Ural 1519 Formula 1( 插头dp )-优快云博客

在Vologda城市准备举办F1赛事时，生态学家阻止了直接建造赛道的计划，因为赛道所在地存在大量土拨鼠洞穴。面对这一难题，当地技术大学的程序员团队提出了一个更复杂的问题：如何计算建造符合规定的赛道方案数量？文章详细介绍了如何通过动态规划解决这个问题，并提供了解决方案的代码示例。

1519. Formula 1

Time limit: 1.0 second
Memory limit: 64 MB

Background

Regardless of the fact, that Vologda could not get rights to hold the Winter Olympic games of 20**, it is well-known, that the city will conduct one of the Formula 1 events. Surely, for such an important thing a new race circuit should be built as well as hotels, restaurants, international airport - everything for Formula 1 fans, who will flood the city soon. But when all the hotels and a half of the restaurants were built, it appeared, that at the site for the future circuit a lot of gophers lived in their holes. Since we like animals very much, ecologists will never allow to build the race circuit over the holes. So now the mayor is sitting sadly in his office and looking at the map of the circuit with all the holes plotted on it.

Problem

Who will be smart enough to draw a plan of the circuit and keep the city from inevitable disgrace? Of course, only true professionals - battle-hardened programmers from the first team of local technical university!.. But our heroes were not looking for easy life and set much more difficult problem: "Certainly, our mayor will be glad, if we find how many ways of building the circuit are there!" - they said.

It should be said, that the circuit in Vologda is going to be rather simple. It will be a rectangle N*M cells in size with a single circuit segment built through each cell. Each segment should be parallel to one of rectangle's sides, so only right-angled bends may be on the circuit. At the picture below two samples are given for N = M = 4 (gray squares mean gopher holes, and the bold black line means the race circuit). There are no other ways to build the circuit here.

Input

The first line contains the integer numbers N and M (2 ≤ N, M ≤ 12). Each of the next N lines contains M characters, which are the corresponding cells of the rectangle. Character "." (full stop) means a cell, where a segment of the race circuit should be built, and character "*" (asterisk) - a cell, where a gopher hole is located.

Output

You should output the desired number of ways. It is guaranteed, that it does not exceed 2⁶³-1.

Samples

input	output
4 4 **.. .... .... ....	2
4 4 .... .... .... ....	6

插头dp的一条入门。

http://wenku.baidu.com/view/4fe4ac659b6648d7c1c74633.html

#include <bits/stdc++.h>
using namespace std ;
const int N = 15 ;
const int M = 30007 ;
const int MAXN = 1000010;
int n , m ;
int maze[N][N] ;
int code[N] ;
int ch[N] ;
int ex , ey ;

struct HASHMAP {
    int head[M] , next[MAXN] , tot  ;
    long long st[MAXN] , f[MAXN] ;
    void init() {
        memset( head , -1 , sizeof head ) ;
        tot = 0 ;
    }
    void push( long long state , long long ans ) {
        int u = state % M ;
        for( int i = head[u] ; ~i ; i = next[i] ) {
            if( st[i] == state ) {
                f[i] += ans ; return ;
            }
        }
        st[tot] = state ;
        f[tot] = ans ;
        next[tot] = head[u] ;
        head[u] = tot++ ;
    }
} mp[2] ;

void decode ( int* code , int m , long long st ) {
    for( int i = m ; i >= 0 ; --i ) {
        code[i] = st&7 ;
        st >>= 3 ;
    }
}

long long encode( int *code , int m ) {
    int cnt = 1 ;
    long long st = 0 ;
    memset( ch , -1 , sizeof ch) ;
    ch[0] = 0 ;
    for( int i = 0 ; i <= m ; ++i ) {
        if( ch[code[i]] == -1 ) ch[ code[i] ] = cnt++ ;
        code[i] = ch[ code[i] ] ;
        st <<= 3 ;
        st |= code[i] ;
    }
    return st ;
}

void shift( int *code , int m ) {
    for( int i = m ; i > 0 ; --i ) {
        code[i] = code[i-1] ;
    } code[0] = 0 ;
}

void dpblank( int i , int j , int cur ) {
    int left , up ;
    for( int k = 0 ; k < mp[cur].tot ; ++k ) {
        decode( code , m , mp[cur].st[k] );
        left = code[j-1] ;
        up = code[j] ;
        if( left && up ) {
            if( left == up ) {
                if( i == ex && j == ey ) {
                    code[j-1] = code[j] = 0 ;
                    if( j == m ) shift(code,m);
                    mp[cur^1].push( encode(code,m) , mp[cur].f[k] );
                }
            }else {
                code[j-1] = code[j] = 0 ;
                for( int t = 0 ; t <= m ; ++t ) {
                    if( code[t] == up )
                        code[t] = left ;
                }
                if( j == m ) shift( code,m );
                mp[cur^1].push(encode(code,m),mp[cur].f[k]) ;
            }
        }
        else if( ( left && ( !up ) ) || ( up && (!left ) ) ) {
            int  t ;
            if( left ) t = left ;
            else t = up ;
            if( maze[i][j+1] ) {
                code[j-1] = 0 ;
                code[j] = t ;
                mp[cur^1].push( encode(code,m) , mp[cur].f[k] ) ;
            }
            if( maze[i+1][j] ) {
                code[j-1] = t ;
                code[j] = 0 ;
                if( j == m ) shift( code , m );
                mp[cur^1].push(encode(code,m),mp[cur].f[k]);

            }
        }
        else {
            if( maze[i][j+1] && maze[i+1][j] ) {
                code[j-1] = code[j] = 13 ;
                mp[cur^1].push( encode(code,m),mp[cur].f[k]);
            }
        }
    }
}
void dpblock( int i , int j , int cur ) {
    for( int k = 0 ; k < mp[cur].tot ; ++k ) {
        decode( code , m , mp[cur].st[k] );
        code[j-1] = code[j] = 0 ;
        if( j == m ) shift( code , m );
        mp[cur^1].push( encode(code,m) , mp[cur].f[k] );
    }
}

void Solve() {
    int v = 0 ;
    mp[v].init();
    mp[v].push(0,1);
    for( int i = 1 ; i <= n ; ++i ) {
        for( int j = 1 ; j <= m ; ++j ) {
            mp[v^1].init() ;
            if( maze[i][j] ) dpblank( i , j , v ) ;
            else dpblock( i , j , v );
            v ^= 1 ;
        }
    }
    long long ans = 0 ;
    for( int i = 0 ; i < mp[v].tot ; ++i )
        ans += mp[v].f[i];
    printf("%lld\n",ans);
}

char s[20];

int main () {
    while( ~scanf("%d%d",&n,&m) ) {
        ex = 0 ;
        memset( maze , 0 , sizeof maze ) ;
        for( int i = 1 ; i <= n ; ++i ) {
            scanf("%s",s);
            for( int j = 0 ; j < m ; ++j ) {
                if( s[j] == '.' ) {
                    ex = i , ey = j + 1 ;
                    maze[i][j+1] = 1 ;
                }
            }
        }
        if( !ex ) { puts("0"); continue ; }
        else Solve();
    }
    return 0 ;
}