Astar算法解八数码问题源码

//STATELIST.H
#pragma once
#ifndef _STATE_LIST_H
#define _STATE_LIST_H

#include <iostream>
#include <algorithm>
#include <string>
#include <set>
#include <list>


/* 表示状态的结构体 */
struct State
{
    std::string state;
    std::string pre_s;
    int space_place;
    int g;
    double h;
    

    State() : state("1234 5678"), space_place(4) {}
    State(const std::string& stat, int _g)
    {
        g = _g;
        state = stat;
        space_place = state.find(' ');
    }

    bool operator==(const State& s) const
    {
        return state == s.state;
    }

    bool operator<(const State& s) const
    {
        return g + h < s.g + s.h; //根据估价函数排序
    }
};


std::ostream& operator<<(std::ostream &o, const State& s)
{
    for (int i = 0; i < 9; i++)
    {
        if (s.pre_s.empty() || s.state[i] == s.pre_s[i])
            o << " " << s.state[i] << " ";
        else
            o << "[" << s.state[i] << "]";

        if (i % 3 == 2)
            o << "\n";
    }
    return o;
}

/* 一系列状态 */
template <typename H>
class StateList
{
public:
    struct Compare
    {
        bool operator()(const State& a, const State& b) const
        {
            return a.state < b.state;//用于保证唯一性
        }
    };
private:
    std::multiset<State> open;        //open表,按f排序
    std::set<State, Compare> open_uni;//唯一性open表
    std::set<State, Compare> closed; //唯一性closed表
    State current;                   //当前状态
    State target;			         //目标状态
    H h_func;                        //h(n)函数

    void generate_sub_state()
    {
        State next_state(current);
        next_state.g += 1; //更新g
        next_state.pre_s = current.state; //更新父状态
        std::string &s = next_state.state;
        int delta[] = { -3, 3, -1, 1 };  //上下左右
        int old_place = next_state.space_place;

        for (int i = 0; i < 4; i++)
        {
            int new_place = old_place + delta[i];
            if (check(old_place, new_place))
            {
                std::swap(s[old_place], s[new_place]);     //更新状态
                next_state.h = h_func(next_state, target); //更新h
                next_state.space_place = new_place;        //更新空位位置
                add_to_list(next_state);
                std::swap(s[old_place], s[new_place]);
            }
        }
    }

    void add_to_list(const State& state)
    {
        auto iter = open_uni.end();
        //如果状态已在open表中
        if ((iter = open_uni.find(state)) != open_uni.end() && iter->g > state.g)
        {
            //且g更小
            if (iter->g > state.g)
            {
                update_state(*iter, state);
                open_uni.erase(iter);
                open_uni.insert(state);
            }

            return;
        }
        //如果状态已在closed表中
        if ((iter = closed.find(state)) != closed.end())
        {
            //且g更小
            if (iter->g > state.g)
            {
                closed.erase(state); //从closed表移动到open表
                open.insert(state);
                open_uni.insert(state);
            }
            return;
        }

        open.insert(state);
        open_uni.insert(state);
    }


    bool check(int old_place, int new_place)
    {
        bool chk = (0 <= new_place && new_place < 9) && //新的空位在范围内
            (abs(new_place % 3 - old_place % 3) != 2);  //针对左右位移导致行数变化的检查
        return chk;
    }

    void update_state(const State& old, const State& news)
    {
        auto i = open.find(old);
        while (!(i->state == news.state))
            ++i;
        open.erase(i);
        open.insert(news);
        
    }


public:

    StateList(const State& from, const State& _target)
    {
        open.insert(from);
        open_uni.insert(from);
        current = from;
        target = _target;
    }


    bool is_arrive_target()
    {
        return current == target;
    }

    bool is_failed()
    {
        return !(open.size());
    }
    
    /* 进行下一步搜索 */
    State next()
    {
        if (!is_arrive_target() && open.size() != 0)
        {
            current = *(open.begin());  //取出n
            open.erase(open.begin());
            open_uni.erase(current);
            closed.insert(current);

            generate_sub_state();   //生成子状态
        }	
        return current;
    }

    /* 利用closed表进行回溯 */
    std::list<State> get_path()
    {
        std::list<State> path;
        path.push_back(current);
        State pre(current);

        if (!is_arrive_target())
        {
            return path;
        }

        while (!pre.pre_s.empty())
        {
            pre.state = pre.pre_s;    //生成父状态
            pre = *(closed.find(pre));//在closed表中找到父状态
            path.push_front(pre);     //添加到path
        }
        return path;
    }

    int open_list_size()
    {
        return open.size();
    }

    int closed_list_size()
    {
        return closed.size();
    }
};


/* 不同数据的数量 */
struct HFunc1
{
    double operator()(const State& cur, const State& tar)
    {
        int cnt = 0;
        for (int i = 0; i < 9; i++)
        {
            cnt += (cur.state[i] != tar.state[i]);
        }
        return cnt;
    }
};

/* 曼哈顿距离 */
struct HFunc2
{
    double operator()(const State& cur, const State& tar)
    {
        int sum = 0;
        for (int i = 0; i < 9; i++)
        {
            int p1 = cur.state.find(tar.state[i]);
            //dis = abs(y1 - y2) + abs(x1 - x2)
            int dis = abs(i / 3 - p1 / 3) + abs(i % 3 - p1 % 3);
            sum += dis;
        }
        return sum;
    }
};

/* 宽度优先搜索 */
struct HFunc3
{
    double operator()(const State& cur, const State& tar)
    {
        return 0;
    }
};

#endif

//main.cpp
#include "StateList.h"
using std::cout;
using std::string;

int main()
{
	typedef HFunc2 HFunc;//估价函数，可选HFunc[1/2/3]
	//1：按不同数字的数量；2：曼哈顿距离；3：0
	State begin("7245 3816", 0);  //起点，第二个参数为g
	State target("1234 5678", 0); //终点，第二个参数无意义

	//初始化状态表
	begin.h = HFunc()(begin, target);
	cout << "from:\n" << begin << "\n";
	cout << "to:\n" << target << "\n";
	StateList<HFunc> slist(begin, target);

	//开始搜索
	while (!slist.is_arrive_target())
	{
		if (slist.is_failed())
		{
			cout << "Failed" << "\n";
			return 0;
		}
		slist.next();
	}
	
	//打印结果
	auto path = slist.get_path();
	for (auto &s : path)
	{
		cout << s;
		printf("(g, f)=(%d, %g)\n\n", s.g, s.g + s.h);
	}

	printf("final open list size: %d\n", slist.open_list_size());
	printf("final closed list size: %d\n", slist.closed_list_size());
	return 0;
}

效果图如下，代码会打印出搜索路径