问题描述：

将8-魔方的起始状态在有限移动步骤内，转换为目标状态，如下图所示。

算法思路：

通过优先队列实现相似度比对，当相似度为9，即当前状态与目标状态一致时，返回当前路径。

源码：

/*
	8-cube problem-Best-First algorithm
	15S103182
	Ethan
	2015.12.21
*/
#include <iostream>
#include <vector>
#include <queue>
#include <fstream>
#include <sstream>
using namespace std ;
class cube{
public:
	vector<vector<int> > m;
	int similarity;
	int x;// 0::i
	int y;// 0::j
	vector<string> path;//up down left right 
	cube(vector<vector<int> > a,int b):m(a),similarity(b){}
	void pos(){//0-position
		for(int i=0;i<m.size();i++){
			for(int j=0;j<m[i].size();j++){
				if(m[i][j]==0){
					x = i;
					y = j;
					return ;
				}
			}
		}
	}
};
bool operator < (const cube& a,const cube& b){
	return a.similarity<=b.similarity;
}
int stringToInt(string i){
	stringstream sf;
	int score=0;
	sf<<i;
	sf>>score;
	return score;
}
cube openFile(const char* dataset){
	fstream file;
	file.open(dataset,ios::in);
	vector<vector<int> > data;
	while(!file.eof()){
		vector<int> tv;
		char temp[8];
		file.getline(temp,6);		
		tv.push_back(temp[0]-48);
		tv.push_back(temp[2]-48);
		tv.push_back(temp[4]-48);
		data.push_back(tv) ;
	}		
	file.close();
	cube res(data,0);
	return res;
}
void output(vector<vector<int> > m){
	for(int i=0;i<m.size();i++){
		for(int j=0;j<m[i].size();j++){
			cout<<m[i][j]<<"	";
		}
		cout<<endl;
	}
}
int calSimilarity(cube a,cube t){
	int s = 0;
	for(int i=0;i<3;i++){
		for(int j=0;j<3;j++){
			if(a.m[i][j]==t.m[i][j])
				s++;
		}
	}
	return s;
}
vector<cube> move(const cube& v){
	vector<cube> res;
	if(v.x>0){
		cube a(v);
		a.m[a.x][a.y] = a.m[a.x-1][a.y];
		a.m[a.x-1][a.y] = 0;
		a.x--;
		a.path.push_back("down");
		res.push_back(a);
	}
	if(v.x<2){
		cube a(v);
		a.m[a.x][a.y] = a.m[a.x+1][a.y];
		a.m[a.x+1][a.y] = 0;
		a.x++;
		a.path.push_back("up");
		res.push_back(a);
	}
	if(v.y>0){
		cube a(v);
		a.m[a.x][a.y] = a.m[a.x][a.y-1];
		a.m[a.x][a.y-1] = 0;
		a.y--;
		a.path.push_back("right");
		res.push_back(a);
	}
	if(v.y<2){
		cube a(v);
		a.m[a.x][a.y] = a.m[a.x][a.y+1];
		a.m[a.x][a.y+1] = 0;
		a.y++;
		a.path.push_back("left");
		res.push_back(a);
	}
	return res;
}
void eightCube(cube orginal,cube target){
	priority_queue<cube,vector<cube>,less<cube> > pq;
	vector<cube> copy;
	orginal.similarity = calSimilarity(orginal,target);
	orginal.pos();
	pq.push(orginal);
	copy.push_back(orginal);
	while(!pq.empty()){//best-first
		cube v = pq.top();
		pq.pop();
		vector<cube> ms = move(v);
		for(int i=0;i<ms.size();i++){
			ms[i].similarity = calSimilarity(ms[i],target);
			ms[i].pos();
			int flag = 1;
			for(int j=copy.size()-1;j>=0;j--){
				if(calSimilarity(ms[i],copy[j])==9){
					flag = 0;
					break;
				}
			}
			if(flag){
				if(ms[i].similarity==9){
					cout<<"Path:"<<endl;
					cout<<"orginal --> ";
					for(int k=0;k<ms[i].path.size();k++){
						cout<<ms[i].path[k]<<" --> ";
					}
					cout<<"target"<<endl;
					return ;
				}
				pq.push(ms[i]);
				copy.push_back(ms[i]);
			}
		}
	}
}

int main()
{
	eightCube(openFile("original.txt"),openFile("target.txt"));
}

测试：

起始状态：

5     6     7

2     0     3

1     4     8

目标状态：

1     2     3

4     5     6

7     8     0

移动路径：