【HDU】5837 Robots【DP】

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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 ;}
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