马的遍历

题目描述：

马只能在棋盘中走日字路，在m*n的棋盘上从任意一点开始让这个马遍历玩所有的点，共有多少种可能

#include <iostream>#include <iterator>#include <vector>#include <map>#include <set>#include <algorithm>using namespace std;struct Position{    int x;    int y;    short b_used:1;    bool operator <(const Position& right) const;    bool operator==(const Position& right) const;};bool Position::operator <(const Position& right) const{    if (x < right.x)    {        return true;    }    else if (x == right.x)    {        if (y < right.y)        {            return true;        }    }    return false;}bool Position::operator==(const Position& right) const{    if (x == right.x && y == right.y)    {        return true;    }    return false;}class ChessHorse{public:    /**    *     **/    ChessHorse(int t_n,int t_m)        :n(t_n),        m(t_m)    {        deriction = 8;  /*共有8个方向*/        SetPos poss;        ChessBoardCol chess_board_col(m,poss);        chess_board_path = ChessBoardPath(n,chess_board_col);        init_path();        VecInt cols(m);        chess_board = ChessBoard(n,cols);        found_count = 0;    }    ~ChessHorse()    {        return;    }    /**     * 初始化路径值     */    int init_path()    {        for (int i = 0;i < n;i ++)        {            for (int j = 0;j < m;j ++)            {                for (int deriction = 1;deriction <= 8;deriction ++)                {                    int x = i;                    int y = j;                    switch (deriction)                    {                        case 1: x += 1;  y += 2; break;                        case 2: x += 1;  y -= 2; break;                        case 3: x -= 1;  y += 2; break;                        case 4: x -= 1;  y -= 2; break;                        case 5: x += 2;  y += 1; break;                        case 6: x += 2;  y -= 1; break;                        case 7: x -= 2;  y += 1; break;                        case 8: x -= 2;  y -= 1; break;                        default: return -1;                    }                    if (check(x,y) == false)                    {                        continue;                    }                    Position pos;                    pos.x = x;                    pos.y = y;                    pos.b_used = 0;                    SetPos &poss = chess_board_path[i][j];                    poss.insert(pos);                }            }        }        return 1;    }    bool check(int x,int y)    {        if (x >= n || x < 0 || y >= m || y < 0)        {            return false;        }        return true;    }    /**     * x,y起始坐标     */    int search(int x,int y,int dep)    {        SetPos &poss = chess_board_path[x][y];        Position pos;        pos.x = x;        pos.y = y;        chess_board[x][y] = dep;        //print_table();        if (dep == n * m)        {            cout << "found:" << endl;            print_table();            cout << "--------------" << endl;            found_count ++;            return 1;        }        if (poss.empty() == true)        {            //无路可走            return 0;        }        for (SetPos::iterator iter = poss.begin();            iter != poss.end();++iter)        {            x = iter->x;            y = iter->y;            SetPos& t_poss = chess_board_path[x][y];            t_poss.erase(pos);        }        for (SetPos::iterator iter = poss.begin();            iter != poss.end();++iter)        {            short b_used = iter->b_used;            if (b_used == 1)            {                continue;            }            x = iter->x;            y = iter->y;            SetPos &t_poss = chess_board_path[x][y];            search(x,y,dep + 1);        }        for (SetPos::iterator iter = poss.begin();            iter != poss.end();++iter)        {            x = iter->x;            y = iter->y;            SetPos& t_poss = chess_board_path[x][y];            t_poss.insert(pos);        }        chess_board[x][y] = 0;        return 1;    }    /**     *      */    void print_table()    {        ChessBoard::iterator iter = chess_board.begin();        for (;iter != chess_board.end();++iter)        {            VecInt cols = *iter;            VecInt::iterator iter_col = cols.begin();            for (;iter_col != cols.end();++iter_col)            {                cout << *iter_col << "\t";            }            cout << endl;        }    }    int get_found_count()    {        return found_count;    }protected:    int n,m;    int deriction;    typedef vector<Position> VecPos;    typedef set<Position> SetPos;    typedef vector<SetPos> ChessBoardCol;    typedef vector<ChessBoardCol> ChessBoardPath;    typedef vector<int> VecInt;    typedef vector<VecInt> ChessBoard;    ChessBoard chess_board;    ChessBoardPath chess_board_path;    int found_count;private:};int main(){    ChessHorse chess_horse(4,3);    chess_horse.search(0,1,1);    cout << "total found:" << chess_horse.get_found_count() << endl;    return 0;};

通过贪心算法可以找到一个解，但不能找到所有的解，通过剪枝可以找到所有的解，但是算法复杂度十分大