HDU 1043 Eight (BFS & #183; octal digital & #183; kangtuo), hdubfs

HDU 1043 Eight (BFS · octal digital · Kento), hdubfs

8. The path from the given status to 12345678x

Use Kanto to expand the lexicographically ordered order and then the basic BFS.

# Include <bits/stdc ++. h> using namespace std; const int N = 5e5, M = 9; int x [4] = {-1, 1, 0, 0 }; int y [4] = {0, 0,-1, 1}; int fac [] = {1, 1, 2, 6, 24,120,720,504 0, 40320 }; int puz [N] [M], nex [N], dir [N], vis [N], q [N]; int getCantor (int a []) // conto expand converts the permutation to an integer {int ret = 0; for (int I = 0; I <M; ++ I) {for (int j = I + 1; j <M; ++ j) if (a [j] <a [I]) ret + = fac [M-I-1];} return ret ;} void bfs () {int t [M] = {1, 2, 3, 4, 5, 6, 7, 8, 0}; int id = getCantor (t); dir [id] =-1; memcpy (puz [id], t, sizeof (t); memset (vis, 0, sizeof (vis); int r, c, k, nr, nc, nk, nid; int front = 0, rear = 0; q [rear ++] = id; vis [id] = 1; while (front <rear) {int id = q [front ++]; memcpy (t, puz [id], sizeof (t); for (k = 0; t [k]; + + k); // locate 0, r = k/3, c = k % 3; // convert one dimension to two dimensional for (int I = 0; I <4; ++ I) {nr = r + x [I], nc = c + Y [I], nk = nr * 3 + nc; if (nr <0 | nr> 2 | nc <0 | nc> 2) continue; swap (t [k], t [nk]); nid = getCantor (t); memcpy (puz [nid], t, sizeof (t )); swap (t [k], t [nk]); if (vis [nid]) continue; vis [nid] = 1; q [rear ++] = nid; nex [nid] = id; dir [nid] = I ;}} int main () {char t [5], sdir [] = "durl "; int s [M], id; bfs (); while (~ Scanf ("% s", t) {s [0] = t [0] = 'X '? 0: t [0]-'0'; for (int I = 1; I <M; ++ I) {scanf ("% s", t ); s [I] = t [0] = 'X '? 0: t [0]-'0';} id = getCantor (s); if (! Vis [id]) puts ("unsolvable"); else {while (dir [id]> = 0) {printf ("% c ", sdir [dir [id]); id = nex [id];} puts ("") ;}} return 0 ;}// Last modified:

Eight
Problem DescriptionThe 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:

 1  2  3  4 5  6  7  8 9 10 11 1213 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 1213 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 extends 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.
 
InputYou will receive, several descriptions of configuration of the 8 puzzle. one description is just a list of the tiles in their initial positions, with the rows listed from top to bottom, and the tiles listed from left to right within a row, where the tiles are represented by numbers 1 to 8, plus 'x '. for example, this puzzle

1 2 3
X 4 6
7 5 8

Is described by this list:

1 2 3x4 6 7 5 8
 
OutputYou will print to standard output either the word ''unsolvable'', if the puzzle has no solution, or a string consisting entirely of the letters 'R', 'l ', 'U' and 'D' that describes a series of moves that produce a solution. the string shoshould include no spaces and start at the beginning of the line. do not print a blank line between cases.
 
Sample Input

2  3  4  1  5  x  7  6  8

 
Sample Output

ullddrurdllurdruldr

 

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