【HDU】5837 Robots【DP】

题目链接：Robots

旋转45度坐标系，x’=x+y,y’=x-y，然后横纵坐标变成独立问题，接下来dp。

#include <bits/stdc++.h>
using namespace std ;

typedef long long LL ;

#define clr( a , x ) memset ( a , x , sizeof a )

const int MAXN = 205 ;
const int MAXM = 2005 ;
const int mod = 1e9 + 7 ;

int n , m , k ;
int L[MAXN] , R[MAXN] ;
int X[MAXN] , Y[MAXN] ;
int f[MAXM] , vf[MAXM] ;
int a[21][2] , b[21][21] ;
int dp[21][MAXM][2] ;
int tmp[MAXM][2] ;

int powmod ( int x , int n ) {
    int r = 1 ;
    while ( n ) {
        if ( n & 1 ) r = ( LL ) r * x % mod ;
        x = ( LL ) x * x % mod ;
        n >>= 1 ;
    }
    return r ;
}

int c ( int x , int y ) {
    if ( x < y ) return 0 ;
    return ( LL ) f[x] * vf[y] % mod * vf[x - y] % mod ;
}

void mul ( int& x , int y ) {
    x = ( LL ) x * y % mod ;
}

void up ( int& x , int y ) {
    x += y ;
    if ( x >= mod ) x -= mod ;
}

void solve () {
    scanf ( "%d%d%d" , &n , &m , &k ) ;
    int l = 0 ;
    for ( int i = 1 ; i <= m ; ++ i ) {
        int x ;
        scanf ( "%d" , &x ) ;
        L[i] = l + 1 ;
        R[i] = l + x ;
        l += x ;
    }
    for ( int i = 1 ; i <= n ; ++ i ) {
        int x , y ;
        scanf ( "%d%d" , &x , &y ) ;
        X[i] = x + y + 1000 ;
        Y[i] = x - y + 1000 ;
    }
    for ( int i = 1 ; i <= m ; ++ i ) {
        for ( int j = 0 ; j < MAXM ; ++ j ) {
            dp[i][j][0] = dp[i][j][1] = 1 ;
        }
    }
    int o = 1 ;
    for ( int i = 1 ; i <= n ; ++ i ) {
        if ( i > R[o] ) ++ o ;
        for ( int j = 0 ; j < MAXM ; ++ j ) {
            int t = abs ( X[i] - j ) ;
            if ( t % 2 != k % 2 || t > k ) dp[o][j][0] = 0 ;
            else mul ( dp[o][j][0] , c ( k , ( k + t ) / 2 ) ) ;
            t = abs ( Y[i] - j ) ;
            if ( t % 2 != k % 2 || t > k ) dp[o][j][1] = 0 ;
            else mul ( dp[o][j][1] , c ( k , ( k + t ) / 2 ) ) ;
        }
    }
    for ( int i = 1 ; i <= m ; ++ i ) {
        for ( int k = 0 ; k < MAXM ; ++ k ) {
            tmp[k][0] = tmp[k][1] = 1 ;
        }
        for ( int j = i ; j <= m ; ++ j ) {
            int x = 0 , y = 0 ;
            for ( int k = 0 ; k < MAXM ; ++ k ) {
                mul ( tmp[k][0] , dp[j][k][0] ) ;
                mul ( tmp[k][1] , dp[j][k][1] ) ;
                up ( x , tmp[k][0] ) ;
                up ( y , tmp[k][1] ) ;
            }
            b[i][j] = ( LL ) x * y % mod ;
        }
    }
    clr ( a , 0 ) ;
    a[0][0] = 1 ;
    for ( int i = 1 ; i <= m ; ++ i ) {
        for ( int j = 1 ; j <= i ; ++ j ) {
            int t = ( j - 1 ) & 1 ;
            up ( a[i][0] , ( LL ) a[i - j][0 ^ t] * b[i - j + 1][i] % mod ) ;
            up ( a[i][1] , ( LL ) a[i - j][1 ^ t] * b[i - j + 1][i] % mod ) ;
        }
    }
    printf ( "%d\n" , ( a[m][0] - a[m][1] + mod ) % mod ) ;
}

int main () {
    int T ;
    f[0] = vf[0] = 1 ;
    for ( int i = 1 ; i < MAXM ; ++ i ) {
        f[i] = ( LL ) f[i - 1] * i % mod ;
        vf[i] = powmod ( f[i] , mod - 2 ) ;
    }
    scanf ( "%d" , &T ) ;
    for ( int i = 1 ; i <= T ; ++ i ) {
        printf ( "Case #%d: " , i ) ;
        solve () ;
    }
    return 0 ;
}