2738: 矩阵乘法（梁 盾）（分块+主席树）

题目：http://www.lydsy.com/JudgeOnline/problem.php?id=2738

实在不想吐槽这个标题什么了，本来想找几道矩阵乘法的水题水水的，结果却成了裸数据结构。。。把X分成sqrt(n)个块，然后在没个块上面套棵主席树就可以啦~

空间复杂度：O( n ^ 2 log n )

时间复杂度：O( n ^ 2 log n + q sqrt( n ) log n )

代码：

#include 

#include 

#include 

#include 

 

using namespace std ;

 

#define MAXN 510

#define L( t ) sgt[ t ].left

#define R( t ) sgt[ t ].right

#define S( t ) sgt[ t ].size

#define MAXV 10001000

#define MAXM 30

#define check( ch ) ( ch >= '0' && ch <= '9' )

 

void getint( int &t ) {

    int ch ; for ( ch = getchar(  ) ; ! check( ch ) ; ch = getchar(  ) ) ;

    t = ch - '0' ;

    for ( ch = getchar(  ) ; check( ch ) ; ch = getchar(  ) ) {

        t *= 10 , t += ch - '0' ;

    }

}

 

int out[ 20 ] ;

 

void putint( int t ) {

    if ( ! t ) putchar( '0' ) ; else {

        out[ 0 ] = 0 ;

        for ( ; t ; t /= 10 ) out[ ++ out[ 0 ] ] = t % 10 ;

        while ( out[ 0 ] -- ) putchar( '0' + out[ out[ 0 ] + 1 ] ) ;

    }

    putchar( '\n' ) ;

}

 

struct node {

    int left , right , size ;

    node(  ) {

        left = right = size = 0 ;

    }

} sgt[ MAXV ] ;

 

int V = 0 ;

 

void Add( int l , int r , int k , int u , int &t ) {

    if ( ! t ) t = ++ V ;

    S( t ) = S( u ) + 1 ;

    if ( l == r ) return ;

    int mid = ( l + r ) >> 1 ;

    if ( k <= mid ) {

        R( t ) = R( u ) ; Add( l , mid , k , L( u ) , L( t ) ) ;

    } else {

        L( t ) = L( u ) ; Add( mid + 1 , r , k , R( u ) , R( t ) ) ;

    }

}

 

struct saver {

    int x , y , v ;

    bool operator < ( const saver &a ) const {

        return v < a.v ;

    }

} c[ MAXN * MAXN ] ;

 

int a[ MAXN ][ MAXN ] , n , N = 0 , b[ MAXN * MAXN ] , q , Rank[ MAXN ][ MAXN ] ;

int len ;

int Begin[ MAXM ] , End[ MAXM ] , M , block[ MAXM ][ MAXN ] , pre[ MAXN ][ MAXN ] ;

 

void Init(  ) {

    getint( n ) , getint( q ) ;

    for ( int i = 0 ; i ++ < n ; ) {

        for ( int j = 0 ; j ++ < n ; ) {

            getint( a[ i ][ j ] ) ;

            c[ ++ N ].v = a[ i ][ j ] ;

            c[ N ].x = i , c[ N ].y = j ;

        }

    }

    sort( c + 1 , c + N + 1 ) ;

    N = 0 ;

    for ( int i = 0 ; i ++ < n * n ; ) {

        if ( i == 1 || c[ i ].v != c[ i - 1 ].v ) b[ ++ N ] = c[ i ].v ;

        Rank[ c[ i ].x ][ c[ i ].y ] = N ;

    }

    len = int( sqrt( n ) ) ; M = n / len ;

    for ( int i = 0 ; i ++ < M ; ) {

        Begin[ i ] = ( i - 1 ) * len + 1 , End[ i ] = i * len ;

    }

    if ( M * len < n ) {

        Begin[ M + 1 ] = M * len + 1 , End[ M + 1 ] = n ;

        ++ M ;

    }

    memset( pre , 0 , sizeof( pre ) ) ;

    memset( block , 0 , sizeof( block ) ) ;

    for ( int i = 0 ; i ++ < n ; ) {

        for ( int j = 0 ; j ++ < n ; ) {

            Add( 1 , N , Rank[ i ][ j ] , pre[ i ][ j - 1 ] , pre[ i ][ j ] ) ;

        }

    }

    for ( int i = 0 ; i ++ < M ; ) {

        for ( int j = 0 ; j ++ < n ; ) {

            int temp = block[ i ][ j - 1 ] ;

            for ( int k = Begin[ i ] ; k <= End[ i ] ; ++ k ) {

                int rec = 0 ;

                Add( 1 , N , Rank[ k ][ j ] , temp , rec ) ;

                temp = rec ;

            }

            block[ i ][ j ] = temp ;

        }

    }

}

 

int range[ MAXN * MAXN ][ 2 ] , rn = 0 ;

 

void getrange( int x1 , int x2 , int y1 , int y2 ) {

    int pos1 = ( x1 - 1 ) / len + 1 , pos2 = ( x2 - 1 ) / len + 1 ;

    rn = 0 ;

    if ( pos1 == pos2 ) {

        if ( x1 == Begin[ pos1 ] && x2 == End[ pos1 ] ) {

            range[ ++ rn ][ 0 ] = block[ pos1 ][ y2 ] ;

            range[ rn ][ 1 ] = block[ pos1 ][ y1 - 1 ] ;

        } else {

            for ( int i = x1 ; i <= x2 ; ++ i ) {

                range[ ++ rn ][ 0 ] = pre[ i ][ y2 ] ;

                range[ rn ][ 1 ] = pre[ i ][ y1 - 1 ] ;

            }

        }

    } else {

        for ( int i = x1 ; i <= End[ pos1 ] ; ++ i ) {

            range[ ++ rn ][ 0 ] = pre[ i ][ y2 ] ;

            range[ rn ][ 1 ] = pre[ i ][ y1 - 1 ] ;

        }

        for ( int i = Begin[ pos2 ] ; i <= x2 ; ++ i ) {

            range[ ++ rn ][ 0 ] = pre[ i ][ y2 ] ;

            range[ rn ][ 1 ] = pre[ i ][ y1 - 1 ] ;

        }

        if ( ( ++ pos1 ) <= ( -- pos2 ) ) {

            for ( int i = pos1 ; i <= pos2 ; ++ i ) {

                range[ ++ rn ][ 0 ] = block[ i ][ y2 ] ;

                range[ rn ][ 1 ] = block[ i ][ y1 - 1 ] ;

            }

        }

    }

}

 

int query( int x1 , int x2 , int y1 , int y2 , int k ) {

    getrange( x1 , x2 , y1 , y2 ) ;

    int l = 1 , r = N ;

    while ( l < r ) {

        int mid = ( l + r ) >> 1 , sum = 0 ;

        for ( int i = 0 ; i ++ < rn ; ) {

            sum += S( L( range[ i ][ 0 ] ) ) , sum -= S( L( range[ i ][ 1 ] ) ) ;

        }

        if ( k <= sum ) {

            r = mid ;

            for ( int i = 0 ; i ++ < rn ; ) {

                range[ i ][ 0 ] = L( range[ i ][ 0 ] ) ;

                range[ i ][ 1 ] = L( range[ i ][ 1 ] ) ;

            }

        } else {

            l = mid + 1 , k -= sum ;

            for ( int i = 0 ; i ++ < rn ; ) {

                range[ i ][ 0 ] = R( range[ i ][ 0 ] ) ;

                range[ i ][ 1 ] = R( range[ i ][ 1 ] ) ;

            }

        }

    }

    return b[ l ] ;

}

 

void Solve(  ) {

    while ( q -- ) {

        int x1 , y1 , x2 , y2 , k ;

        getint( x1 ) , getint( y1 ) , getint( x2 ) , getint( y2 ) ;

        getint( k ) ;

        putint( query( x1 , x2 , y1 , y2 , k ) ) ;

    }

}

 

int main(  ) {

    Init(  ) ;

    Solve(  ) ;

    return 0 ;

}