POJ 3239 Solution to the n Queens Puzzle

Solution to the n Queens Puzzle

Time Limit: 1000MS Memory Limit: 131072KTotal 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.

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

80

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;}