luogu P1379 八数码难题

Posted 2020-10-11 ioioioioioio

 

题目描述

在3×3的棋盘上，摆有八个棋子，每个棋子上标有1至8的某一数字。棋盘中留有一个空格，空格用0来表示。空格周围的棋子可以移到空格中。要求解的问题是：给出一种初始布局（初始状态）和目标布局（为了使题目简单,设目标状态为123804765），找到一种最少步骤的移动方法，实现从初始布局到目标布局的转变。

输入输出格式

输入格式：

 

输入初始状态，一行九个数字，空格用0表示

 

输出格式：

 

只有一行，该行只有一个数字，表示从初始状态到目标状态需要的最少移动次数(测试数据中无特殊无法到达目标状态数据)

 

输入输出样例

输入样例#1：

283104765

输出样例#1：

4

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <map>
#include <queue>
#include <cstring>
#include <string> 

using namespace std;
const string s_end = "123804765";

struct Node{
    string s;
    int step;
};
queue <Node> Q1;
map <string, bool> mp;
string s_start;
int Step;

inline void pd(string ss, int answer)
{
    if(ss == s_end)
    {
        printf("%d",answer);
        exit(0);
    }
}

inline void bfs()
{
    while(!Q1.empty())
    {
        Node topp = Q1.front();
        Q1.pop();
        string s1 = topp.s;
        Step = topp.step;
        int f = s1.find(‘0‘);
        Node nxt;
        if(f == 0)
        {
            swap(s1[0], s1[1]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; } swap(s1[0], s1[1]);
            swap(s1[0], s1[3]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }continue;
        }
        if(f == 1)
        {
            swap(s1[0], s1[1]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }swap(s1[0], s1[1]);
            swap(s1[1], s1[2]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }swap(s1[1], s1[2]);
            swap(s1[1], s1[4]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }continue;
        }
        if(f == 2)
        {
            swap(s1[1], s1[2]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }swap(s1[1], s1[2]);
            swap(s1[2], s1[5]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }continue;
        }
        if(f == 3)
        {
            swap(s1[0], s1[3]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }swap(s1[0], s1[3]);
            swap(s1[3], s1[4]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }swap(s1[3], s1[4]);
            swap(s1[3], s1[6]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }continue;
        }
        if(f == 4)
        {
            swap(s1[1], s1[4]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }swap(s1[1], s1[4]);
            swap(s1[3], s1[4]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }swap(s1[3], s1[4]);
            swap(s1[5], s1[4]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }swap(s1[5], s1[4]);
            swap(s1[7], s1[4]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }continue;
        }
        if(f == 5)
        {
            swap(s1[5], s1[2]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }swap(s1[5], s1[2]);
            swap(s1[5], s1[4]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }swap(s1[5], s1[4]);
            swap(s1[5], s1[8]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }continue;
        }
        if(f == 6)
        {
            swap(s1[6], s1[3]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }swap(s1[6], s1[3]);
            swap(s1[6], s1[7]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }continue;
        }
        if(f == 7)
        {//4 7    6 7    8 7
            swap(s1[4], s1[7]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }swap(s1[4], s1[7]);
            swap(s1[6], s1[7]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }swap(s1[6], s1[7]);
            swap(s1[8], s1[7]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }continue;
        }
        if(f == 8)
        {//58   78
            swap(s1[5], s1[8]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1; }swap(s1[5], s1[8]);
            swap(s1[7], s1[8]);pd(s1, topp.step + 1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = 1;}continue;
        }
    }
}

int main()
{
    cin >> s_start;
    Node now;
    now.s = s_start; 
    now.step = 0;
    Q1.push(now);
    bfs();
    return 0;
}
//283104765

双向bfs竟然超时

// 双向 bfs 
/*
    是否已经被正向搜到了,且用了多少步  map <string, int> is_front;  注意，这个map只存储正向搜到的状态 
    正反两个队列
    分别存储当前状态以及所用步数
    正反交替进行
        每当反向搜到 map[当前状态] ！= 0 时， answer = map[当前状态] + 反向搜到的步数 
*/
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <map>
#include <queue>
#include <cstring>
#include <string> 

using namespace std;
const string s_end = "123804765";

struct Node{
    string s;
    int step;
};

string s_start;
queue <Node> Q1;
queue <Node> Q2;
map <string, int> mp;
map <string, int> mp_back;

inline void pd(string ss, int answer){if(ss == s_end){printf("%d", answer);exit(0);}}
inline void pd_out(int a, int answer, string ss){if(a){printf("%d",answer);exit(0);}}
void bfs_front();

inline void bfs_back() 
{
    while(1)
    {
        Node topp = Q2.front();
        Q2.pop();
        string now = topp.s;
        int f = now.find(‘0‘);
        string s1 = now;
        Node nxt;
        if(f == 0)
        {
            swap(s1[0], s1[1]);pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}swap(s1[0], s1[1]); 
            swap(s1[0], s1[3]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}continue;
        }
        if(f == 1)
        {
            swap(s1[0], s1[1]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}swap(s1[0], s1[1]);
            swap(s1[1], s1[2]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}swap(s1[1], s1[2]);
            swap(s1[1], s1[4]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}continue;
        }
        if(f == 2)
        {
            swap(s1[1], s1[2]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}swap(s1[1], s1[2]);
            swap(s1[2], s1[5]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}continue;
        }
        if(f == 3)
        {
            swap(s1[0], s1[3]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}swap(s1[0], s1[3]);
            swap(s1[3], s1[4]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}swap(s1[3], s1[4]);
            swap(s1[3], s1[6]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}continue;
        }
        if(f == 4)
        {
            swap(s1[1], s1[4]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}swap(s1[1], s1[4]);
            swap(s1[3], s1[4]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}swap(s1[3], s1[4]);
            swap(s1[5], s1[4]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}swap(s1[5], s1[4]);
            swap(s1[7], s1[4]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}continue;
        }
        if(f == 5)
        {
            swap(s1[5], s1[2]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}swap(s1[5], s1[2]);
            swap(s1[5], s1[4]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}swap(s1[5], s1[4]);
            swap(s1[5], s1[8]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}continue;
        }
        if(f == 6)
        {
            swap(s1[6], s1[3]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}swap(s1[6], s1[3]);
            swap(s1[6], s1[7]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}continue;
        }
        if(f == 7)
        {//4 7    6 7    8 7
            swap(s1[4], s1[7]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}swap(s1[4], s1[7]);
            swap(s1[6], s1[7]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}swap(s1[6], s1[7]);
            swap(s1[8], s1[7]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}continue;
        }
        if(f == 8)
        {//58   78
            swap(s1[5], s1[8]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}swap(s1[5], s1[8]);
            swap(s1[7], s1[8]); pd_out(mp[s1], topp.step + mp[s1] + 1, s1);
            if(!mp_back[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q2.push(nxt);mp_back[s1] = nxt.step;}continue;
        }
        return ;
    }
}

inline void bfs_front()//正向 bfs 
{
    while(1)
    {
        Node topp = Q1.front();
        Q1.pop();
        string now = topp.s;
        int f = now.find(‘0‘);
        Node nxt;
        string s1 = now;
        if(f == 0)
        {
            swap(s1[0], s1[1]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}swap(s1[0], s1[1]);
            swap(s1[0], s1[3]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}continue;
        }
        if(f == 1)
        {
            swap(s1[0], s1[1]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}swap(s1[0], s1[1]);
            swap(s1[1], s1[2]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}swap(s1[1], s1[2]);
            swap(s1[1], s1[4]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}continue;
        }
        if(f == 2)
        {
            swap(s1[1], s1[2]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}swap(s1[1], s1[2]);
            swap(s1[2], s1[5]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}continue;
        }
        if(f == 3)
        {
            swap(s1[0], s1[3]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}swap(s1[0], s1[3]);
            swap(s1[3], s1[4]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}swap(s1[3], s1[4]);
            swap(s1[3], s1[6]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}continue;
        }
        if(f == 4)
        {
            swap(s1[1], s1[4]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}swap(s1[1], s1[4]);
            swap(s1[3], s1[4]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}swap(s1[3], s1[4]);
            swap(s1[5], s1[4]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}swap(s1[5], s1[4]);
            swap(s1[7], s1[4]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}continue;
        }
        if(f == 5)
        {
            swap(s1[5], s1[2]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}swap(s1[5], s1[2]);
            swap(s1[5], s1[4]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}swap(s1[5], s1[4]);
            swap(s1[5], s1[8]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}continue;
        }
        if(f == 6)
        {
            swap(s1[6], s1[3]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}swap(s1[6], s1[3]);
            swap(s1[6], s1[7]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}continue;
        }
        if(f == 7)
        {//4 7    6 7    8 7
            swap(s1[4], s1[7]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}swap(s1[4], s1[7]);
            swap(s1[6], s1[7]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}swap(s1[6], s1[7]);
            swap(s1[8], s1[7]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}continue;
        }
        if(f == 8)
        {//58   78
            swap(s1[5], s1[8]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}swap(s1[5], s1[8]);
            swap(s1[7], s1[8]);pd(s1, topp.step + 1);pd_out(mp_back[s1], topp.step + mp_back[s1] + 1, s1);
            if(!mp[s1]){nxt.s = s1;nxt.step = topp.step + 1;Q1.push(nxt);mp[s1] = nxt.step;}continue;
        }
        bfs_back();
    }
    
}
 
int main()
{
    cin >> s_start;Node now;now.s = s_start; now.step = 0;Q1.push(now);
    now.s = s_end;Q2.push(now);
    bfs_front();
    return 0;
}
//283104765
//273645801
//15 
//103824765
//120843765
//123805746