HDU 4771 Stealing Harry Potter's Precious(BFS)

Stealing Harry Potter's Precious

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1961    Accepted Submission(s): 921

Problem 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.

 

 

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

 

 

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

 

 

Source

2013 Asia Hangzhou Regional Contest

 

 这道题就是求出能拿到所有宝物的最小路程，如果拿不到就输出-1

暴力得出所有的拿宝物的顺序，然后再用BFS来搜索出最短路径

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<stdlib.h>
#include<queue>
#include<stack>
#include<algorithm>
#define LL __int64
using namespace std;
const int MAXN=100+5;
const int MAX=10+5;
const int INF=0x3f3f3f3f;
const double EPS=1e-9;
int dir4[4][2]={{0,1},{1,0},{0,-1},{-1,0}};
int dir8[8][2]={{0,1},{1,1},{1,0},{1,-1},{0,-1},{-1,-1},{-1,0},{-1,1}};
int dir_8[8][2]={{-2,1},{-1,2},{1,2},{2,1},{2,-1},{1,-2},{-1,-2},{-2,-1}};
int n,m,k,vis[MAXN][MAXN],d[MAX][MAX];
char map[MAXN][MAXN];
struct node
{
    int x,y;
    int step;
}p[5];

void init()
{
    memset(map,0,sizeof(map));
    for(int i=1;i<=n;i++)
    {
        scanf("%s",map[i]+1);
        for(int j=1;j<=m;j++)
            if(map[i][j]=='@')
            {
                p[0].x=i;
                p[0].y=j;
            }
    }
    scanf("%d",&k);
    for(int i=1;i<=k;i++)
         scanf("%d %d",&p[i].x,&p[i].y);
}

int BFS(node star,node en)
{
    queue<node> Q;
    memset(vis,0,sizeof(vis));
    vis[star.x][star.y]=1;
    star.step=0;
    Q.push(star);
    while(!Q.empty())
    {
        node now,next;
        now=Q.front();
        Q.pop();
        if(now.x==en.x && now.y==en.y)
            return now.step;
        for(int i=0;i<4;i++)
        {
            next.x=now.x+dir4[i][0];
            next.y=now.y+dir4[i][1];
            if(0<next.x && next.x<=n && 0<next.y && next.y<=m && !vis[next.x][next.y] && map[next.x][next.y]!='#')
            {
                vis[next.x][next.y]=1;
                next.step=now.step+1;
                Q.push(next);
            }
        }
    }
    return -1;
}

bool judge()
{
    memset(d,0,sizeof(d));
    for(int i=0;i<=k;i++)
    {
        for(int j=i+1;j<=k;j++)
        {
            int dis=BFS(p[i],p[j]);
            if(dis==-1) return false;
            d[i][j]=d[j][i]=dis;
        }
    }
    return true;
}

int solve()
{
    int p[MAX],ans=INF;
    for(int i=0;i<=k;i++)
        p[i]=i;
    do
    {
        int sum=0;
        for(int i=0;i<k;i++)
            sum+=d[p[i]][p[i+1]];
        ans=min(sum,ans);
    }while(next_permutation(p+1,p+1+k));

    return ans;
}

int main()
{
    while(scanf("%d %d",&n,&m) && (n||m))
    {
        init();
        if(judge()) printf("%d\n",solve());
        else printf("-1\n");
    }
    return 0;
}