1644: [Usaco2007 Oct]Obstacle Course 障碍训练课

1644: [Usaco2007 Oct]Obstacle Course 障碍训练课

Time Limit: 5 Sec  Memory Limit: 64 MB
Submit: 383  Solved: 196
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Description

考虑一个 N x N (1 <= N <= 100)的有1个个方格组成的正方形牧场。有些方格是奶牛们不能踏上的，它们被标记为了'x'。例如下图：

. . B x .
. x x A .
. . . x .
. x . . .
. . x . .

贝茜发现自己恰好在点A处，她想去B处的盐块舔盐。缓慢而且笨拙的动物，比如奶牛，十分讨厌转弯。尽管如此，当然在必要的时候她们还是会转弯的。对于一个给定的牧场，请你计算从A到B最少的转弯次数。开始的时候，贝茜可以使面对任意一个方向。贝茜知道她一定可以到达。

Input

第 1行: 一个整数 N 行

2..N + 1: 行 i+1 有 N 个字符 ('.', 'x', 'A', 'B')，表示每个点的状态。

Output

行 1: 一个整数，最少的转弯次数。

Sample Input

3
.xA
...
Bx.

Sample Output

2

HINT

 

Source

Silver

题解：（HansBug：太开心啦，这道题我又逗比啦哈哈哈 wnjxyk：汗= =）

其实虽然这道题也是个BFS水题，但是和一般的走迷宫问题相比，这道题有个坑点——对于一个点先遍历到的未必是最优的，其实就算是当前最优也由于在本题中由于涉及方向问题，所以对后续来说也未必最优，而如果简单的灌水法的话，则会由于遍历过了而导致真正的最优值无法被更新

如，数据中的第5个点：

33
.......xA.....x.......x..........
...x...........x.........x.......
........x.xx.....x.x.............
.....x.....x.........x...........
.....x................x.x........
......x..x....x.........xx.......
...................x......x......
...x.....x....................x..
....x..........................x.
x................................
.................................
.....x...x..x....................
.............................x...
...................x.........x...
...............x...x....x...x....
..........xx.......x..x..........
................................x
..............................xx.
..x...............x.x............
.x....x...............x....x....x
..x......xx.......x.x.......x....
................x...xx.....x.x..x
.x.............x........x...x.x..
.............................x.x.
.........................x......x
.....x.......x............xx...xx
........x....x.....xx.x.....xx.x.
...........x...x........x.x...xxB
.x.x.x.............x...........x.
x.............x................x.
.........x.x.....x.....x.....x...
........x..............xx.....x..
..............xx......x.x.....x..

（2，10）位置上最优值显然是1，而且无论怎么遍历都是1

但是（3，10）由于涉及来源于（2，10）的方向问题，所以很可能弄出个2作最优解，但事实上正解是1

说了这些就没了，继续AC

/**************************************************************
    Problem: 1644
    User: HansBug
    Language: Pascal
    Result: Accepted
    Time:32 ms
    Memory:1728 kb
****************************************************************/
 
const dd:array[1..4,1..2] of longint=((1,0),(-1,0),(0,1),(0,-1));
var
   i,j,k,l,m,n,x0,y0,x1,y1,f,r,x,y:longint;
   b:array[0..205,0..205] of longint;
   a:array[0..205,0..205] of longint;
   d:array[0..100000,0..2] of longint;
   ch:char;
function min(x,y:longint):longint;
         begin
              if x<y then min:=x else min:=y;
         end;
function max(x,y:longint):longint;
         begin
              if x>y then max:=x else max:=y;
         end;
 
begin
     readln(n);
     fillchar(b,sizeof(b),0);
     fillchar(a,sizeof(a),0);
     for i:=0 to n+1 do
         begin
              b[0,i]:=1;
              b[n+1,i]:=1;
              b[i,0]:=1;
              b[i,n+1]:=1;
         end;
     for i:=1 to n do
         begin
              for j:=1 to n do
                  begin
                       read(ch);
                       case upcase(ch) of
                            '.':b[i,j]:=0;
                            'A':begin
                                     x0:=i;y0:=j;
                                     b[i,j]:=1;
                            end;
                            'B':begin
                                     x1:=i;y1:=j;
                                     b[i,j]:=0;
                            end;
                            'X':b[i,j]:=1;
                       end;
                  end;
              readln;
         end;
     f:=1;r:=2;d[1,1]:=x0;d[1,2]:=y0;
     a[x0,y0]:=1;a[x0,y0]:=1;a[x0,y0]:=1;a[x0,y0]:=1;
     while f<r do
           begin
                for i:=1 to 4 do
                    begin
                         x:=d[f,1];y:=d[f,2];
                         while true do
                               begin
                                    x:=x+dd[i,1];
                                    y:=y+dd[i,2];
                                    if b[x,y]=1 then break;
                                    l:=a[d[f,1],d[f,2]]+1;
                                    if (l>=a[x,y]) and (a[x,y]>0) then continue;
                                    a[x,y]:=l;
                                    if (x=x1) and (y=y1) then
                                       begin
                                            writeln(a[x,y]-2);
                                            readln;
                                            halt;
                                       end;
                                    d[r,1]:=x;d[r,2]:=y;
                                    inc(r);
                               end;
 
                    end;
                inc(f);
           end;
end.