with_stdio(false);

    while (1) {
        Queen q;
        int n;
        cin >> n;
        if (n == 0) break;

        vector<vector<char> > ans = q.Return_an_ans(n);

        for (int i = 0; i < ans.size(); i++) {
            for (int j = 0; j < ans[i].size(); j++) {
                if (ans[i][j] == 'Q') {
                    if (i) cout << " ";
                    cout << j + 1;
                }
            }
        }
        cout << endl;



    }

    return 0;
}