八数码问题

#pragma warning(disable:4786)
#include<iostream>
#include<set>
#include<queue>
#include<cmath>
using namespace std;

int gOrient[4][2] = {-1,0, 1,0, 0,-1, 0,1};

//-----------------------------------------------------------------------------

class State
{
public:
    int findPos(int n) const;
    bool operator < (const State& s) const;
    void print() const;
    void distance(int ans[]);
    void calHash();
    void calc(int ans[]);
public:
    int a[9];
    int step;
    int dis;
    int hash;
};

//-----------------------------------------------------------------------------

class EightFigure
{
public:
    EightFigure(int* init, int* ans = NULL);
    bool hasAnswer() const;
    void setInitState(int init[]);
    void setAnswer(int ans[]);
    void astar();
private:
    int answer[9];
    set<int> calculated;
    priority_queue<State> states;
};

//-----------------------------------------------------------------------------

int State::findPos(int n) const
{
    for (int i=0; i<9; i++)
        if (a[i] == n)
            return i;
    return -1;
}

//优先队列默认大的优先,这里实际是求大于
bool State::operator < (const State& s) const
{
    return s.step + s.dis < step + dis;
}

void State::print() const
{
    for (int i=0; i<9; i++)
    {
        if (i % 3 == 0)
            cout<<endl;
        cout<<a[i]<<' ';
    }
    cout<<endl;
}

void State::distance(int ans[])
{
    dis = 0;
    for (int i=0; i<9; i++)
        dis += abs(ans[i]-a[i]);
}

void State::calHash()
{
    int fac[] = {1,1,2,6,24,120,720,4050,40320};
    hash = 0;
    for (int i=0; i<9; i++)
    {
        int reverse = 0;
        for (int j=i+1; j<9; j++)
            if (a[j] < a[i])
                reverse++;
        hash += reverse * fac[a[i]];
    }
}

void State::calc(int ans[])
{
    step++;
    distance(ans);
    calHash();
}

//-----------------------------------------------------------------------------

EightFigure::EightFigure(int* init, int* ans)
{
    if (ans == NULL)
        for (int i=0; i<9; i++)
            answer[i] = i;
    else
        memcpy(answer, ans, 9*sizeof(int));

    State s;
    memcpy(s.a, init, 9*sizeof(int));
    s.step = 0;
    s.distance(ans);
    s.calHash();

    states.push(s);
    calculated.insert(s.hash);
}

//判断是否无解
bool EightFigure::hasAnswer() const
{
    State now = states.top();
    int reverseInit = 0, reverseAns = 0;
    for (int i=0; i<9; i++)
    {
        int countInit = 0, countAns = 0;
        for (int j=i+1; j<9; j++)
        {
            if (now.a[j] < now.a[i])
                countInit++;
            if (answer[j] < answer[i])
                countAns++;
        }

        reverseInit += countInit;
        reverseAns += countAns;
    }

    return reverseInit%2 == reverseAns%2;
}

void EightFigure::setAnswer(int ans[])
{
    memcpy(answer, ans, 9*sizeof(int));
}

void EightFigure::astar()
{
    if (!hasAnswer())
    {
        cout<<"无解\n";
        return;
    }

    while (!states.empty())
    {
        State now = states.top();
        states.pop();
        now.print();
        if (now.dis == 0)
            break;

        int zero = now.findPos(0);
        int x = zero/3;
        int y = zero%3;

        for (int i=0; i<4; i++)
        {
            int xx = x + gOrient[i][0];
            int yy = y + gOrient[i][1];
            if (xx < 0 || xx >= 3 || yy < 0 || yy >= 3)
                continue;

            State s = now;
            s.a[zero] = s.a[xx*3+yy];
            s.a[xx*3+yy] = 0;
            s.calc(answer);

            if (calculated.find(s.hash) == calculated.end())
            {
                calculated.insert(s.hash);
                states.push(s);
            }
        }
    }
}

//-----------------------------------------------------------------------------

void main()
{
    int init[9] = {3,5,1,2,8,6,7,4,0};
    int ans[] = {1,2,3,4,5,6,7,8,0};
    EightFigure eightFigure(init, ans);
    eightFigure.astar();
}