八数码

法一：广搜 + stl 实现

#include<stdio.h>
#include<set>
#include<iostream>
#include<string.h>
using namespace std;

typedef int State[9];
const int MAXSTATE = 1000000;
State st[MAXSTATE], goal ; 
int dist[MAXSTATE];

set<int>vis;
void init_lookup_table(){ vis.clear();}
int try_to_insert(int s){
	int v=0;
	for(int i = 0 ;i < 9 ; i ++ )v = v*10 + st[s][i];
	if(vis.count(v))return 0;
	vis.insert(v);
	return 1;
}

const int dx[] = {-1,1,0,0};
const int dy[] = {0,0,-1,1};
int bfs()
{
	init_lookup_table();
	int front = 1 , rear = 2 ;
	while(front<rear)
	{
		State& s = st[front];
		if(memcmp(goal,s,sizeof(s))==0)return front ;
		int z ;
		for(z = 0 ; z < 9 ; z++)if(!s[z])break;
		int x = z / 3 ,y = z%3;
		for(int i = 0 ; i< 4 ;i++)
		{
			int newx = x + dx[i];
			int newy = y + dy[i];
			int newz = newx*3+newy;
			if(newx<3 && newy<3 && newx>=0 && newy>=0)
			{
				State& t = st[rear];
				memcpy(&t,&s,sizeof(s));
				t[z] = s[newz] ;
    			t[newz] = s[z];
	    		dist[rear] = dist[front]+1;
		    	if(try_to_insert(rear))rear++;
			}
		}
		front++;
	}
	return 0;
}
int main()
{
	for(int i = 0 ; i<9 ; i++ )cin>>st[1][i];
	for(int i = 0 ; i<9 ; i++ )cin>>goal[i];
	int ans = bfs();
	if(ans>0)cout<<dist[ans]<<endl;
	else cout<<"-1"<<endl;
	return 0;
}

法二：bfs + 编码解码（康托展开）

int vis[36288],fact[9] ;

void init_lookup_table()
{
    fact[0]=1;
    for(int i = 0 ; i < 9 ; i++)fact[i] = fact[i-1]*i;
}

int try_to_insert(int s)
{
    int code = 0;
    for(int i = 0 ; i < 9 ; i++)
    {
        int cnt = 0;
        for(int j = 0 ; j < 9 ; j++)if(st[s][j]<st[s][i])cnt++;
        code+=fact[8-i]*cnt;
    }
    if(vis[code])return 0;
    return vis[code] = 1;
}

法三：bfs + 哈希

法四：双向bfs

法五：A*

法六：IDA*