HDU 3681 Prison Break

二分答案+状压DFS+BFS预处理

答案是通过二分得到的，每次得到的mid进行验证，验证可以状压DP也可以DFS

DFS||DP的时候，如果一格一格走，会TLE。事实上我们只关心Y、G、F这几个格子的状态，对于S不知道情况对得到答案毫无影响，所以采用BFS预处理，求出Y、G、F这几个格子两两之间的最短路程。

#include <stdio.h>
#include <algorithm>
#include <string.h>
#include <queue>
#include <stack>
#include <map>
#include <vector>
using namespace std;

const int maxn=20;
int n,m;
char s[maxn][maxn];
int flag[maxn][maxn];
int dp[maxn][(1<<15)+10];
int dir[4][2]={{-1,0},{1,0},{0,-1},{0,1}};
int dis[maxn][maxn];
int Min[maxn][maxn];
int sx,sy;
bool now_ans;
int all_state;
int id,num_Y,num_G;
struct cha
{
    int a,b;
}cha[maxn];
struct Node{
    int a,b;
    int tot;
    Node(int v1,int v2,int v3) {a=v1,b=v2;tot=v3;}
};

void read()
{
    for(int i=0; i<n; i++) scanf("%s",s[i]);
}

bool f(int a,int b)
{
    if(a>=0&&a<n&&b>=0&&b<m) return 1;
    return 0;
}

void bfs(int a,int b)
{
    queue<Node>Q;
    for(int i=0;i<n;i++)
        for(int j=0;j<m;j++)
            Min[i][j]=0x7fffffff;
    Min[a][b]=0;
    Node node(a,b,0); Q.push(node);
    while(!Q.empty())
    {
        Node head=Q.front(); Q.pop();
        if(flag[head.a][head.b]!=-1)
        {
            dis[flag[a][b]][flag[head.a][head.b]]=head.tot;
            dis[flag[head.a][head.b]][flag[a][b]]=head.tot;
        }

        for(int i=0;i<4;i++)
        {
            int newx=head.a+dir[i][0];
            int newy=head.b+dir[i][1];

            if(!f(newx,newy)) continue;
            if(s[newx][newy]=='D') continue;

            if(head.tot+1<Min[newx][newy])
            {
                Min[newx][newy]=head.tot+1;
                Node node(newx,newy,head.tot+1);
                Q.push(node);
            }
        }
    }
}

void init()
{
    for(int i=0; i<n; i++)
        for(int j=0; j<m; j++)
            if(s[i][j]=='F')
                sx=i,sy=j;

    memset(flag,-1,sizeof flag);
    num_Y=0,num_G=0;
    for(int i=0; i<n; i++)
        for(int j=0; j<m; j++){
            if(s[i][j]=='G') num_G++;
            else if(s[i][j]=='Y') num_Y++;
        }
    id=0;
    for(int i=0; i<n; i++)
        for(int j=0; j<m; j++)
            if(s[i][j]=='Y')
            {
                cha[id].a=i,cha[id].b=j;
                flag[i][j]=id++;
            }
    for(int i=0; i<n; i++)
        for(int j=0; j<m; j++)
            if(s[i][j]=='G')
            {
                cha[id].a=i,cha[id].b=j;
                flag[i][j]=id++;
            }

    cha[id].a=sx,cha[id].b=sy;
    flag[sx][sy]=id++;
    all_state=(1<<num_Y)-1;

    for(int i=0;i<id;i++)
        for(int j=0;j<id;j++)
            dis[i][j]=0x7fffffff;

    for(int i=0;i<n;i++)
        for(int j=0;j<m;j++)
            if(flag[i][j]!=-1)
                bfs(i,j);
}

void dfs(int now_id,int state,int now,int MAX)
{
    if((state&all_state)==all_state) { now_ans=1; return; }

    if(now==0) return;

    for(int i=0;i<id;i++)
    {
        int new_state;
        if(i==now_id) continue;
        if(dis[now_id][i]==0x7fffffff) continue;

        int newx=cha[i].a;
        int newy=cha[i].b;

        if(s[newx][newy]=='G')
        {
            //不使用
            new_state=state;
            if(now-dis[i][now_id]>dp[i][new_state])
            {
                dp[i][new_state]=now-dis[i][now_id];
                dfs(i,new_state,now-dis[i][now_id],MAX);
                if(now_ans) return;
            }

            //使用
            new_state=(state|(1<<i));
            if(now-dis[i][now_id]>=0&&MAX>dp[i][new_state])
            {
                s[newx][newy]='S';
                dp[i][new_state]=MAX;
                dfs(i,new_state,MAX,MAX);
                s[newx][newy]='G';
                if(now_ans) return;
            }

        }
        else if(s[newx][newy]=='Y')
        {
            new_state=(state|(1<<i));
            if(now-dis[i][now_id]>dp[i][new_state])
            {
                s[newx][newy]='S';
                dp[i][new_state]=now-dis[i][now_id];
                dfs(i,new_state,now-dis[i][now_id],MAX);
                s[newx][newy]='Y';
                if(now_ans) return;
            }
        }
        else
        {
            new_state=state;
            if(now-dis[i][now_id]>dp[i][new_state])
            {
                dp[i][new_state]=now-dis[i][now_id];
                dfs(i,new_state,now-dis[i][now_id],MAX);
                if(now_ans) return;
            }
        }
    }
}

bool judge(int lim)
{
    now_ans=0;
    memset(dp,-1,sizeof dp);
    dp[id-1][0]=lim;
    dfs(id-1,0,lim,lim);
    return now_ans;
}

void work()
{
    int ans=-1;
    int l=0,r=300;
    while(l<=r)
    {
        int mid=(l+r)/2;
        if(judge(mid))
        {
            ans=mid;
            r=mid-1;
        }
        else l=mid+1;
    }
    printf("%d\n",ans);
}

int main()
{

    while(~scanf("%d%d",&n,&m))
    {
        if(!n&&!m) break;
        read();
        init();
        work();
    }
    return 0;
}