BFS UVA (intermediate) 11513 - 9 Puzzle

 9 Puzzle 

Alex has a puzzle her father gave her last Christmas. It has nine numbered squares arranged in a3×3 matrix (three rows and three columns) and it's mechanically designed to allow the following types of movements:

• A horizontal right move shifts one position to the right each of the squares in the corresponding horizontal row (circularly).
• A vertical up move shifts one position upwards each of the squares in the corresponding vertical column (circularly).

Alex's troublemaker little brother Jim snuck last night into his sister's bedroom and somehow tore the puzzle apart and put it back together. However, when Jim assembled the puzzle back, he might have done it in a configuration different from theoriginal configuration of the puzzle.

The next morning, when Alex found her puzzle had been scrambled, she called you to help her to reset her puzzle to itsoriginal configuration (shown below) as quickly as possible, so her father won't realize that the puzzle was torn and scrambled. Of course, you should do it using only valid movements, as above described.

123456789

Your task is to write a program that, given a configuration, finds a way to set the puzzle to its original configuration spending the minimum possible number of moves to accomplish it, if the given puzzle is solvable. If this is not the case, the program should point it out.

Input 

The problem input consists of several cases, each one defined by three lines that describe a puzzle configuration. That is, lines correspond to a top-down description of the rows of the given configuration, and each line consist of three digits, separated by one blank character.

The end of the input is indicated by a line with a number 0.

Output 

For each puzzle in the input, you must print a line containing S, the minimum number of moves required to set the puzzle to its original configuration, followed by a space and2*S characters indicating any sequence ofS moves that solves the puzzle.

A move is described by two characters: the first one must be H or V (H specifies a horizontal move, andV a vertical move), and the second one must be1, 2, or3 to indicate the row or the column to move.

If the puzzle is not solvable, you must output a line with the text ``Not solvable''.

Sample Input 

2 3 14 5 67 8 97 3 92 5 14 8 61 2 34 5 67 9 80

Sample Output 

1 H13 V1V3H1Not solvable

题意：有一个3x3的类似八数码这样的东西，每次能整行往右移或者整列往上移，问最少需要多少步到达目标状态。

思路：我们直接从目标状态开始转移，就是（1,2,3,4,5,6,7,8,9）开始转移，行移动变成往左移，列变成往下移，直接bfs，记录路径就行了。

代码：

#include <iostream>#include <queue>#include <cstdio>#include <cstring>#include <string>#include <string.h>#include <algorithm>#include <cassert>#include <cmath>#include <set>using namespace std;#define clr(a,x) memset(a,(x),sizeof(a));#define rep(i,a,b) for(int i=(a);i<(b);++i)#define rrep(i,a,b) for(int i=a;i>=b;--i)#define eps 1e-8#define LL long long#define mp make_pairconst int maxn=9*8*7*6*5*4*3*2+100;const int C = 3;int A[11];inline int getx(int r,int c) { return r*C+c; }inline int row(int x) { return x / C; }inline int col(int x) { return x % C; }struct Chess{    int M[C][C];    int Key;    void setKey()    {        int cnt = 0;        Key = 0;        int * a = &M[0][0];        rep(i,0,C*C) {            cnt = 0;            rep(j,i+1,C*C)            if(a[i] > a[j]) ++cnt;            Key += cnt * A[C*C-1-i];        }    }    void Upwards(int c)    {        int ch = M[C-1][c];        rrep(r,C-1,1) M[r][c] = M[r-1][c];        M[0][c] = ch;        setKey();    }    void Rightwards(int r)    {        setKey();        int ch = M[r][0];        rep(c,0,C-1) M[r][c] = M[r][c+1];        M[r][C-1] = ch;        setKey();    }    void out() const    {        rep(i,0,C) {            rep(j,0,C) printf("%2d",M[i][j]);            puts("");        }    }}in;bool read(){    rep(i,0,3) rep(j,0,3) {        scanf("%d",&in.M[i][j]);        if(in.M[i][j]==0) return false;    }    in.setKey();    return true;}char act[maxn][3];int d[maxn];Chess q[maxn];int front,rear;int pre[maxn];void output(int s){    if(s == 0) return;    printf("%s",act[s]);    output(pre[s]);}void pre_init(){    rep(i,0,C) rep(j,0,C) in.M[i][j] = getx(i,j)+1;    in.Key = 0;    clr(d,0x3f); clr(pre,-1); clr(act,0);    d[0] = 0;    front = rear = 0; q[rear++] = in;    Chess tmp,now;    while(front < rear) {        tmp = q[front++];        int u = tmp.Key;        rep(r,0,C) {            now = tmp;            now.Rightwards(r);          //  now.out(); puts("");            int v = now.Key;            if(d[v] <= d[u] + 1) continue;            d[v] = d[u] + 1;            pre[v] = u;            act[v][0] = 'H'; act[v][1] = '1'+r;            q[rear++] = now;        }        rep(c,0,C) {            now = tmp;            now.Upwards(c);            //now.out(); puts("");            int v = now.Key;            if(d[v] <= d[u] + 1) continue;            d[v] = d[u] + 1;            pre[v] = u;            act[v][0] = 'V'; act[v][1] = '1'+c;            q[rear++] = now;        }    }}void solve(){    int x = in.Key;    if(d[x] >= 100) printf("Not solvable");    else { printf("%d ",d[x]); output(x); }    printf("\n");}void Getinput(){    freopen("in.txt","w",stdout);    int a[9];    rep(i,0,9) a[i] = i;    do {        reverse(a,a+9);        rep(i,0,9) printf(" %d",a[i]+1);        reverse(a,a+9);        puts("");    } while (next_permutation(a,a+9));    puts("0");}int main(){   // Getinput(); return 0;    A[0] = 1;    clr(act,0);    rep(i,1,11) A[i] = A[i-1] * i;    pre_init();//    freopen("in.txt","r",stdin);    while(read()) {        solve();    }}

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Colombia'2008