On Planet MM-21, after their Olympic games this year, curling is getting popular. But the rules are somewhat different from ours. The game is played on an ice game board on which a square mesh is marked. They use only a single stone. The purpose of the game is to lead the stone from the start to the goal with the minimum number of moves.
Fig. 1 shows an example of a game board. Some squares may be occupied with blocks. There are two special squares namely the start and the goal, which are not occupied with blocks. (These two squares are distinct.) Once the stone begins to move, it will proceed until it hits a block. In order to bring the stone to the goal, you may have to stop the stone by hitting it against a block, and throw again.
Fig. 1: Example of board (S: start, G: goal)
The movement of the stone obeys the following rules:
- At the beginning, the stone stands still at the start square.
- The movements of the stone are restricted to x and y directions. Diagonal moves are prohibited.
- When the stone stands still, you can make it moving by throwing it. You may throw it to any direction unless it is blocked immediately(Fig. 2(a)).
- Once thrown, the stone keeps moving to the same direction until one of the following occurs:
- The stone hits a block (Fig. 2(b), (c)).
- The stone stops at the square next to the block it hit.
- The block disappears.
- The stone gets out of the board.
- The game ends in failure.
- The stone reaches the goal square.
- The stone stops there and the game ends in success.
- The stone hits a block (Fig. 2(b), (c)).
- You cannot throw the stone more than 10 times in a game. If the stone does not reach the goal in 10 moves, the game ends in failure.
Fig. 2: Stone movements
Under the rules, we would like to know whether the stone at the start can reach the goal and, if yes, the minimum number of moves required.
2.1 最基础的"穷竭搜索" 深度优先搜索
扔石头，上下左右四个方向如果某一个方向紧挨着block就不能扔这个方向，否则碰到block停住，block消失，再次四个方向扔。DFS老一套，不过一定要注意判断紧挨着的情况。超过最小步数剪枝也是个很有意思的技巧。
int w, h;int map[32][32];int sx, sy;int min_step;const int direction[4][2] = { { -1, 0 }, { 1, 0 }, { 0, -1 }, { 0, 1 },};void dfs(const int& x, const int& y, int step){ if (step >= 10 || step > min_step) { return; } for (int i = 0; i < 4; ++i) { int nx = x; int ny = y; // 让石头往固定的方向一直飞 while(nx >= 0 && nx < w && ny >= 0 && ny < h) { switch (map[nx][ny]) { case 0: { // 继续飞 nx += direction[i][0]; ny += direction[i][1]; }break; case 3: { // 到家了 if (step + 1 < min_step) { min_step = step + 1; } nx = -1; }break; case 1: { // 撞到了block if (!(nx - direction[i][0] == x && ny - direction[i][1] == y)) { // 中间有空地，不是紧挨着block // 石头消失 map[nx][ny] = 0; // 后退一步扔石头 dfs(nx - direction[i][0], ny - direction[i][1], step + 1); // 复原地图，供下一个方向尝试 map[nx][ny] = 1; } // 开始下一个方向 nx = -1; }break; default: break; } } }}///////////////////////////SubMain//////////////////////////////////int main(int argc, char *argv[]){#ifndef ONLINE_JUDGE freopen("in.txt", "r", stdin); freopen("out.txt", "w", stdout);#endif while (cin >> w >> h, w != 0) { for (int i = 0; i < h; ++i) { for (int j = 0; j < w; ++j) { cin >> map[j][i]; } } for (int i = 0; i < h; ++i) { for (int j = 0; j < w; ++j) { if (2 == map[j][i]) { sx = j; sy = i; i = h; break; } } } map[sx][sy] = 0; min_step = 11; dfs(sx, sy, 0); if (min_step > 10) { min_step = -1; } cout << min_step << endl; }#ifndef ONLINE_JUDGE fclose(stdin); fclose(stdout); system("out.txt");#endif return 0;}