/
information.py
149 lines (101 loc) · 2.42 KB
/
information.py
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from matrix import subscripts
from combinatorics import choose
def info ( M , m , n ) :
# fill M
# we assume that for all j > i --> ai < aj and bi < bj
# M[i][j] = -1 means ai < bj
# M[i][j] = 1 means ai > bj
# M[i][j] = 0 means ai and bj are incomparable
# generate random info
positions = sorted( choose( m + n , m ) )
for i , j in enumerate( positions ) :
M[i][:j-i] = [ 1 ] * ( j - i )
M[i][j-i:] = [ -1 ] * ( n - j + i )
return M
def fix ( M , m , n ) :
"""
>>> M = [ [ -1 , -1 ] , [ 1 , 1 ] ]
>>> fix( M , 2 , 2 )
>>> M
[[-1, -1], [1, 1]]
>>> M = [ [ -1 , 0 ] , [ 0 , 1 ] ]
>>> fix( M , 2 , 2 )
>>> M
[[-1, -1], [1, 1]]
>>> M = [ [ 0 , 0 , 0 ] , [ -1 , -1 , -1 ] ]
>>> fix( M , 2 , 3 )
>>> M
[[-1, -1, -1], [-1, -1, -1]]
>>> M = [ [ 0 , 0 , 0 ] , [ 1 , 1 , 1 ] ]
>>> fix( M , 2 , 3 )
>>> M
[[0, 0, 0], [1, 1, 1]]
>>> M = [ [ -1 , -1 , -1 ] , [ 0 , 0 , 0 ] ]
>>> fix( M , 2 , 3 )
>>> M
[[-1, -1, -1], [0, 0, 0]]
>>> M = [ [ 1 , 1 , 1 ] , [ 0 , 0 , 0 ] ]
>>> fix( M , 2 , 3 )
>>> M
[[1, 1, 1], [1, 1, 1]]
"""
# fix transitivity
for i in range ( m ) :
hi , lo = n , 0
for j in range( n ) :
if M[i][j] > 0 :
lo = j
elif M[i][j] < 0 :
hi = j
break
for j in range( lo ) : M[i][j] = 1
for j in range( hi , n ) : M[i][j] = -1
for j in range ( n ) :
hi , lo = m , 0
for i in range( m ) :
if M[i][j] < 0 :
lo = i
elif M[i][j] > 0 :
hi = i
break
for i in range( lo ) : M[i][j] = -1
for i in range( hi , m ) : M[i][j] = 1
def comparator ( M ) :
"""
>>> from matrix import mat
>>> M = mat( 3 , 2 )
>>> compare = comparator( M )
>>> for i , j in subscripts( 0 , 3 , 0 , 2 ) : M[i][j] = 2 * i + j
>>> compare( 0 , 0 ) == M[0][0]
True
>>> compare( 0 , 1 ) == M[0][1]
True
>>> compare( 1 , 0 ) == M[1][0]
True
>>> compare( 1 , 1 ) == M[1][1]
True
>>> compare( 2 , 0 ) == M[2][0]
True
>>> compare( 2 , 1 ) == M[2][1]
True
"""
def compare ( i , j ) :
return M[i][j]
return compare
class Oracle ( object ) :
def __init__ ( self , M ) :
self.M = M
self.count = 0
def __call__ ( self , i , j ) :
self.count += 1
return self.M[i][j]
def __len__ ( self ) :
return self.count
def main ( m , n ) :
from matrix import mat , show
M = mat( m , n )
info( M , m , n )
print( show( M ) , end = "" )
if __name__ == "__main__" :
import sys
main( *map( int , sys.argv[1:] ) )