[UVA][IDA*] 10181 - 15-Puzzle Problem
Problem N
15-Puzzle Problem
Input: standard input
Output: standard output
Time Limit: 45 seconds
The 15-puzzle is a very popular game; 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. The object of the puzzle is to arrange the tiles so that they are ordered as below:
Here the only legal operation is to exchange missing tile with one of the tiles with which it shares an edge. As an example, the following sequence of moves changes the status of a puzzle
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A random puzzle position |
The missing Tile moves to right. Denoted by R |
The missing Tile moves upwards. Denoted by U |
The missing Tile moves to the left. Denoted by L |
The letters in the previous row indicate which neighbor of the missing tile is swapped with it at each step; legal values are 'R','L','U' and 'D', for RIGHT, LEFT, UP, and DOWN, respectively.
Given an initial configuration of a 15-puzzle you will have to determine the steps that would make you reach the final stage. The input 15-puzzles requires at most 45 steps to be solved with our judge solution. So you will not be allowed to use more than 50 steps to solve a puzzle. If the given initial configuration is not solvable you just need to print the line “This puzzle is not solvable.”
Input
The first line of the input contains one integer N, which indicates how many sets of puzzle, will be given as input. Next 4N lines contain N sets of inputs. It means four lines make one set of input. Zero denotes the missing tile.
Output
For each set of input you will have to give one line of output. If the input puzzle is not solvable then print the line “This puzzle is not solvable.” If the puzzle is solvable then print the move sequence as described above to solve the puzzle.
Sample Input:
2
2 3 4 0
1 5 7 8
9 6 10 12
13 14 11 15
13 1 2 4
5 0 3 7
9 6 10 12
15 8 11 14
Sample Output:
LLLDRDRDRThis puzzle is not solvable.
對於
6 2 8 4
12 14 1 10
13 15 3 9
11 0 5 7
輸出 48 步的走法如下
UULURDRDDLLUURURDLDRRULLULDDRRULLDRRRDLLURRULDDR
但是討論區卻顯示 50 步的做法。
#include <stdio.h>
#include <stdlib.h>
#include <algorithm>
using namespace std;
struct status {
int board[4][4];
int ix, iy;
} init;
int pos[16][2], mxdep;
int dir[4][2] = {{-1,0},{0,-1},{0,1},{1,0}};/*u,l,r,d*/
char dirc[4] = {'U', 'L', 'R', 'D'}, path[100];
int solved;
bool solvable() {
int sum = 0, row, i, j;
for(i = 0; i < 16; i++) {
if(init.board[i/4][i%4] == 0) {
row = i/4 + 1;
continue;
}
for(j = i+1; j < 16; j++) {
if(init.board[j/4][j%4] < init.board[i/4][i%4]) {
if(init.board[j/4][j%4])
sum++;
}
}
}
return 1-(sum+row)%2;
}
int H() {
static int i, j, sum, num;
sum = 0;
for(i = 0; i < 4; i++) {
for(j = 0; j < 4; j++) {
num = init.board[i][j];
if(num == 0)
continue;
sum += abs(i-pos[num][0]) + abs(j-pos[num][1]);
}
}
return sum;
}
int singleH(int x, int y, int num) {
return abs(x - pos[num][0]) + abs(y - pos[num][1]);
}
int IDA(int dep, int hv, int prestep) {
if(hv == 0) {
solved = dep;
path[dep] = '\0';
puts(path);
return dep;
}
if(dep+hv > mxdep) return dep+hv;
int i, tx, ty, x = init.ix, y = init.iy;
int submxdep = 0xffff, val, shv;/*
for(int i = 0; i < 4; i++, puts(""))
for(int j = 0; j < 4; j++)
printf("%d ", init.board[i][j]);
getchar();*/
for(i = 0; i < 4; i++) {
if(i + prestep == 3) continue;
tx = x + dir[i][0], ty = y + dir[i][1];
if(tx < 0 || ty < 0 || tx > 3 || ty > 3)
continue;
shv = hv;
shv -= singleH(tx, ty, init.board[tx][ty]);
shv += singleH( x, y, init.board[tx][ty]);
init.ix = tx, init.iy = ty;
swap(init.board[x][y], init.board[tx][ty]);
path[dep] = dirc[i];
val = IDA(dep+1, shv, i);
swap(init.board[x][y], init.board[tx][ty]);
init.ix = x, init.iy = y;
if(solved) return solved;
submxdep = min(submxdep, val);
}
return submxdep;
}
int main() {
int test, i, j, k, initH;
int cases = 0;
for(i = 0, k = 0; i < 4; i++)
for(j = 0; j < 4; j++)
pos[++k][0] = i, pos[k][1] = j;
scanf("%d", &test);
while(test--) {
cases++;
for(i = 0; i < 4; i++) {
for(j = 0; j < 4; j++) {
scanf("%d", &init.board[i][j]);
if(init.board[i][j] == 0) {
init.ix = i, init.iy = j;
}
}
}
if(solvable()) {
solved = 0, initH = mxdep = H();
if(!mxdep) {
puts("");
continue;
}
while(solved == 0 && mxdep <= 100) {
mxdep = IDA(0, initH, -1);
}
if(solved);
else while(1);
}else {
puts("This puzzle is not solvable.");
}
}
return 0;
}
/*
2
6 2 8 4
12 14 1 10
13 15 3 9
11 0 5 7
0 1 3 8
5 7 4 6
9 2 10 11
13 14 15 12
*/