Description
Harry Potter has some precious. For example, his invisible robe, his wand and his owl. When Hogwarts school is in holiday, Harry Potter has to go back to uncle Vernon's home. But he can't bring his precious with him. As you know, uncle Vernon never allows such magic things in his house. So Harry has to deposit his precious in the Gringotts Wizarding Bank which is owned by some goblins. The bank can be considered as a N × M grid consisting of N × M rooms. Each room has a coordinate. The coordinates of the upper-left room is (1,1) , the down-right room is (N,M) and the room below the upper-left room is (2,1)..... A 3×4 bank grid is shown below:
Some rooms are indestructible and some rooms are vulnerable. Goblins always care more about their own safety than their customers' properties, so they live in the indestructible rooms and put customers' properties in vulnerable rooms. Harry Potter's precious are also put in some vulnerable rooms. Dudely wants to steal Harry's things this holiday. He gets the most advanced drilling machine from his father, uncle Vernon, and drills into the bank. But he can only pass though the vulnerable rooms. He can't access the indestructible rooms. He starts from a certain vulnerable room, and then moves in four directions: north, east, south and west. Dudely knows where Harry's precious are. He wants to collect all Harry's precious by as less steps as possible. Moving from one room to another adjacent room is called a 'step'. Dudely doesn't want to get out of the bank before he collects all Harry's things. Dudely is stupid.He pay you $1,000,000 to figure out at least how many steps he must take to get all Harry's precious.
Some rooms are indestructible and some rooms are vulnerable. Goblins always care more about their own safety than their customers' properties, so they live in the indestructible rooms and put customers' properties in vulnerable rooms. Harry Potter's precious are also put in some vulnerable rooms. Dudely wants to steal Harry's things this holiday. He gets the most advanced drilling machine from his father, uncle Vernon, and drills into the bank. But he can only pass though the vulnerable rooms. He can't access the indestructible rooms. He starts from a certain vulnerable room, and then moves in four directions: north, east, south and west. Dudely knows where Harry's precious are. He wants to collect all Harry's precious by as less steps as possible. Moving from one room to another adjacent room is called a 'step'. Dudely doesn't want to get out of the bank before he collects all Harry's things. Dudely is stupid.He pay you $1,000,000 to figure out at least how many steps he must take to get all Harry's precious.
Input
There are several test cases.
In each test cases:
The first line are two integers N and M, meaning that the bank is a N × M grid(0<N,M <= 100).
Then a N×M matrix follows. Each element is a letter standing for a room. '#' means a indestructible room, '.' means a vulnerable room, and the only '@' means the vulnerable room from which Dudely starts to move.
The next line is an integer K ( 0 < K <= 4), indicating there are K Harry Potter's precious in the bank.
In next K lines, each line describes the position of a Harry Potter's precious by two integers X and Y, meaning that there is a precious in room (X,Y).
The input ends with N = 0 and M = 0
In each test cases:
The first line are two integers N and M, meaning that the bank is a N × M grid(0<N,M <= 100).
Then a N×M matrix follows. Each element is a letter standing for a room. '#' means a indestructible room, '.' means a vulnerable room, and the only '@' means the vulnerable room from which Dudely starts to move.
The next line is an integer K ( 0 < K <= 4), indicating there are K Harry Potter's precious in the bank.
In next K lines, each line describes the position of a Harry Potter's precious by two integers X and Y, meaning that there is a precious in room (X,Y).
The input ends with N = 0 and M = 0
Output
For each test case, print the minimum number of steps Dudely must take. If Dudely can't get all Harry's things, print -1.
Sample Input
2 3
##@
#.#
1
2 2
4 4
#@##
....
####
....
2
2 1
2 4
0 0
Sample Output
-1
5
感想:这题应该做的快一点的,结果花了24分钟,主要是中途变思路一开始是用spfa来做的,但是注意到只有四个宝物
思路:bfs出两点最少步数,枚举所有排列得到最优结果
#include <cstdio> #include <cstring> #include <queue> #include <algorithm> using namespace std; typedef pair<int,int> P; const int inf=0x7ffffff; int n,m,k; int px[5],py[5];//记录珍宝坐标,德拉克坐标设为第0个 int d[5][5];//记录珍宝间最短距离 char maz[101][101];//记录迷宫状态 int ind[101][101];//记录珍宝编号 bool vis[101][101];//bfs用 int dis[101][101];//bfs用,最短距 const int dx[4]={1,-1,0,0};const int dy[4]={0,0,-1,1}; bool ok(int x,int y){ return x>=0&&x<n&&y>=0&&y<m&&maz[x][y]!='#'; } void bfs(int index){ int sx=px[index],sy=py[index]; for(int i=0;i<n;i++)for(int j=0;j<m;j++)dis[i][j]=inf; memset(vis,0,sizeof(vis)); vis[sx][sy]=true; d[index][index]=0; dis[sx][sy]=0; queue<P>que; que.push(P(sx,sy)); while(!que.empty()){ sx=que.front().first;sy=que.front().second;que.pop(); for(int i=0;i<4;i++){ int tx=sx+dx[i],ty=sy+dy[i]; if(ok(tx,ty)&&!vis[tx][ty]){ vis[tx][ty]=true;dis[tx][ty]=dis[sx][sy]+1; if(ind[tx][ty]!=0||maz[tx][ty]=='@'){ d[index][ind[tx][ty]]=dis[tx][ty];} que.push(P(tx,ty)); } } } } int getlength(int a[5]){ int ans=0; for(int i=0;i<k;i++)ans+=d[a[i]][a[i+1]]; return ans; } int pre(){ int a[5];//暴力枚举所有可能排列 for(int i=0;i<=k;i++)a[i]=i;//需注意第一个排列 int ans=getlength(a); while(next_permutation(a+1,a+k+1)){//注意不要直接排列k ans=min(ans,getlength(a)); } return ans; } int main(){ while(scanf("%d%d",&n,&m)){ if(n==0&&m==0)break; for(int i=0;i<n;i++){ scanf("%s",maz[i]); } scanf("%d",&k); memset(ind,0,sizeof(ind)); for(int i=1;i<=k;i++){scanf("%d%d",px+i,py+i);px[i]--;py[i]--;ind[px[i]][py[i]]=i;} for(int i=0;i<n;i++){ for(int j=0;j<m;j++){ if(maz[i][j]=='@'){ px[0]=i; py[0]=j; ind[i][j]=0; break; } } } for(int i=0;i<5;i++)for(int j=0;j<5;j++)d[i][j]=inf; for(int i=0;i<=k;i++)bfs(i); int ans=pre(); printf("%d ",ans==inf?-1:ans); } return 0; }