[USACO11OPEN]Corn Maze S
题面翻译
奶牛们去一个
N
×
M
N\times M
N×M 玉米迷宫,
2
≤
N
≤
300
,
2
≤
M
≤
300
2 \leq N \leq 300,2 \leq M \leq300
2≤N≤300,2≤M≤300。
迷宫里有一些传送装置,可以将奶牛从一点到另一点进行瞬间转移。这些装置可以双向使用。
如果一头奶牛处在这个装置的起点或者终点,这头奶牛就必须使用这个装置。
玉米迷宫除了唯一的一个出口都被玉米包围。
迷宫中的每个元素都由以下项目中的一项组成:
- 玉米,
#
表示,这些格子是不可以通过的。 - 草地,
.
表示,可以简单的通过。 - 传送装置,每一对大写字母
A
\tt{A}
A 到
Z
\tt{Z}
Z 表示。
- 出口,
=
表示。 - 起点,
@
表示
奶牛能在一格草地上可能存在的四个相邻的格子移动,花费
1
1
1 个单位时间。从装置的一个结点到另一个结点不花时间。
题目描述
This past fall, Farmer John took the cows to visit a corn maze. But this wasn’t just any corn maze: it featured several gravity-powered teleporter slides, which cause cows to teleport instantly from one point in the maze to another. The slides work in both directions: a cow can slide from the slide’s start to the end instantly, or from the end to the start. If a cow steps on a space that hosts either end of a slide, she must use the slide.
The outside of the corn maze is entirely corn except for a single exit.
The maze can be represented by an N x M (2 <= N <= 300; 2 <= M <= 300) grid. Each grid element contains one of these items:
* Corn (corn grid elements are impassable)
* Grass (easy to pass through!)
* A slide endpoint (which will transport a cow to the other endpoint)
* The exit
A cow can only move from one space to the next if they are adjacent and neither contains corn. Each grassy space has four potential neighbors to which a cow can travel. It takes 1 unit of time to move from a grassy space to an adjacent space; it takes 0 units of time to move from one slide endpoint to the other.
Corn-filled spaces are denoted with an octothorpe (#). Grassy spaces are denoted with a period (.). Pairs of slide endpoints are denoted with the same uppercase letter (A-Z), and no two different slides have endpoints denoted with the same letter. The exit is denoted with the equals sign (=).
Bessie got lost. She knows where she is on the grid, and marked her current grassy space with the ‘at’ symbol (@). What is the minimum time she needs to move to the exit space?
输入格式
第一行:两个用空格隔开的整数
N
N
N 和
M
M
M。
第
2
∼
N
+
1
2\sim N+1
2∼N+1 行:第
i
+
1
i+1
i+1 行描述了迷宫中的第
i
i
i 行的情况(共有
M
M
M个字符,每个字符中间没有空格)。
输出格式
一个整数,表示起点到出口所需的最短时间。
样例 #1
样例输入 #1
5 6
###=##
#.W.##
#.####
#.@W##
######
样例输出 #1
3
提示
例如以下矩阵,
N
=
5
,
M
=
6
N=5,M=6
N=5,M=6。
###=##
#.W.##
#.####
#.@W##
######
唯一的一个装置的结点用大写字母
W
\tt{W}
W 表示。
最优方案为:先向右走到装置的结点,花费一个单位时间,再到装置的另一个结点上,花费
0
0
0 个单位时间,然后再向右走一个,再向上走一个,到达出口处,总共花费了
3
3
3 个单位时间。
分析
- 此题就是迷宫问题求最短路,加上n,m的范围,直接bfs,第一眼看见传送门想到了T1215 拯救公主——bfs+三维数组标记+二进制状态压缩,以为麻烦来了,但是发现此题简单,不需要去拿宝石之类,空手到达终点即可;
- 注意点:在找传送门的另一半时,需要加上 (i != x || j != y),别找了个他自己本身;其次就是如果走到传送门必须传送,如下图样例,不能直接@到A然后A再直接到终点=,这是错的,此题走到传送门要求必须传送,然后传送门不用打标记(vis),因为传送门可以来回传送;
![在这里插入图片描述](https://img-blog.csdnimg.cn/b9d49c2f30594eadb848e5ea0a53019a.png)
![在这里插入图片描述](https://img-blog.csdnimg.cn/2e9f44fb612145f5967b8a6765248ba2.png)
#include<bits/stdc++.h>
using namespace std;
struct node {
int x, y, step;
node(int xx, int yy, int ste) {
x = xx, y = yy, step = ste;
}
};
int n, m;
char a[305][305];
int vis[305][305];
queue<node> q;
int dx[] = {-1, 0, 1, 0};
int dy[] = {0, 1, 0, -1};
pair<int, int> findDoor(char c, int x, int y) {
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) {
if (a[i][j] == c && (i != x || j != y))
return {i, j};
}
}
}
void bfs() {
while (!q.empty()) {
node now = q.front();
q.pop();
int x = now.x, y = now.y, step = now.step;
if (a[x][y] == '=') {
cout << step;
return;
}
for (int i = 0; i < 4; i++) {
int xx = x + dx[i];
int yy = y + dy[i];
if (xx >= 0 && yy >= 0 && xx < n && yy < m && !vis[xx][yy] && a[xx][yy] != '#') {
vis[xx][yy] = 1;
if (a[xx][yy] >= 'A' && a[xx][yy] <= 'Z') {
pair<int, int> p = findDoor(a[xx][yy], xx, yy);
xx = p.first, yy = p.second;
vis[p.first][p.second] = 0;
}
q.push(node(xx, yy, step + 1));
}
}
}
}
int main() {
cin >> n >> m;
int startx, starty;
for (int i = 0; i < n; ++i) {
for (int j = 0; j < m; ++j) {
cin >> a[i][j];
if (a[i][j] == '@')
startx = i, starty = j;
}
}
q.push(node(startx, starty, 0));
vis[startx][starty] = 1;
bfs();
return 0;
}
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