luogu P1379 八数码难题
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
