【启发式搜索】[ZOJ1217]Eight
2016-01-30 19:43
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题目描述
ScenarioThe 15-puzzle has been around for over 100 years; even if you don’t know it by that name, you’ve seen it. It is constructed with 15 sliding tiles, each with a number from 1 to 15 on it, and all packed into a 4 by 4 frame with one tile missing. Let’s call the missing tile ‘x’; the object of the puzzle is to arrange the tiles so that they are ordered as:
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 x
where the only legal operation is to exchange ‘x’ with one of the tiles with which it shares an edge. As an example, the following sequence of moves solves a slightly scrambled puzzle:
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
5 6 7 8 5 6 7 8 5 6 7 8 5 6 7 8
9 x 10 12 9 10 x 12 9 10 11 12 9 10 11 12
13 14 11 15 13 14 11 15 13 14 x 15 13 14 15 x
r-> d-> r->
The letters in the previous row indicate which neighbor of the ‘x’ tile is swapped with the ‘x’ tile at each step; legal values are ‘r’,’l’,’u’ and ‘d’, for right, left, up, and down, respectively.
Not all puzzles can be solved; in 1870, a man named Sam Loyd was famous for distributing an unsolvable version of the puzzle, and
frustrating many people. In fact, all you have to do to make a regular puzzle into an unsolvable one is to swap two tiles (not counting the missing ‘x’ tile, of course).
In this problem, you will write a program for solving the less well-known 8-puzzle, composed of tiles on a three by three
arrangement.
题目分析
就是根据每两个位置之间的曼哈顿距离作为估值函数。。。然后用康拓展开判重。代码
[code]#include <cstdio> #include <algorithm> #include <cstring> #include <iostream> #include <vector> #include <queue> #include <stack> #include <iostream> #include <string> using namespace std; const int MAXVIS = 363900; struct State{ unsigned short s[9]; int h, g, mh; bool operator < (const State& s) const { return (g+h)>(s.g+s.h); } bool operator > (const State& s) const { if((g+h) == (s.g+s.h)) return g < (s.g+s.h); return (g+h)<(s.g+s.h); } }st, ed; priority_queue<State> que; char now[MAXVIS+5]; int pre[MAXVIS+5]; int _pow[9]; pair<int, int> show[9]; int fx[4][2] = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}}; int ppos[9][2] = {{0, 0}, {0, 1}, {0, 2}, {1, 0}, {1, 1}, {1, 2}, {2, 0}, {2, 1}, {2, 2}}; int fppos[3][3] = {{0, 1, 2}, {3, 4, 5}, {6, 7, 8}}; char ch[4] = {'d', 'r', 'u', 'l'}; int vis[MAXVIS+5]; int _hash(unsigned short s[]){ int ret = 0, count =0 ; for(int i=0;i<9;i++){ count = 0; for(int j=i+1;j<9;j++) count += int(s[j]<s[i]); ret += count * _pow[8-i]; } return ret; } int _abs(int u){return u>0?u:-u;} int _h(unsigned short s[]){ int ret = 0; for(int i=0;i<9;i++) if(s[i]) ret += _abs(ppos[i][0]-show[s[i]].first) + _abs(ppos[i][1]-show[s[i]].second); return ret; } bool check_pos(const int& a, const int& b){ if(a > 2 || b > 2 || a < 0 || b < 0) return false; return true; } stack<char> sta; void Print(){ while(!sta.empty()) sta.pop(); int nowm = ed.mh; while(nowm != st.mh) { sta.push(now[nowm]); nowm = pre[nowm]; } while(!sta.empty()){ putchar(sta.top()); sta.pop(); } puts(""); } void solve(){ int counter = 0; for(int i=0;i<9;i++) if(st.s[i]){ for(int j=i+1;j<9;j++) if(st.s[j]){ if(st.s[i] > st.s[j]) counter++; } } if(counter & 1){ cout<<"unsolvable"<<endl; return ; } memset(vis, 0x3f, sizeof vis); while(!que.empty()) que.pop(); State tmp=st; State t2; now[tmp.mh] = 0; int pos; vis[tmp.mh] = tmp.h = _h(st.s); tmp.g = 0; que.push(tmp); while(!que.empty()){ tmp = que.top(); que.pop(); pos=0; if(tmp.mh == ed.mh){ Print(); return ; } if(tmp.g + tmp.h > vis[tmp.mh]) continue; while(tmp.s[pos]) pos++; for(int i=0;i<4;i++) { if(check_pos(ppos[pos][0] + fx[i][0], ppos[pos][1] + fx[i][1])){ t2 = tmp; swap(t2.s[pos], t2.s[fppos[ppos[pos][0] + fx[i][0]][ppos[pos][1] + fx[i][1]]]); t2.mh = _hash(t2.s); t2.h = _h(t2.s); (++t2.g); if(t2.g + t2.h > vis[t2.mh]) continue; vis[t2.mh] = t2.g + t2.h; now[t2.mh] = ch[i]; pre[t2.mh] = tmp.mh; que.push(t2); } } } cout<<"unsolvable"<<endl; } int main(){ char tstr[5]; _pow[0] = 1; for(int i=1;i<=8;i++) _pow[i] = _pow[i-1] * i; ed.s[0] = 1; ed.s[1] = 2; ed.s[2] = 3; ed.s[3] = 4; ed.s[4] = 5; ed.s[5] = 6; ed.s[6] = 7; ed.s[7] = 8; ed.s[8] = 0; ed.mh = _hash(ed.s); for(int i=0;i<9;i++){show[ed.s[i]] = make_pair(i/3, i%3);} while(true){ for(int i=0;i<9;i++){ if(scanf("%s", tstr) == EOF) return 0; if(tstr[0] != 'x') st.s[i]=tstr[0]-'0'; else st.s[i] = 0; } st.mh = _hash(st.s); if(st.mh == ed.mh) puts(""); else solve(); } return 0; }
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