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| Play nim against a perfect oponent. This interaction exemplifies the use of persistent data, and the auto_update=False option coded by mhansen and included in sage 3.3. | Play nim against a perfect opponent. This interaction exemplifies the use of persistent data, and the auto_update=False option coded by mhansen and included in sage 3.3. |
Sage Interactions - Games and Diversions
goto interact main page
Zeros
Have you ever wished you could count the number of zero digits in a long number like Rainman?
by William Stein and Sequoia Lefthand
import random
def init():
global B,Br,n,round,tm,t,v
B = 40
Br = 15
n = 1
round = 0
tm = 0
t = walltime()
init()
print "<html><h1 align=center>Zeros</h1></html>"
print "<html><h2 align=center><font color='blue'>How many zeros?</font></h2></html>"
@interact
def zeros(a=("",selector(buttons=True, nrows=1, values=['Reset'] + [1..B], default=1))):
if a == 'Reset':
init()
print "<html><center>"
global B,Br,n,round,tm,t,v
if a == n:
if round > 0:
print "<font size=+3 color='red'>RIGHT</font>"
r = walltime() - t
tm += r
round += 1
t = walltime()
while True:
n2 = random.randrange(1,Br)
if n2 != n:
n = n2
break
if Br < B:
Br += 2
elif round > 0:
print "<font size=+2 color='blue'>Wrong. Try again...</font>"
print "</center>"
print "<font size=+%s color='#333'>"%random.randrange(-2,5)
print ' '*random.randrange(20) + '0'*n
print "</font>"
if round > 0:
print "<br><br><center>Score: %s rounds, Average time: %.1f seconds</center>"%(
round, float(tm)/round)
print "</html>"
Queens on board
An interaction to play with the problem of placing eight queens on a board so that they do not threaten each other. This interaction exemplifies the use of persistent data, and the auto_update=False option coded by mhansen and included in sage 3.3. by Pablo Angulo
queens=[]
opciones=['Clean board', 'Add queen', 'Remove queen' ]
@interact
def _(queen=input_box(default=(0,0)), opcion=selector(opciones, buttons=True), auto_update=False ):
global queens
if opcion=='Clean board':
queens=[]
elif opcion=='Add queen':
if queen not in queens:
queens.append(queen)
else:
queens.remove(queen)
board=matrix(ZZ,8,8)
for x in range(8):
for y in range(8):
board[x,y]=(x+y)%2*7
for x,y in queens:
for i in range(8):
if i!=y: board[x,i]=1+(x+i)%2*5
if i!=x: board[i,y]=1+(i+y)%2*5
for i in range(-min(x,y),min(8-x,8-y)):
if i!=0: board[x+i,y+i]=1+(x+y)%2*5
for i in range(max(-x,y-7),min(8-x,y+1)):
if i!=0: board[x+i,y-i]=1+(x+y)%2*5
for x,y in queens:
if ( board[x,y]==1 or board[x,y]==6 ):
print 'Queen at (%d,%d) is threatened by another queen'%(x,y)
board[x,y]=4
else:
board[x,y]=3
show(matrix_plot(board, cmap='Oranges' ))
Nim
Play nim against a perfect opponent. This interaction exemplifies the use of persistent data, and the auto_update=False option coded by mhansen and included in sage 3.3. by Pablo Angulo
#El juego del nim
def game_repr(heap_sizes):
return '\n'.join('%d:'%i+'*'*n for i,n in enumerate(heap_sizes))
def bitlist2number(bitlist):
return int('0'+''.join([str(bit) for bit in reversed(bitlist)]),2)
def move_nim(heap_sizes):
'''Given a nim game, returns the next move (heap and amount)
'''
all_digits=[n.bits() for n in heap_sizes]
N=max(len(l) for l in all_digits)
digi=[0]*N
for l in all_digits:
for i in range(len(l)):
digi[i]+=l[i]
digi2=[digi[i]%2 for i in range(len(digi))]
if max(digi2)==0:raise Exception("I cannot win!")
maxInd=max(i for i in range(N) if digi2[i])
heap=min(i for i in range(len(heap_sizes)) if len(all_digits[i])>maxInd and all_digits[i][maxInd]>0)
localbits=heap_sizes[heap].bits()[0:maxInd]
globalbits=digi2[0:maxInd]
correction=bitlist2number( [b2 if b2 and not b1 else 0 for b1,b2 in zip(localbits,globalbits)] ) - bitlist2number( [b2 if b2 and b1 else 0 for b1,b2 in zip(localbits,globalbits)] )
amount=2^maxInd -correction
return (heap,amount)nim=[1,3,5,6]
@interact
def _(heap=selector(range(len(nim)), buttons=True),
amount=selector(range(max(nim)+1), buttons=True),
auto_update=False):
global nim
if max(nim)==0:
print 'You have lost'
return
else:
print 'Try to take the last item'
if heap>=0 and 0<amount<=nim[heap]:
print 'Previous situation:'
print game_repr(nim)
nim[heap]-=amount
print 'Your move:'
print game_repr(nim)
if max(nim)==0:
print 'You win'
return
print 'My move:'
try:
myheap,myamount=move_nim(nim)
except:
#cannot win, choose arbitrarily
myheap=min(heap_number for heap_number, heap_size in enumerate(nim) if heap_size>0)
myamount=1
nim[myheap]-=myamount
print game_repr(nim)
if max(nim)==0:
print 'I win'
else:
print 'Please move again'
else:
print 'Choose a heap and the amount to substract from that heap'
print game_repr(nim)